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Using Type Inference and Induced Rules to Provide Intensional Answers Wesley W. Chu Rei-Chi Lee Qiming Chen

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2 What is Intensional Answer? Intensional answer to a query provides the characteristics that describes the database values (the extensional answers) that satisfy the query Intensional answers provide the users with: Summarized or approximate descriptions about the extensional answers Additional insight into the nature of extensional answers

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3 An Example of Intensional Answer Consider a personnel database containing the relation: EMPLOYEE = (ID, Name, Position, Salary) To find the person whose annual salary is more than 100K, the query can be specified as Q = SELECT * FROM EMPLOYEE WHERE Salary >100K; A traditional answer would be: {“Smith”, “Jones”,...} An intensional answer would be: “All the managers.”

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4 Prior Work: Constraint-based approach for intensional query answering (Motro 89) Aggregate response using type hierarchy (Shum 88) Only limited form of intentional answers can be generated New Approach: Use both type hierarchy and database intensional knowledge Two Phases: Knowledge Acquisition Use rule induction to derive intensional knowledge from database content Type Inference Based on type hierarch, use the derived rules to generate the specific intensional answers

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5 Traditional Views of Type Hierarchy In semantic or object-oriented data modeling, there are two traditional views of type hierarchy: 1. IS_A Hierarchy: A IS_A B means every member of type A is also a member of type B. 2. PART_OF Hierarchy: A is PART_OF B means A is a component of B. These two views are mainly used for data modeling which provides a language for: describing and storing data accessing and manipulating the data

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6 The Notion of Type Hierarchy Classes and Types: Any of the entities being modeled that share some common characteristics are gathered into classes. All elements of the class have the same class type. Type Hierarchy is a partial order for the set of types: Types (referred to as super-types) at higher positions are more generalized than types at lower positions. Types (referred to as sub-types) at lower positions are more specialized than types at higher positions.

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7 An IS_A Type Hierarchy Example

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8 Type Inference Type Inference is a process if traversing the type hierarchy that is based on the query condition and the induced rules. Traversing of the type hierarchy can be performed in two directions: Forward Inference Backward Inference

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9 Deriving Intensional Answers Using Forward Inference Forward Inference uses the known facts to derive more facts. That is, given a rule, “If X then Y” and a fact “X is true”, then we can conclude “Y is true”. We perform forward inference by traversing along the type hierarchies downward from the type that is involved in the query. As a result, The search scope for answering the query can be reduced The lowest (the most specific) type description satisfying the query condition are returned as the intensional answers

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10 A Forward Inference Example To find the submarine whose displacement is greater than 8000, the query can be specified as: Q = SELECT * FROM SUBMARINE WHERE Displacement > 8000. The extensional answer to the query is: id SSBN730 SSBN130 name Rhode Island Typhoon class 0101 1301 type SSBN Using forward inference with R 4, we can derive the following intensional answer: “Ships are SSBN submarines.”

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11 Derive Intensional Answers Using Backward Inference Backward Inference uses the known facts to infer what must be true according to the type hierarchies and induced rules Using backward inference, we traverse upward along the type hierarchies to provide the set of with constraints as intensional answers.

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12 A Backward Inference Example To find the names and classes of the SSBN submarines, the query can be specified as: Q = SELECT Name, Class FROM SUBMARINE, CLASS WHERE Type = “SSBN”; The extensional answer to the query is: Using backward inference, we can derive the following intensional answer: “Some ships have classes in the range of 0101 to 0103.” name Nathaniel Hale Daniel Boone Sam Rayburn Lewis and Clark Mariano G. Vallejo Rhode Island Typhoon class 0103 0102 0101 1301

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13 Deriving Intensional Answers via Type Inference Using forward inference, the intensional answer gives a set of type descriptions that includes the answers. Using backward inference, the intensional answer gives only a description of partial answers. Therefore, the intensional answers derived from forward inference characterize a set of instances containing the extensional answers, whereas the intensional answers derived from backward inference characterize a set of answers contained in the extensional answers. Forward inference and backward inference can also be combined to derive more specific intensional answers.

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14 A Forward and Backward Inference Example To find the names, classes, and types of the SUBMARINES equipped with sonar BQS-04, the query can be specified as: Q =SELECT SUBMARINE.Name, SUBMARINE.Class, CLASS.Type FROM SUBMARINE, CLASS, INSTALL WHERE SUBMARINE.Class = CLASS.Class AND SUBMARINE.Id = INSTALL.Ship AND INSTALL.Sonar = “BQS-04” The extensional answer to the query is: name Bonefish Seadragon Snook Robert E. Lee class 0215 0212 0209 0208 type SSN Using both forward inference and backward inference, we can derive the following intensional answer: “Ship type SSN with class in the range of 0208 to 0215 is equipped with sonar BQS-04.”

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15 Conclusions In this research, we have proposed an approach to provide intensional answers using type inference and induced rules: Type Inference Inference Backward inference Combine forward and backward inference Type inference with multiple type hierarchies Rule Induction Model-based inductive learning technique derives rules form database contents. For databases with strong type hierarchy and semantic knowledge, type inference is more effective than integrity constraints to derive intensional answers

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17 Fault Tolerant DDBMS Via Data Inference Network Partition Causes: Failures of: Channels Nodes Effects: Queries cannot be processed if the required data is inaccessible Replicated files in different partitions may be inconsistent Updates may only be allowed in one partition. Transactions may be aborted

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18 Conventional Approach for Handling Network Partitioning Based on syntax to serialize the operations To assure data consistency Not all queries can be processed Based on data availability, determine which partition is allowed to perform database update POOR AVAILABILITY!!

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19 New Approach Exploit data and transaction semantics Use Data Inference Approach Assumption: Data are correlated Examples Salary and rank Ship type and weapon Infer in accessible data from the accessible data Use semantic information to permit update under network partitioning

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20 Query Processing System with Data Inference Consists of DDBMS Knowledge-Base (rule-based) Inference Engine

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21 DDBMS with Data Inference Query Parser and Analyzer Database Fragments Allocation Availability Inference Engine Rule Based Knowledge-Based System Inference System Information Module Query Input Query Output DDBMS

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22 Fault Tolerant DDBMS with Inference Systems SF LANY KB 2 IE DB 2 KB 1 IE DB 1 KB 3 IE DB 3 KB SHIP(SID) INSTALL (TYPE) INSTALL(TYPE) INSTALL(WEAPON)

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23 Architecture of Distributed Database with Inference

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24 Motivation of Open Data Inference Correlated knowledge is incomplete Incomplete rules Incomplete objects

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25 Example of Incomplete Object Type -------> Weapon IF type in {CG, CGN} THEN weapon = SAM01 IF type = DDG THEN weapon = SAM02 TYPEWEAPON CG SAM01 CGN SAM01 DDG SAM02 SSGN ?? Result: Incomplete rules generate incomplete object.

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26 Merge of Incomplete Objects Observation: Relational join is not adequate for combining incomplete objects Lose information Questions: What kind of algebraic tools do we need to combine incomplete objects without losing information? Any correctness criteria to evaluate the incomplete results?

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27 Merge of Incomplete Objects TYPE ---> WEAPON and WEAPON --->WARFARE Type WeaponWeapon Warfare CG SAM01SAM01 WF1C CGN SAM01SAM03 WF1D DDG SAM02 SSGN ? Use relational join to combine the above two paths: TypeWeapon Warfare CG SAM01 WF1C CGN SAM01 WFIC Other way to combine: TYPE WEAPON WARFARE CG SAM01 WF1C CGN SAM01 WF1C DDG SAM02 ? ? SAM03 WF1D SSGN ? ?

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28 New Algebraic Tools for Incomplete Objects S-REDUCTION Reduce redundant tuples in the object OPEN S-UNION Combine incomplete objects

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29 S-Reduction Remove redundant tuples in the object Object RR with key attribute A is reduced to R RRR ABCABC a1aaa1aa b2_b2bb c_ccc_cc a1aa b_bb c__

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30 Open S-Union Modify join operation to accommodate incomplete information Used to combine closed/open objects R1 R2 ----> R sidtypetypeweapon sid typeweapon s101 DD DDSAM01s101 DDSAM01 s102 DD CG -s102 DDSAM01 s103 CGs103 CG -

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31 Open S-Union and Toleration Performing open union on two objects R1, R2 generates the third object which tolerates both R1 and R2. R1 U R2 ----> R sidtypetypeweapon sidtypeweapon s101 DD DDSAM01s101 DDSAM01 s102 DD CG -s102 DDSAM01 s103 CGs103 CG - R tolerates R1 R tolerates R2

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32 Example of Open Inference site LA: SHIP(sid,sname,class) site SF: INSTALL(sid,weapon) site NY: CLASS(class,type,tname) Query: Find the ship names that carry weapon ‘SAM01’ (assuming site SF is partitioned) SF NY LA Rule: If SHIP TYPE = DD, Then WEAPON = SAM01 SHIP INSTALL CLASS Network Partition

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33 Implementation Derive missing relations from accessible relations and correlated knowledge Three types of derivations: View mechanism to derive new relations based on certain source relations Valuations of incomplete relations based on correlated knowledge Combine two intermediate results via open s-union operation

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34 Example of Open Inference DERIVATION 1: select sid, type from SHIP, CLASS DERIVATION 2: CLASS(type) --> INSTALL(weapon) R1 R2 ----> INSTALL_INF sid typetypeweapon sidtypeweapon s101DD DDSAM01s101 DDSAM01 s102DD CG -s102 DDSAM01 s103CGs103 CG - INSTALL_INF can be used to replace missing relation INSTALL

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35 Fault Tolerant DDBMS via Inference Techniques Query Processing Under Network Partitioning Open Inference: Inference with incomplete information Algebraic tools for manipulating incomplete objects Toleration: weaker correctness criteria for evaluating incomplete information

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36 Conclusion Data Inference is an effective method for providing database fault tolerance during network partitioning.

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37 Intelligent Dictionary and Directory (IDD) The role of the IDD and the emerging technology of Object-Oriented Database Systems The integration of Artificial Intelligence and Database Management tools and techniques to explore new architectures for the IDD The support of future applications: heterogeneous, distributed, cooperating data/knowledge systems guided by active, intelligent dictionaries and directories and managed by Data and Knowledge Administrators

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38 Object-Oriented Dictionary Modeling Information Resource Dictionary System Functional Specification of the IDD Role of Machine Learning in IDD Mining Knowledge from Data Schema Evolution System Optimization Issues Support for Hypermedia

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39 The Knowledge/Data Model (KDM) The KDM modeling primitives are: Generalization: Generalization provides the facility in the KDM to group similar objects into a more general object. This generalization hierarchy defines the inheritance structure. Classification: Classification provides a means whereby specific object instances can be considered as a higher-level object-type (an object-type is a collection of similar objects). This is done through the use of the “is-instance-of” relationship. Aggregation: Aggregation is an abstraction mechanism in which an object is related to its components via the “is-part-of” relationship. Membership: Membership is an abstraction mechanism that specifically supports the “is-a-member-of” relationship.

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40 The Knowledge/Data Model Temporal: Temporal relationship primitives relate object- types by means of synchronous and asynchronous relationships. Constraints: This primitive is used to place a constraint on some aspect of an object, operation, or relationship via the “is- constraint-on” relationship. Heuristic: A heuristic can be associated with an object via the “is-heuristic-on” relationship. These are used to allow the specifications of rules and knowledge to be associated with an object. In this way, object properties can be inferred using appropriate heuristics.

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41 The KDL Template for Object-Type Specification object-type: OBJECT-TYPE-NAME has [attributes: {ATTRIBUTE-NAME: [set of/list of] VALUE-TYPE /*default is single-valued composed of [ATTRIBUTE-NAME,}] with constraints {predicate,}] with heuristics {RULE,}];}] [subtypes: {OBJECT-TYPE-NAME,}] [supertypes: {OBJECT-TYPE-NAME,}] [constraints: {predicate,}] [heuristics: {rule,}]

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42 The KDL Template for Object-Type Specification (Cont’d) /*successors predecessors, and concurrents are temporal primitives [successors: {OBJECT-TYPE-NAME,}] [predecessors: {OBJECT-TYPE-NAME,}] [concurrents: {OBJECT-TYPE-NAME,}] [members: {MEMBER-NAME: MEMBER-TYPE}] [instances: {INSTANCE,}] end-object-type

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43 Three Services Database Schemata

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44 Knowledge Source Schemata in the KDM Paradigm

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45 KDL Object Type Specification Template

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46 The THESAURUS_OBJECT Meta- Schema

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47 The THESAURUS_OBJECT Meta-Object-Type Specification

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48 The KNOWLEDGE_SOURCE_OBJECT Meta-Object-Type Specification

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49 Three-Level Specification – Local, FM, and Federation

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50 A sample export data/knowledge/task schema for a federation interface manager

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51 Conclusions IDD based on the Knowledge Data Model can provide the modeling power needed to: 1. Extend the notions of the Information Resource Dictionary System 2. Support Object-Oriented DBMS 3. Act as an Intelligent Thesaurus to support Cooperating Knowledge Sources for Heterogeneous Databases Scheme Evolution will require a meta-level characterization of the KDM constructs so that inference tools can reason about the effects of changes to schema.

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53 Intelligent Heterogeneous Autonomous Database Architecture (INHEAD) Reference: D. Weishar and L. Kershberg, “An Intelligent Heterogeneous Autonomous Database Architecture for Semantic Heterogeneity Support”, Proceedings of the First International Workshop on Interoperability in Multi-Database Systems. Kyoto, Japan, pp. 152-155, 1991.

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54 INHEAD Place query on blackboard KS (domain experts) of the DBMS KS cooperatively tries to find a solution to the query If no request is found, further clarifications and request information needed by the users. Thesaurus performs semantic query processing of users original query, Controller provides: necessary query translation and optimization integrates the results

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55 IDD for an Intelligent Front End to Heterogeneous Databases

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56 BLACKBOARD Dynamic Control - make inferences related to solution formation at each step Focus of Attention - determine what part of the emerging solution should be attended to next Flexibility of Programming the Control - knowledge about how control should be applied in various domains can be codified in control rules or in complex control regimes

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57 Modularity Well suited to the class of problems possessing one or more of the following characteristics: The need to represent many specialized and distinct kinds of knowledge The need to integrate disparate information A natural domain hierarchy Having continuous data input (e.g., Signal tracking) Having sparse knowledge/data Supporting semantic heterogeneity in a system of heterogeneous autonomous database exhibits many of these characteristics.

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58 Opportunistic Query Processing Opportunistic - query can be processed based on goal, sub-goal, and hypothesis changes. Redundant and overlapping data provides parallel processing Incrementally Query Processing - can halt the processing of the query when the control structure determines that the query has been satisfied.

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59 The Active and Intelligent Thesaurus Validating and performing consistency check on the input to the thesaurus itself Indexing and converting data values Translating queries using different variants of names Actively participating in on-line HELP (i.e., offer suggestions) The thesaurus can be used as: A repository of knowledge of data item An incorporation of newly discovered knowledge An integration with existing knowledge

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60 Data/Knowledge Packets Object Encapsulation Encapsulating Object structure Relationships Operations Constraints Rules Data/Knowledge Packet allows the specification of abstract object types at the global level and the encapsulation of optional and structural semantics.

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61 An Example: The Artillery Movement Problem Goal: provision 10 M110 Howitzer Weapon System for departure to Middle East in 5 days. 1) Characteristics DB: describes the physical characteristics of the component parts of the weapons system 2) Weapon system DB: describes the components of weapons system 3) Logistics database: describes the logistics support required to sustain weapons systems in combat 4) Personnel DB for crew requisitioning 5) Ship DB for obtaining space on seagoing vessels.

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62 Overall Goal: Provision 10M110 Howitzer Weapon System for departure to the Middle East in 5 days. Subgoals 1.0Determine availability of 10 M110 Howitzer Weapon Systems 1.1Determine the locations of such items, subject to constraints of being within 500 miles of Norfolk, Virginia 1.2Send requests for items to locations to hold for shipment 2.0Determine Availability of Logistic Support Units 2.1Specialize camouflage to desert conditions 2.2Specialize radar to desert night vision 2.3Specialize rations to high water content rations 2.4Specialize clothing to lightweight, chemically resistant

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63 3.0Determine Availability of Sealift Capability along the Eastern Seaboard 3.1Calculate total weight and volume for each system 3.2Provision crews for each system 3.3Assign crews and weapons to ships 3.3.1Notify Crews 3.3.2Send shipment requisitions to sites holding weapons systems

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Uncertainty Management Using Rough Sets

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66 Why Deal with Uncertainty Most tasks requiring intelligent behavior have some uncertainty Forms of uncertainty in KB systems Uncertainty in the data Missing data Imprecise representation, etc. Uncertainty in the knowledge-base Best guesses Not applicable in all domains

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67 Why Deal with Uncertainty (cont’d) Some approaches to handle uncertainty: Probability and Bayesian statistics Confidence (or certainty) factors Dempster Shafer theory of evidence Fuzzy sets and fuzzy logic Problems with these approaches Make strong statistical assumptions such as follow a probability distribution model E.g., Bayesian approach Cannot recognize structural properties of data qualitatively Represent through numbers E.g., Fuzzy Logic – concept of “Tall”, “Very Tall”, etc.

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68 Rough Sets Good for reasoning from qualitative and imprecise data No approximation by numbers No probability distribution model required Uses set theory to provide insight into the structural properties of data Theory developed by Z. Pawlak in 1982 Well known experimental applications in Medical diagnosis (Pawlak, Slowinski & Slowinski, 1986) Machine learning (Wong & Ziarko, 1986b) Information Retrieval (Gupta, 1988) Conceptual Engineering design (Arciszewski and Ziarko, 1986) Approximate Reasoning (Rasiowa and Epstein, 1987) BASIC IDEA Lower the degree of precision in the representation of objects Make data regularities more visible and easier to characterize in terms of rules

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69 Example 1

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70 Rough Sets vs. Classical Sets Classical sets have well defined boundaries since the data representation is exact Rough sets have fuzzy boundaries since knowledge is insufficient to determine exact membership of an object in the set Example: U: Universal set of all cars X: Set of all fuel efficient cars In the rough set approach, fuel efficiency is indirectly determined from attributes such as: Weight of car Size of engine Number of cylinders, etc. Attribute Dependency Qualitatively determine the significance of one or more attributes (such as Weight, Size) on a decision attribute (such as Fuel eff.)

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73 Indiscernibility Relation (IND) Equivalence Class

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74 Definitions

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75 Definition (cont’d) Boundary region BND(X) Consists of objects whose membership cannot be determined exactly. BND(X) = IND(X) – IND(X) Negative region NEG(X) Union of those elementary sets of IND that are entirely outside X. NEG(X) = U – IND(X) Accuracy measure AM(X) If lower approximation is different from upper approximation, the set is rough. AM(X) = Card(IND(X)) / Card(IND(X))

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76 Example 2

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77 What is the accuracy measure when the set of melons is classified on the attribute “size”? Let c be the condition attribute ‘size’ Let x be the ‘set of all melons’ x= {p1, p2, p4, p5} The elementary classes of the attribute ‘size’ are as follows: x1 = {p3,p6, p7,p9}size = small x2 = {p1, p5}size = med x3 = {p2, p4, p8}size = large IND(x, c) = {p1, p5} IND(x, c) = {p1, p2, p4, p5, p8} BND(x, c) = {p2, p4, p8} NEG(x c) = {p3, p6, p7, p9} Accuracy measure, AM(x, c) = 2/5

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78 Attribute Dependency

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79 Example 3 How useful is {shape, taste} in determining the {kind of products}? C: {shape, taste} D: {kind of product} D’= the elementary classes of IND(D) = {{set of all melons}, {set of all other fruits}} = {{p, p2, p4, p5}, {p3, p6, p7, p8, p9}} Elementary classes of IND(C) = { {p1},For (syp, sweet) {p2, p4, p5, p6},For (cyl, sweet) {p3, p8},For (syp, normal) {p9},For (cyl, normal) {p7},For (sph, sour) { },For (cyl, sour) }

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80 POS (C, D) = the union of all positive regions = { p1 (contained in class Melon), p3, p8 (contained in class Other), p9, (contained in class Other), p7, (contained in class Other) } Dependency = card (POS(C, D))/card (U) = 5/9 Since 0 < 5/9 < 1, we have a partial dependency of D = {kind of product} on C = {shape, taste}

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81 Interpretation of K(C,D) IF K(C,D) = 1, we have full dependency Any class of object in D can be completely determined by the attributes in C. IF 0 < K(C,D) < 1, we have only partial dependency The class of only some objects in D can be completely determined by attributes in C. IF K(C,D) = 0, we have no dependency No object in D can be completely determined by the attributes in C.

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82 Similarly, we can calculate the dependency of {kind of product} on other attribute groupings: Dependency on {shape, size} = 1 Dependency on {size, taste} = 1 Dependency on {shape, size, taste} = 1

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83 Minimal Set of Attributes or REDUCTS Objective Find the minimal set (or sets) of interacting attributes that would have the same discriminating power as the original set of attributes. This would allow us to eliminate irrelevant or noisy attributes without loss of essential information. In our example, {size, shape} and {size, taste} are minimal sets of attributes. Advantages: Irrelevant attributes can be eliminated from a diagnostic procedure, thereby reducing the costs of testing and obtaining those values. The knowledge-base system can form decision rules based on minimal sets. For example, we can form the rules if (size = large) and (taste = sweet) then kind of product = melon if (shape = cyl) and (size = small) then kind of product = other

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84 Deterministic and Non-Deterministic Rules Deterministic rules have only one outcome. They are obtained from the positive and negative regions of the approximation space. Non-deterministic rules can have more than one outcome. They are formed from the boundary regions of the approximation space. Selection of the best minimal set If there are more than one minimal set, which is the best one? If we assign a cost function to the attributes, selection can be based on minimum cost criterion E.g., In medical domain, some diagnostic procedures are more expensive than others. If there is no cost function, select the set with the minimal number of attributes

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85 Example 4

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86 If Condition Attributes C = {size, cyl, turbo, fuelsys, displace, comp, power, trans, weight} and Decision Attribute D = {mileage} K(C,D) was calculated to be 1 If C = {size, power}, D = {mileage} K(C,D) was calculated to be 0.269 Thus, “size” and “power” are definitely not good enough to determine mileage. The following were determined to be minimal sets of attributes {cyl, fuelsys, comp, power, weight} {size, fuelsys, comp, power, weight} {size, fuelsys, displace, weight} {size, cyl, fuelsys, power, weight} {cyl, turbo, fuelsys, displace, comp, trans, weight} {size, cyl, fuelsys, comp, weight} {size, cyl, turbo, fuelsys, trans, weight}

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87 View of Table After Attribute Reduction Best minimal set: {size, fuelsys, displace, weight}

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88 Set of Rules Produced from the Reduced Table Blanks represent “don’t cares” CNo is the number of cases in the original table that support the given rule It provides a measure of the strength of confidence in the rule. Higher Cno, the more the rule is confirmed. Dno is the number of cases in the table with the same decision value Interpreting Row 5, if (fuelsys = EFI) and (displace = small) then mileage = high

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89 Applications Speech recognition The method of reduct computation was used to eliminate unnecessary spectral frequencies to find he best representation for a group of spoken words Medical domain Analysis of records of patients who suffered from duodenal ulcer (Pawlak, Slowinski & Slowinski, 1986) Analysis of clinical data of patients with Cardiac valve diseases (Abdalla S. A. Mohammed, 1991) Architecture Structural design optimization by obtaining characteristic design rules from a database of existing designs and verified performance data (Arciszewski et al, 1987; Arciszewski, Ziarko, 1986)

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90 Summary The theory of rough sets is very good for handling qualitative, imprecise data. In this respect it is an improvement over probabilistic and statistical methods. Since the data are not covered to numbers but handled in qualitative form, set theory is used to identify structural relationships. The strength of the dependency of any set of condition attributes on a decision attribute can be determined numerically. By forming minimal sets of attributes we can filter noisy or irrelevant attributes. Minimal sets also identify strong data patterns that help the KB system form rules

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91 References “Rough Sets”, Zdislaw Pawlak, Kluwer Academic Publishers, 1991. “Rough Sets as the Basis of a Learning System” – Chapter 2, pp. 5-13. “An Application of the Rough Sets Model to Analysis of Data Tables” – Chapter 3, pp. 15-29. “The Discovery, Analysis, and Representation of Data Dependencies in Databases”, Wojciech Ziarko, Knowledge Discovery in Databases by Shapiro, Frawley, pp. 195-209. Applications of Rough Set Theory for Clinical Data Analysis: A Case Study”, Abdalla S.A. Mohammed, Journal of Mathematical and Computer Modeling, Vol. 15, No. 10, pp. 19-37, 1991. “Intelligent Information Retrieval Using Rough Set Approximations”, Padmini Srinivasan, Information Processing and Management, Vol. 25, No. 4, pp. 347-361, 1989. “Uncertainty Management”, Avelino J. Gonzalez, Douglas D. Dankel, The Engineering of Knowledge-Base Systems, Chapter 8, pp. 232-262.

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Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 4 — ©Jiawei Han and Micheline Kamber Intelligent Database Systems Research Lab School of Computing Science Simon Fraser University, Canada http://www.cs.sfu.ca

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94 Chapter 4: Data Mining Primitives, Languages, and System Architectures Data mining primitives: What defines a data mining task? A data mining query language Design graphical user interfaces based on a data mining query language Architecture of data mining systems Summary

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95 Why Data Mining Primitives and Languages? Finding all the patterns autonomously in a database? — unrealistic because the patterns could be too many but uninteresting Data mining should be an interactive process User directs what to be mined Users must be provided with a set of primitives to be used to communicate with the data mining system Incorporating these primitives in a data mining query language More flexible user interaction Foundation for design of graphical user interface Standardization of data mining industry and practice

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96 What Defines a Data Mining Task ? Task-relevant data Type of knowledge to be mined Background knowledge Pattern interestingness measurements Visualization of discovered patterns

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97 Task-Relevant Data (Minable View) Database or data warehouse name Database tables or data warehouse cubes Condition for data selection Relevant attributes or dimensions Data grouping criteria

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98 Types of knowledge to be mined Characterization Discrimination Association Classification/prediction Clustering Outlier analysis Other data mining tasks

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99 Background Knowledge: Concept Hierarchies Schema hierarchy E.g., street < city < province_or_state < country Set-grouping hierarchy E.g., {20-39} = young, {40-59} = middle_aged Operation-derived hierarchy email address: login-name < department < university < country Rule-based hierarchy low_profit_margin (X) <= price(X, P1) and cost (X, P2) and (P1 - P2) < $50

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100 Measurements of Pattern Interestingness Simplicity e.g., (association) rule length, (decision) tree size Certainty e.g., confidence, P(A|B) = n(A and B)/ n (B), classification reliability or accuracy, certainty factor, rule strength, rule quality, discriminating weight, etc. Utility potential usefulness, e.g., support (association), noise threshold (description) Novelty not previously known, surprising (used to remove redundant rules, e.g., Canada vs. Vancouver rule) implication support ratio

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101 Visualization of Discovered Patterns Different backgrounds/usages may require different forms of representation E.g., rules, tables, crosstabs, pie/bar chart etc. Concept hierarchy is also important Discovered knowledge might be more understandable when represented at high level of abstraction Interactive drill up/down, pivoting, slicing and dicing provide different perspective to data Different kinds of knowledge require different representation: association, classification, clustering, etc.

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102 Chapter 4: Data Mining Primitives, Languages, and System Architectures Data mining primitives: What defines a data mining task? A data mining query language Design graphical user interfaces based on a data mining query language Architecture of data mining systems Summary

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103 A Data Mining Query Language (DMQL) Motivation A DMQL can provide the ability to support ad-hoc and interactive data mining By providing a standardized language like SQL Hope to achieve a similar effect like that SQL has on relational database Foundation for system development and evolution Facilitate information exchange, technology transfer, commercialization and wide acceptance Design DMQL is designed with the primitives described earlier

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104 Syntax for DMQL Syntax for specification of task-relevant data the kind of knowledge to be mined concept hierarchy specification interestingness measure pattern presentation and visualization Putting it all together — a DMQL query

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105 Syntax for task-relevant data specification use database database_name, or use data warehouse data_warehouse_name from relation(s)/cube(s) [where condition] in relevance to att_or_dim_list order by order_list group by grouping_list having condition

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106 Specification of task-relevant data

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107 Syntax for specifying the kind of knowledge to be mined Characterization Mine_Knowledge_Specification ::= mine characteristics [as pattern_name] analyze measure(s) Discrimination Mine_Knowledge_Specification ::= mine comparison [as pattern_name] for target_class where target_condition {versus contrast_class_i where contrast_condition_i} analyze measure(s) Association Mine_Knowledge_Specification ::= mine associations [as pattern_name]

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108 Syntax for specifying the kind of knowledge to be mined (cont.) v Classification Mine_Knowledge_Specification ::= mine classification [as pattern_name] analyze classifying_attribute_or_dimension v Prediction Mine_Knowledge_Specification ::= mine prediction [as pattern_name] analyze prediction_attribute_or_dimension {set {attribute_or_dimension_i= value_i}}

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109 Syntax for concept hierarchy specification To specify what concept hierarchies to use use hierarchy for We use different syntax to define different type of hierarchies schema hierarchies define hierarchy time_hierarchy on date as [date,month quarter,year] set-grouping hierarchies define hierarchy age_hierarchy for age on customer as level1: {young, middle_aged, senior} < level0: all level2: {20,..., 39} < level1: young level2: {40,..., 59} < level1: middle_aged level2: {60,..., 89} < level1: senior

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110 Syntax for concept hierarchy specification (Cont.) operation-derived hierarchies define hierarchy age_hierarchy for age on customer as {age_category(1),..., age_category(5)} := cluster(default, age, 5) < all(age) rule-based hierarchies define hierarchy profit_margin_hierarchy on item as level_1: low_profit_margin < level_0: all if (price - cost)< $50 level_1: medium-profit_margin < level_0: all if ((price - cost) > $50) and ((price - cost) <= $250)) level_1: high_profit_margin < level_0: all if (price - cost) > $250

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111 Syntax for interestingness measure specification Interestingness measures and thresholds can be specified by the user with the statement: with threshold = threshold_value Example: with support threshold = 0.05 with confidence threshold = 0.7

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112 Syntax for pattern presentation and visualization specification We have syntax which allows users to specify the display of discovered patterns in one or more forms display as To facilitate interactive viewing at different concept level, the following syntax is defined: Multilevel_Manipulation ::= roll up on attribute_or_dimension | drill down on attribute_or_dimension | add attribute_or_dimension | drop attribute_or_dimension

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113 Putting it all together: the full specification of a DMQL query use database AllElectronics_db use hierarchy location_hierarchy for B.address mine characteristics as customerPurchasing analyze count% in relevance to C.age, I.type, I.place_made from customer C, item I, purchases P, items_sold S, works_at W, branch where I.item_ID = S.item_ID and S.trans_ID = P.trans_ID and P.cust_ID = C.cust_ID and P.method_paid = ``AmEx'' and P.empl_ID = W.empl_ID and W.branch_ID = B.branch_ID and B.address = ``Canada" and I.price >= 100 with noise threshold = 0.05 display as table

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114 Other Data Mining Languages & Standardization Efforts Association rule language specifications MSQL (Imielinski & Virmani’99) MineRule (Meo Psaila and Ceri’96) Query flocks based on Datalog syntax (Tsur et al’98) OLEDB for DM (Microsoft’2000) Based on OLE, OLE DB, OLE DB for OLAP Integrating DBMS, data warehouse and data mining CRISP-DM (CRoss-Industry Standard Process for Data Mining) Providing a platform and process structure for effective data mining Emphasizing on deploying data mining technology to solve business problems

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115 Designing Graphical User Interfaces based on a data mining query language What tasks should be considered in the design GUIs based on a data mining query language? Data collection and data mining query composition Presentation of discovered patterns Hierarchy specification and manipulation Manipulation of data mining primitives Interactive multilevel mining Other miscellaneous information

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116 Data Mining System Architectures Coupling data mining system with DB/DW system No coupling—flat file processing, not recommended Loose coupling Fetching data from DB/DW Semi-tight coupling—enhanced DM performance Provide efficient implement a few data mining primitives in a DB/DW system, e.g., sorting, indexing, aggregation, histogram analysis, multiway join, precomputation of some stat functions Tight coupling—A uniform information processing environment DM is smoothly integrated into a DB/DW system, mining query is optimized based on mining query, indexing, query processing methods, etc.

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117 Summary Five primitives for specification of a data mining task task-relevant data kind of knowledge to be mined background knowledge interestingness measures knowledge presentation and visualization techniques to be used for displaying the discovered patterns Data mining query languages DMQL, MS/OLEDB for DM, etc. Data mining system architecture No coupling, loose coupling, semi-tight coupling, tight coupling

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118 References E. Baralis and G. Psaila. Designing templates for mining association rules. Journal of Intelligent Information Systems, 9:7-32, 1997. Microsoft Corp., OLEDB for Data Mining, version 1.0, http://www.microsoft.com/data/oledb/dm, Aug. 2000. J. Han, Y. Fu, W. Wang, K. Koperski, and O. R. Zaiane, “DMQL: A Data Mining Query Language for Relational Databases”, DMKD'96, Montreal, Canada, June 1996. T. Imielinski and A. Virmani. MSQL: A query language for database mining. Data Mining and Knowledge Discovery, 3:373-408, 1999. M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, and A.I. Verkamo. Finding interesting rules from large sets of discovered association rules. CIKM’94, Gaithersburg, Maryland, Nov. 1994. R. Meo, G. Psaila, and S. Ceri. A new SQL-like operator for mining association rules. VLDB'96, pages 122-133, Bombay, India, Sept. 1996. A. Silberschatz and A. Tuzhilin. What makes patterns interesting in knowledge discovery systems. IEEE Trans. on Knowledge and Data Engineering, 8:970-974, Dec. 1996. S. Sarawagi, S. Thomas, and R. Agrawal. Integrating association rule mining with relational database systems: Alternatives and implications. SIGMOD'98, Seattle, Washington, June 1998. D. Tsur, J. D. Ullman, S. Abitboul, C. Clifton, R. Motwani, and S. Nestorov. Query flocks: A generalization of association-rule mining. SIGMOD'98, Seattle, Washington, June 1998.

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119 http://www.cs.sfu.ca/~han Thank you !!!

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Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 5 — ©Jiawei Han and Micheline Kamber Intelligent Database Systems Research Lab School of Computing Science Simon Fraser University, Canada http://www.cs.sfu.ca

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122 Chapter 5: Concept Description: Characterization and Comparison What is concept description? Data generalization and summarization-based characterization Analytical characterization: Analysis of attribute relevance Mining class comparisons: Discriminating between different classes Mining descriptive statistical measures in large databases Discussion Summary

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What is Concept Description? Descriptive vs. predictive data mining Descriptive mining: describes concepts or task-relevant data sets in concise, summarative, informative, discriminative forms Predictive mining: Based on data and analysis, constructs models for the database, and predicts the trend and properties of unknown data Concept description: Characterization: provides a concise and succinct summarization of the given collection of data Comparison: provides descriptions comparing two or more collections of data

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124 Concept Description vs. OLAP Concept description: can handle complex data types of the attributes and their aggregations a more automated process OLAP: restricted to a small number of dimension and measure types user-controlled process

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125 Chapter 5: Concept Description: Characterization and Comparison What is concept description? Data generalization and summarization-based characterization Analytical characterization: Analysis of attribute relevance Mining class comparisons: Discriminating between different classes Mining descriptive statistical measures in large databases Discussion Summary

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126 Data Generalization and Summarization-based Characterization Data generalization A process which abstracts a large set of task-relevant data in a database from a low conceptual levels to higher ones. Approaches: Data cube approach(OLAP approach) Attribute-oriented induction approach 1 2 3 4 5 Conceptual levels

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127 Characterization: Data Cube Approach (without using AO-Induction) Perform computations and store results in data cubes Strength An efficient implementation of data generalization Computation of various kinds of measures e.g., count( ), sum( ), average( ), max( ) Generalization and specialization can be performed on a data cube by roll-up and drill-down Limitations handle only dimensions of simple nonnumeric data and measures of simple aggregated numeric values. Lack of intelligent analysis, can’t tell which dimensions should be used and what levels should the generalization reach

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128 Attribute-Oriented Induction Proposed in 1989 (KDD ‘89 workshop) Not confined to categorical data nor particular measures. How it is done? Collect the task-relevant data( initial relation) using a relational database query Perform generalization by attribute removal or attribute generalization. Apply aggregation by merging identical, generalized tuples and accumulating their respective counts. Interactive presentation with users.

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Basic Principles of Attribute- Oriented Induction Data focusing: task-relevant data, including dimensions, and the result is the initial relation. Attribute-removal: remove attribute A if there is a large set of distinct values for A but (1) there is no generalization operator on A, or (2) A’s higher level concepts are expressed in terms of other attributes. Attribute-generalization: If there is a large set of distinct values for A, and there exists a set of generalization operators on A, then select an operator and generalize A. Attribute-threshold control: typical 2-8, specified/default. Generalized relation threshold control: control the final relation/rule size. see example see example

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Basic Algorithm for Attribute- Oriented Induction InitialRel: Query processing of task-relevant data, deriving the initial relation. PreGen: Based on the analysis of the number of distinct values in each attribute, determine generalization plan for each attribute: removal? or how high to generalize? PrimeGen: Based on the PreGen plan, perform generalization to the right level to derive a “prime generalized relation”, accumulating the counts. Presentation: User interaction: (1) adjust levels by drilling, (2) pivoting, (3) mapping into rules, cross tabs, visualization presentations. See ImplementationSee Implementation See example See complexity See exampleSee complexity

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131 Example DMQL: Describe general characteristics of graduate students in the Big-University database use Big_University_DB mine characteristics as “Science_Students” in relevance to name, gender, major, birth_place, birth_date, residence, phone#, gpa from student where status in “graduate” Corresponding SQL statement: Select name, gender, major, birth_place, birth_date, residence, phone#, gpa from student where status in {“Msc”, “MBA”, “PhD” }

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Class Characterization: An Example See PrinciplesSee Algorithm Prime Generalized Relation Initial Relation See ImplementationSee Analytical Characterization

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Presentation of Generalized Results Generalized relation: Relations where some or all attributes are generalized, with counts or other aggregation values accumulated. Cross tabulation: Mapping results into cross tabulation form (similar to contingency tables). Visualization techniques: Pie charts, bar charts, curves, cubes, and other visual forms. Quantitative characteristic rules: Mapping generalized result into characteristic rules with quantitative information associated with it, e.g.,

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134 Presentation—Generalized Relation

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135 Presentation—Crosstab

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136 Implementation by Cube Technology Construct a data cube on-the-fly for the given data mining query Facilitate efficient drill-down analysis May increase the response time A balanced solution: precomputation of “subprime” relation Use a predefined & precomputed data cube Construct a data cube beforehand Facilitate not only the attribute-oriented induction, but also attribute relevance analysis, dicing, slicing, roll-up and drill-down Cost of cube computation and the nontrivial storage overhead

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137 Characterization vs. OLAP Similarity: Presentation of data summarization at multiple levels of abstraction. Interactive drilling, pivoting, slicing and dicing. Differences: Automated desired level allocation. Dimension relevance analysis and ranking when there are many relevant dimensions. Sophisticated typing on dimensions and measures. Analytical characterization: data dispersion analysis.

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138 Attribute Relevance Analysis Why? Which dimensions should be included? How high level of generalization? Automatic vs. interactive Reduce # attributes; easy to understand patterns What? statistical method for preprocessing data filter out irrelevant or weakly relevant attributes retain or rank the relevant attributes relevance related to dimensions and levels analytical characterization, analytical comparison

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139 Attribute relevance analysis (cont’d) How? Data Collection Analytical Generalization Use information gain analysis (e.g., entropy or other measures) to identify highly relevant dimensions and levels. Relevance Analysis Sort and select the most relevant dimensions and levels. Attribute-oriented Induction for class description On selected dimension/level OLAP operations (e.g. drilling, slicing) on relevance rules

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140 Relevance Measures Quantitative relevance measure determines the classifying power of an attribute within a set of data. Methods information gain (ID3) gain ratio (C4.5) gini index 2 contingency table statistics uncertainty coefficient

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141 Information-Theoretic Approach Decision tree each internal node tests an attribute each branch corresponds to attribute value each leaf node assigns a classification ID3 algorithm build decision tree based on training objects with known class labels to classify testing objects rank attributes with information gain measure minimal height the least number of tests to classify an object See example

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142 Top-Down Induction of Decision Tree Attributes = {Outlook, Temperature, Humidity, Wind} Outlook Humidity Wind sunnyrain overcast yes noyes high normal no strong weak yes PlayTennis = {yes, no}

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143 Entropy and Information Gain S contains s i tuples of class C i for i = {1, …, m} Information measures info required to classify any arbitrary tuple Entropy of attribute A with values {a 1,a 2,…,a v } Information gained by branching on attribute A

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144 Example: Analytical Characterization Task Mine general characteristics describing graduate students using analytical characterization Given attributes name, gender, major, birth_place, birth_date, phone#, and gpa Gen(a i ) = concept hierarchies on a i U i = attribute analytical thresholds for a i T i = attribute generalization thresholds for a i R = attribute relevance threshold

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145 Example: Analytical Characterization (cont’d) 1. Data collection target class: graduate student contrasting class: undergraduate student 2. Analytical generalization using U i attribute removal remove name and phone# attribute generalization generalize major, birth_place, birth_date and gpa accumulate counts candidate relation: gender, major, birth_country, age_range and gpa

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146 Example: Analytical characterization (2) Candidate relation for Target class: Graduate students ( =120) Candidate relation for Contrasting class: Undergraduate students ( =130)

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147 Example: Analytical characterization (3) 3. Relevance analysis Calculate expected info required to classify an arbitrary tuple Calculate entropy of each attribute: e.g. major Number of grad students in “Science” Number of undergrad students in “Science”

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148 Example: Analytical Characterization (4) Calculate expected info required to classify a given sample if S is partitioned according to the attribute Calculate information gain for each attribute Information gain for all attributes

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149 Example: Analytical characterization (5) 4. Initial working relation (W 0 ) derivation R = 0.1 remove irrelevant/weakly relevant attributes from candidate relation => drop gender, birth_country remove contrasting class candidate relation 5. Perform attribute-oriented induction on W 0 using T i Initial target class working relation W 0 : Graduate students

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150 Chapter 5: Concept Description: Characterization and Comparison What is concept description? Data generalization and summarization-based characterization Analytical characterization: Analysis of attribute relevance Mining class comparisons: Discriminating between different classes Mining descriptive statistical measures in large databases Discussion Summary

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Mining Class Comparisons Comparison: Comparing two or more classes. Method: Partition the set of relevant data into the target class and the contrasting class(es) Generalize both classes to the same high level concepts Compare tuples with the same high level descriptions Present for every tuple its description and two measures: support - distribution within single class comparison - distribution between classes Highlight the tuples with strong discriminant features Relevance Analysis: Find attributes (features) which best distinguish different classes.

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152 Example: Analytical comparison Task Compare graduate and undergraduate students using discriminant rule. DMQL query use Big_University_DB mine comparison as “grad_vs_undergrad_students” in relevance to name, gender, major, birth_place, birth_date, residence, phone#, gpa for “graduate_students” where status in “graduate” versus “undergraduate_students” where status in “undergraduate” analyze count% from student

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153 Example: Analytical comparison (2) Given attributes name, gender, major, birth_place, birth_date, residence, phone# and gpa Gen(a i ) = concept hierarchies on attributes a i U i = attribute analytical thresholds for attributes a i T i = attribute generalization thresholds for attributes a i R = attribute relevance threshold

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154 Example: Analytical comparison (3) 1. Data collection target and contrasting classes 2. Attribute relevance analysis remove attributes name, gender, major, phone# 3. Synchronous generalization controlled by user-specified dimension thresholds prime target and contrasting class(es) relations/cuboids

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155 Example: Analytical comparison (4) Prime generalized relation for the target class: Graduate students Prime generalized relation for the contrasting class: Undergraduate students

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156 Example: Analytical comparison (5) 4. Drill down, roll up and other OLAP operations on target and contrasting classes to adjust levels of abstractions of resulting description 5. Presentation as generalized relations, crosstabs, bar charts, pie charts, or rules contrasting measures to reflect comparison between target and contrasting classes e.g. count%

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157 Quantitative Discriminant Rules Cj = target class q a = a generalized tuple covers some tuples of class but can also cover some tuples of contrasting class d-weight range: [0, 1] quantitative discriminant rule form

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158 Example: Quantitative Discriminant Rule Quantitative discriminant rule where 90/(90+120) = 30% Count distribution between graduate and undergraduate students for a generalized tuple

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159 Class Description Quantitative characteristic rule necessary Quantitative discriminant rule sufficient Quantitative description rule necessary and sufficient

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160 Example: Quantitative Description Rule Quantitative description rule for target class Europe Crosstab showing associated t-weight, d-weight values and total number (in thousands) of TVs and computers sold at AllElectronics in 1998

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161 Chapter 5: Concept Description: Characterization and Comparison What is concept description? Data generalization and summarization-based characterization Analytical characterization: Analysis of attribute relevance Mining class comparisons: Discriminating between different classes Mining descriptive statistical measures in large databases Discussion Summary

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162 Mining Data Dispersion Characteristics Motivation To better understand the data: central tendency, variation and spread Data dispersion characteristics median, max, min, quantiles, outliers, variance, etc. Numerical dimensions correspond to sorted intervals Data dispersion: analyzed with multiple granularities of precision Boxplot or quantile analysis on sorted intervals Dispersion analysis on computed measures Folding measures into numerical dimensions Boxplot or quantile analysis on the transformed cube

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163 Measuring the Central Tendency Mean Weighted arithmetic mean Median: A holistic measure Middle value if odd number of values, or average of the middle two values otherwise estimated by interpolation Mode Value that occurs most frequently in the data Unimodal, bimodal, trimodal Empirical formula:

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164 Measuring the Dispersion of Data Quartiles, outliers and boxplots Quartiles: Q 1 (25 th percentile), Q 3 (75 th percentile) Inter-quartile range: IQR = Q 3 – Q 1 Five number summary: min, Q 1, M, Q 3, max Boxplot: ends of the box are the quartiles, median is marked, whiskers, and plot outlier individually Outlier: usually, a value higher/lower than 1.5 x IQR Variance and standard deviation Variance s 2 : (algebraic, scalable computation) Standard deviation s is the square root of variance s 2

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165 Boxplot Analysis Five-number summary of a distribution: Minimum, Q1, M, Q3, Maximum Boxplot Data is represented with a box The ends of the box are at the first and third quartiles, i.e., the height of the box is IRQ The median is marked by a line within the box Whiskers: two lines outside the box extend to Minimum and Maximum

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166 A Boxplot A boxplot

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167 Visualization of Data Dispersion: Boxplot Analysis

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168 Mining Descriptive Statistical Measures in Large Databases Variance Standard deviation: the square root of the variance Measures spread about the mean It is zero if and only if all the values are equal Both the deviation and the variance are algebraic

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169 Histogram Analysis Graph displays of basic statistical class descriptions Frequency histograms A univariate graphical method Consists of a set of rectangles that reflect the counts or frequencies of the classes present in the given data

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170 Quantile Plot Displays all of the data (allowing the user to assess both the overall behavior and unusual occurrences) Plots quantile information For a data x i data sorted in increasing order, f i indicates that approximately 100 f i % of the data are below or equal to the value x i

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171 Quantile-Quantile (Q-Q) Plot Graphs the quantiles of one univariate distribution against the corresponding quantiles of another Allows the user to view whether there is a shift in going from one distribution to another

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172 Scatter plot Provides a first look at bivariate data to see clusters of points, outliers, etc Each pair of values is treated as a pair of coordinates and plotted as points in the plane

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173 Loess Curve Adds a smooth curve to a scatter plot in order to provide better perception of the pattern of dependence Loess curve is fitted by setting two parameters: a smoothing parameter, and the degree of the polynomials that are fitted by the regression

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174 Graphic Displays of Basic Statistical Descriptions Histogram: (shown before) Boxplot: (covered before) Quantile plot: each value x i is paired with f i indicating that approximately 100 f i % of data are x i Quantile-quantile (q-q) plot: graphs the quantiles of one univariant distribution against the corresponding quantiles of another Scatter plot: each pair of values is a pair of coordinates and plotted as points in the plane Loess (local regression) curve: add a smooth curve to a scatter plot to provide better perception of the pattern of dependence

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175 Chapter 5: Concept Description: Characterization and Comparison What is concept description? Data generalization and summarization-based characterization Analytical characterization: Analysis of attribute relevance Mining class comparisons: Discriminating between different classes Mining descriptive statistical measures in large databases Discussion Summary

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176 AO Induction vs. Learning-from- example Paradigm Difference in philosophies and basic assumptions Positive and negative samples in learning-from-example: positive used for generalization, negative - for specialization Positive samples only in data mining: hence generalization- based, to drill-down backtrack the generalization to a previous state Difference in methods of generalizations Machine learning generalizes on a tuple by tuple basis Data mining generalizes on an attribute by attribute basis

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177 Comparison of Entire vs. Factored Version Space

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178 Incremental and Parallel Mining of Concept Description Incremental mining: revision based on newly added data DB Generalize DB to the same level of abstraction in the generalized relation R to derive R Union R U R, i.e., merge counts and other statistical information to produce a new relation R’ Similar philosophy can be applied to data sampling, parallel and/or distributed mining, etc.

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179 Chapter 5: Concept Description: Characterization and Comparison What is concept description? Data generalization and summarization-based characterization Analytical characterization: Analysis of attribute relevance Mining class comparisons: Discriminating between different classes Mining descriptive statistical measures in large databases Discussion Summary

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180 Summary Concept description: characterization and discrimination OLAP-based vs. attribute-oriented induction Efficient implementation of AOI Analytical characterization and comparison Mining descriptive statistical measures in large databases Discussion Incremental and parallel mining of description Descriptive mining of complex types of data

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181 References Y. Cai, N. Cercone, and J. Han. Attribute-oriented induction in relational databases. In G. Piatetsky-Shapiro and W. J. Frawley, editors, Knowledge Discovery in Databases, pages 213- 228. AAAI/MIT Press, 1991. S. Chaudhuri and U. Dayal. An overview of data warehousing and OLAP technology. ACM SIGMOD Record, 26:65-74, 1997 C. Carter and H. Hamilton. Efficient attribute-oriented generalization for knowledge discovery from large databases. IEEE Trans. Knowledge and Data Engineering, 10:193-208, 1998. W. Cleveland. Visualizing Data. Hobart Press, Summit NJ, 1993. J. L. Devore. Probability and Statistics for Engineering and the Science, 4th ed. Duxbury Press, 1995. T. G. Dietterich and R. S. Michalski. A comparative review of selected methods for learning from examples. In Michalski et al., editor, Machine Learning: An Artificial Intelligence Approach, Vol. 1, pages 41-82. Morgan Kaufmann, 1983. J. Gray, S. Chaudhuri, A. Bosworth, A. Layman, D. Reichart, M. Venkatrao, F. Pellow, and H. Pirahesh. Data cube: A relational aggregation operator generalizing group-by, cross-tab and sub-totals. Data Mining and Knowledge Discovery, 1:29-54, 1997. J. Han, Y. Cai, and N. Cercone. Data-driven discovery of quantitative rules in relational databases. IEEE Trans. Knowledge and Data Engineering, 5:29-40, 1993.

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182 References (cont.) J. Han and Y. Fu. Exploration of the power of attribute-oriented induction in data mining. In U.M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy, editors, Advances in Knowledge Discovery and Data Mining, pages 399-421. AAAI/MIT Press, 1996. R. A. Johnson and D. A. Wichern. Applied Multivariate Statistical Analysis, 3rd ed. Prentice Hall, 1992. E. Knorr and R. Ng. Algorithms for mining distance-based outliers in large datasets. VLDB'98, New York, NY, Aug. 1998. H. Liu and H. Motoda. Feature Selection for Knowledge Discovery and Data Mining. Kluwer Academic Publishers, 1998. R. S. Michalski. A theory and methodology of inductive learning. In Michalski et al., editor, Machine Learning: An Artificial Intelligence Approach, Vol. 1, Morgan Kaufmann, 1983. T. M. Mitchell. Version spaces: A candidate elimination approach to rule learning. IJCAI'97, Cambridge, MA. T. M. Mitchell. Generalization as search. Artificial Intelligence, 18:203-226, 1982. T. M. Mitchell. Machine Learning. McGraw Hill, 1997. J. R. Quinlan. Induction of decision trees. Machine Learning, 1:81-106, 1986. D. Subramanian and J. Feigenbaum. Factorization in experiment generation. AAAI'86, Philadelphia, PA, Aug. 1986.

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183 http://www.cs.sfu.ca/~han/dmbook Thank you !!!

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Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 6 — ©Jiawei Han and Micheline Kamber Intelligent Database Systems Research Lab School of Computing Science Simon Fraser University, Canada http://www.cs.sfu.ca

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186 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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187 What Is Association Mining? Association rule mining: Finding frequent patterns, associations, correlations, or causal structures among sets of items or objects in transaction databases, relational databases, and other information repositories. Applications: Basket data analysis, cross-marketing, catalog design, loss-leader analysis, clustering, classification, etc. Examples. Rule form: “Body ead [support, confidence]”. buys(x, “diapers”) buys(x, “beers”) [0.5%, 60%] major(x, “CS”) ^ takes(x, “DB”) grade(x, “A”) [1%, 75%]

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188 Association Rule: Basic Concepts Given: (1) database of transactions, (2) each transaction is a list of items (purchased by a customer in a visit) Find: all rules that correlate the presence of one set of items with that of another set of items E.g., 98% of people who purchase tires and auto accessories also get automotive services done Applications * Maintenance Agreement (What the store should do to boost Maintenance Agreement sales) Home Electronics * (What other products should the store stocks up?) Attached mailing in direct marketing Detecting “ping-pong”ing of patients, faulty “collisions”

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189 Rule Measures: Support and Confidence Find all the rules X & Y Z with minimum confidence and support support, s, probability that a transaction contains {X Y Z} confidence, c, conditional probability that a transaction having {X Y} also contains Z Let minimum support 50%, and minimum confidence 50%, we have A C (50%, 66.6%) C A (50%, 100%) Customer buys diaper Customer buys both Customer buys beer

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190 Association Rule Mining: A Road Map Boolean vs. quantitative associations (Based on the types of values handled) buys(x, “SQLServer”) ^ buys(x, “DMBook”) buys(x, “DBMiner”) [0.2%, 60%] age(x, “30..39”) ^ income(x, “42..48K”) buys(x, “PC”) [1%, 75%] Single dimension vs. multiple dimensional associations (see ex. Above) Single level vs. multiple-level analysis What brands of beers are associated with what brands of diapers? Various extensions Correlation, causality analysis Association does not necessarily imply correlation or causality Maxpatterns and closed itemsets Constraints enforced E.g., small sales (sum 1,000)?

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191 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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192 Mining Association Rules—An Example For rule A C: support = support({A C}) = 50% confidence = support({A C})/support({A}) = 66.6% The Apriori principle: Any subset of a frequent itemset must be frequent Min. support 50% Min. confidence 50%

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193 Mining Frequent Itemsets: the Key Step Find the frequent itemsets: the sets of items that have minimum support A subset of a frequent itemset must also be a frequent itemset i.e., if {AB} is a frequent itemset, both {A} and {B} should be a frequent itemset Iteratively find frequent itemsets with cardinality from 1 to k (k- itemset) Use the frequent itemsets to generate association rules.

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194 The Apriori Algorithm Join Step: C k is generated by joining L k-1 with itself Prune Step: Any (k-1)-itemset that is not frequent cannot be a subset of a frequent k-itemset Pseudo-code: C k : Candidate itemset of size k L k : frequent itemset of size k L 1 = {frequent items}; for (k = 1; L k != ; k++) do begin C k+1 = candidates generated from L k ; for each transaction t in database do increment the count of all candidates in C k+1 that are contained in t L k+1 = candidates in C k+1 with min_support end return k L k ;

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195 The Apriori Algorithm — Example Database D Scan D C1C1 L1L1 L2L2 C2C2 C2C2 C3C3 L3L3

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196 How to Generate Candidates? Suppose the items in L k-1 are listed in an order Step 1: self-joining L k-1 insert into C k select p.item 1, p.item 2, …, p.item k-1, q.item k-1 from L k-1 p, L k-1 q where p.item 1 =q.item 1, …, p.item k-2 =q.item k-2, p.item k-1 < q.item k-1 Step 2: pruning forall itemsets c in C k do forall (k-1)-subsets s of c do if (s is not in L k-1 ) then delete c from C k

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197 How to Count Supports of Candidates? Why counting supports of candidates a problem? The total number of candidates can be very huge One transaction may contain many candidates Method: Candidate itemsets are stored in a hash-tree Leaf node of hash-tree contains a list of itemsets and counts Interior node contains a hash table Subset function: finds all the candidates contained in a transaction

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198 Example of Generating Candidates L 3 ={abc, abd, acd, ace, bcd} Self-joining: L 3 *L 3 abcd from abc and abd acde from acd and ace Pruning: acde is removed because ade is not in L 3 C 4 ={abcd}

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199 Methods to Improve Apriori’s Efficiency Hash-based itemset counting: A k-itemset whose corresponding hashing bucket count is below the threshold cannot be frequent Transaction reduction: A transaction that does not contain any frequent k- itemset is useless in subsequent scans Partitioning: Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB Sampling: mining on a subset of given data, lower support threshold + a method to determine the completeness Dynamic itemset counting: add new candidate itemsets only when all of their subsets are estimated to be frequent

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200 Is Apriori Fast Enough? — Performance Bottlenecks The core of the Apriori algorithm: Use frequent (k – 1)-itemsets to generate candidate frequent k-itemsets Use database scan and pattern matching to collect counts for the candidate itemsets The bottleneck of Apriori: candidate generation Huge candidate sets: 10 4 frequent 1-itemset will generate 10 7 candidate 2-itemsets To discover a frequent pattern of size 100, e.g., {a 1, a 2, …, a 100 }, one needs to generate 2 100 10 30 candidates. Multiple scans of database: Needs (n +1 ) scans, n is the length of the longest pattern

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201 Mining Frequent Patterns Without Candidate Generation Compress a large database into a compact, Frequent- Pattern tree (FP-tree) structure highly condensed, but complete for frequent pattern mining avoid costly database scans Develop an efficient, FP-tree-based frequent pattern mining method A divide-and-conquer methodology: decompose mining tasks into smaller ones Avoid candidate generation: sub-database test only!

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202 Construct FP-tree from a Transaction DB {} f:4c:1 b:1 p:1 b:1c:3 a:3 b:1m:2 p:2m:1 Header Table Item frequency head f4 c4 a3 b3 m3 p3 min_support = 0.5 TIDItems bought (ordered) frequent items 100{f, a, c, d, g, i, m, p}{f, c, a, m, p} 200{a, b, c, f, l, m, o}{f, c, a, b, m} 300 {b, f, h, j, o}{f, b} 400 {b, c, k, s, p}{c, b, p} 500 {a, f, c, e, l, p, m, n}{f, c, a, m, p} Steps: 1.Scan DB once, find frequent 1-itemset (single item pattern) 2.Order frequent items in frequency descending order 3.Scan DB again, construct FP-tree

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203 Benefits of the FP-tree Structure Completeness: never breaks a long pattern of any transaction preserves complete information for frequent pattern mining Compactness reduce irrelevant information—infrequent items are gone frequency descending ordering: more frequent items are more likely to be shared never be larger than the original database (if not count node- links and counts) Example: For Connect-4 DB, compression ratio could be over 100

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204 Mining Frequent Patterns Using FP-tree General idea (divide-and-conquer) Recursively grow frequent pattern path using the FP-tree Method For each item, construct its conditional pattern-base, and then its conditional FP-tree Repeat the process on each newly created conditional FP- tree Until the resulting FP-tree is empty, or it contains only one path (single path will generate all the combinations of its sub-paths, each of which is a frequent pattern)

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205 Major Steps to Mine FP-tree 1)Construct conditional pattern base for each node in the FP-tree 2)Construct conditional FP-tree from each conditional pattern-base 3)Recursively mine conditional FP-trees and grow frequent patterns obtained so far If the conditional FP-tree contains a single path, simply enumerate all the patterns

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206 Step 1: From FP-tree to Conditional Pattern Base Starting at the frequent header table in the FP-tree Traverse the FP-tree by following the link of each frequent item Accumulate all of transformed prefix paths of that item to form a conditional pattern base Conditional pattern bases itemcond. pattern base cf:3 afc:3 bfca:1, f:1, c:1 mfca:2, fcab:1 pfcam:2, cb:1 {} f:4c:1 b:1 p:1 b:1c:3 a:3 b:1m:2 p:2m:1 Header Table Item frequency head f4 c4 a3 b3 m3 p3

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207 Properties of FP-tree for Conditional Pattern Base Construction Node-link property For any frequent item a i, all the possible frequent patterns that contain a i can be obtained by following a i 's node-links, starting from a i 's head in the FP-tree header Prefix path property To calculate the frequent patterns for a node a i in a path P, only the prefix sub-path of a i in P need to be accumulated, and its frequency count should carry the same count as node a i.

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208 Step 2: Construct Conditional FP- tree For each pattern-base Accumulate the count for each item in the base Construct the FP-tree for the frequent items of the pattern base m-conditional pattern base: fca:2, fcab:1 {} f:3 c:3 a:3 m-conditional FP-tree All frequent patterns concerning m m, fm, cm, am, fcm, fam, cam, fcam {} f:4c:1 b:1 p:1 b:1c:3 a:3 b:1m:2 p:2m:1 Header Table Item frequency head f4 c4 a3 b3 m3 p3

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209 Mining Frequent Patterns by Creating Conditional Pattern-Bases Empty f {(f:3)}|c{(f:3)}c {(f:3, c:3)}|a{(fc:3)}a Empty{(fca:1), (f:1), (c:1)}b {(f:3, c:3, a:3)}|m{(fca:2), (fcab:1)}m {(c:3)}|p{(fcam:2), (cb:1)}p Conditional FP-treeConditional pattern-base Item

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210 Step 3: Recursively mine the conditional FP-tree {} f:3 c:3 a:3 m-conditional FP-tree Cond. pattern base of “am”: (fc:3) {} f:3 c:3 am-conditional FP-tree Cond. pattern base of “cm”: (f:3) {} f:3 cm-conditional FP-tree Cond. pattern base of “cam”: (f:3) {} f:3 cam-conditional FP-tree

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211 Single FP-tree Path Generation Suppose an FP-tree T has a single path P The complete set of frequent pattern of T can be generated by enumeration of all the combinations of the sub-paths of P {} f:3 c:3 a:3 m-conditional FP-tree All frequent patterns concerning m m, fm, cm, am, fcm, fam, cam, fcam

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212 Principles of Frequent Pattern Growth Pattern growth property Let be a frequent itemset in DB, B be 's conditional pattern base, and be an itemset in B. Then is a frequent itemset in DB iff is frequent in B. “abcdef ” is a frequent pattern, if and only if “abcde ” is a frequent pattern, and “f ” is frequent in the set of transactions containing “abcde ”

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213 Why Is Frequent Pattern Growth Fast? Our performance study shows FP-growth is an order of magnitude faster than Apriori, and is also faster than tree-projection Reasoning No candidate generation, no candidate test Use compact data structure Eliminate repeated database scan Basic operation is counting and FP-tree building

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214 FP-growth vs. Apriori: Scalability With the Support Threshold Data set T25I20D10K

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215 FP-growth vs. Tree-Projection: Scalability with Support Threshold Data set T25I20D100K

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216 Presentation of Association Rules (Table Form )

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217 Visualization of Association Rule Using Plane Graph

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218 Visualization of Association Rule Using Rule Graph

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219 Iceberg Queries Icerberg query: Compute aggregates over one or a set of attributes only for those whose aggregate values is above certain threshold Example: select P.custID, P.itemID, sum(P.qty) from purchase P group by P.custID, P.itemID having sum(P.qty) >= 10 Compute iceberg queries efficiently by Apriori: First compute lower dimensions Then compute higher dimensions only when all the lower ones are above the threshold

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220 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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221 Multiple-Level Association Rules Items often form hierarchy. Items at the lower level are expected to have lower support. Rules regarding itemsets at appropriate levels could be quite useful. Transaction database can be encoded based on dimensions and levels We can explore shared multi- level mining Food bread milk skim SunsetFraser 2%white wheat

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222 Mining Multi-Level Associations A top_down, progressive deepening approach: First find high-level strong rules: milk bread [20%, 60%]. Then find their lower-level “weaker” rules: 2% milk wheat bread [6%, 50%]. Variations at mining multiple-level association rules. Level-crossed association rules: 2% milk Wonder wheat bread Association rules with multiple, alternative hierarchies: 2% milk Wonder bread

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223 Multi-level Association: Uniform Support vs. Reduced Support Uniform Support: the same minimum support for all levels + One minimum support threshold. No need to examine itemsets containing any item whose ancestors do not have minimum support. – Lower level items do not occur as frequently. If support threshold too high miss low level associations too low generate too many high level associations Reduced Support: reduced minimum support at lower levels There are 4 search strategies: Level-by-level independent Level-cross filtering by k-itemset Level-cross filtering by single item Controlled level-cross filtering by single item

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224 Uniform Support Multi-level mining with uniform support Milk [support = 10%] 2% Milk [support = 6%] Skim Milk [support = 4%] Level 1 min_sup = 5% Level 2 min_sup = 5%

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225 Reduced Support Multi-level mining with reduced support 2% Milk [support = 6%] Skim Milk [support = 4%] Level 1 min_sup = 5% Level 2 min_sup = 3% Milk [support = 10%]

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226 Multi-level Association: Redundancy Filtering Some rules may be redundant due to “ancestor” relationships between items. Example milk wheat bread [support = 8%, confidence = 70%] 2% milk wheat bread [support = 2%, confidence = 72%] We say the first rule is an ancestor of the second rule. A rule is redundant if its support is close to the “expected” value, based on the rule’s ancestor.

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227 Multi-Level Mining: Progressive Deepening A top-down, progressive deepening approach: First mine high-level frequent items: milk (15%), bread (10%) Then mine their lower-level “weaker” frequent itemsets: 2% milk (5%), wheat bread (4%) Different min_support threshold across multi-levels lead to different algorithms: If adopting the same min_support across multi-levels then toss t if any of t’s ancestors is infrequent. If adopting reduced min_support at lower levels then examine only those descendents whose ancestor’s support is frequent/non-negligible.

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228 Progressive Refinement of Data Mining Quality Why progressive refinement? Mining operator can be expensive or cheap, fine or rough Trade speed with quality: step-by-step refinement. Superset coverage property: Preserve all the positive answers—allow a positive false test but not a false negative test. Two- or multi-step mining: First apply rough/cheap operator (superset coverage) Then apply expensive algorithm on a substantially reduced candidate set (Koperski & Han, SSD’95).

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229 Progressive Refinement Mining of Spatial Association Rules Hierarchy of spatial relationship: “g_close_to”: near_by, touch, intersect, contain, etc. First search for rough relationship and then refine it. Two-step mining of spatial association: Step 1: rough spatial computation (as a filter) Using MBR or R-tree for rough estimation. Step2: Detailed spatial algorithm (as refinement) Apply only to those objects which have passed the rough spatial association test (no less than min_support)

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230 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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231 Multi-Dimensional Association: Concepts Single-dimensional rules: buys(X, “milk”) buys(X, “bread”) Multi-dimensional rules: 2 dimensions or predicates Inter-dimension association rules (no repeated predicates) age(X,”19-25”) occupation(X,“student”) buys(X,“coke”) hybrid-dimension association rules (repeated predicates) age(X,”19-25”) buys(X, “popcorn”) buys(X, “coke”) Categorical Attributes finite number of possible values, no ordering among values Quantitative Attributes numeric, implicit ordering among values

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232 Techniques for Mining MD Associations Search for frequent k-predicate set: Example: {age, occupation, buys} is a 3-predicate set. Techniques can be categorized by how age are treated. 1. Using static discretization of quantitative attributes Quantitative attributes are statically discretized by using predefined concept hierarchies. 2. Quantitative association rules Quantitative attributes are dynamically discretized into “bins”based on the distribution of the data. 3. Distance-based association rules This is a dynamic discretization process that considers the distance between data points.

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233 Static Discretization of Quantitative Attributes Discretized prior to mining using concept hierarchy. Numeric values are replaced by ranges. In relational database, finding all frequent k-predicate sets will require k or k+1 table scans. Data cube is well suited for mining. The cells of an n-dimensional cuboid correspond to the predicate sets. Mining from data cubes can be much faster. (income)(age) () (buys) (age, income)(age,buys)(income,buys) (age,income,buys)

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234 Quantitative Association Rules age(X,”30-34”) income(X,”24K - 48K”) buys(X,”high resolution TV”) Numeric attributes are dynamically discretized Such that the confidence or compactness of the rules mined is maximized. 2-D quantitative association rules: A quan1 A quan2 A cat Cluster “adjacent” association rules to form general rules using a 2-D grid. Example:

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235 ARCS (Association Rule Clustering System) How does ARCS work? 1. Binning 2. Find frequent predicateset 3. Clustering 4. Optimize

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236 Limitations of ARCS Only quantitative attributes on LHS of rules. Only 2 attributes on LHS. (2D limitation) An alternative to ARCS Non-grid-based equi-depth binning clustering based on a measure of partial completeness. “Mining Quantitative Association Rules in Large Relational Tables” by R. Srikant and R. Agrawal.

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237 Mining Distance-based Association Rules Binning methods do not capture the semantics of interval data Distance-based partitioning, more meaningful discretization considering: density/number of points in an interval “closeness” of points in an interval

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238 S[X] is a set of N tuples t 1, t 2, …, t N, projected on the attribute set X The diameter of S[X]: dist x :distance metric, e.g. Euclidean distance or Manhattan Clusters and Distance Measurements

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239 The diameter, d, assesses the density of a cluster C X, where Finding clusters and distance-based rules the density threshold, d 0, replaces the notion of support modified version of the BIRCH clustering algorithm Clusters and Distance Measurements(Cont.)

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240 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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241 Interestingness Measurements Objective measures Two popular measurements: ¶ support; and · confidence Subjective measures (Silberschatz & Tuzhilin, KDD95) A rule (pattern) is interesting if ¶ it is unexpected (surprising to the user); and/or · actionable (the user can do something with it)

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242 Criticism to Support and Confidence Example 1: (Aggarwal & Yu, PODS98) Among 5000 students 3000 play basketball 3750 eat cereal 2000 both play basket ball and eat cereal play basketball eat cereal [40%, 66.7%] is misleading because the overall percentage of students eating cereal is 75% which is higher than 66.7%. play basketball not eat cereal [20%, 33.3%] is far more accurate, although with lower support and confidence

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243 Criticism to Support and Confidence (Cont.) Example 2: X and Y: positively correlated, X and Z, negatively related support and confidence of X=>Z dominates We need a measure of dependent or correlated events P(B|A)/P(B) is also called the lift of rule A => B

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244 Other Interestingness Measures: Interest Interest (correlation, lift) taking both P(A) and P(B) in consideration P(A^B)=P(B)*P(A), if A and B are independent events A and B negatively correlated, if the value is less than 1; otherwise A and B positively correlated

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245 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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246 Constraint-Based Mining Interactive, exploratory mining giga-bytes of data? Could it be real? — Making good use of constraints! What kinds of constraints can be used in mining? Knowledge type constraint: classification, association, etc. Data constraint: SQL-like queries Find product pairs sold together in Vancouver in Dec.’98. Dimension/level constraints: in relevance to region, price, brand, customer category. Rule constraints small sales (price $200). Interestingness constraints: strong rules (min_support 3%, min_confidence 60%).

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247 Rule Constraints in Association Mining Two kind of rule constraints: Rule form constraints: meta-rule guided mining. P(x, y) ^ Q(x, w) takes(x, “database systems”). Rule (content) constraint: constraint-based query optimization (Ng, et al., SIGMOD’98). sum(LHS) 20 ^ count(LHS) > 3 ^ sum(RHS) > 1000 1-variable vs. 2-variable constraints (Lakshmanan, et al. SIGMOD’99 ): 1-var: A constraint confining only one side (L/R) of the rule, e.g., as shown above. 2-var: A constraint confining both sides (L and R). sum(LHS) < min(RHS) ^ max(RHS) < 5* sum(LHS)

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248 Constrain-Based Association Query Database: (1) trans (TID, Itemset ), (2) itemInfo (Item, Type, Price) A constrained asso. query (CAQ) is in the form of {(S 1, S 2 )|C }, where C is a set of constraints on S 1, S 2 including frequency constraint A classification of (single-variable) constraints: Class constraint: S A. e.g. S Item Domain constraint: S v, { , , , , , }. e.g. S.Price < 100 v S, is or . e.g. snacks S.Type V S, or S V, { , , , , } e.g. {snacks, sodas } S.Type Aggregation constraint: agg(S) v, where agg is in {min, max, sum, count, avg}, and { , , , , , }. e.g. count(S 1.Type) 1, avg(S 2.Price) 100

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249 Constrained Association Query Optimization Problem Given a CAQ = { (S 1, S 2 ) | C }, the algorithm should be : sound: It only finds frequent sets that satisfy the given constraints C complete: All frequent sets satisfy the given constraints C are found A naïve solution: Apply Apriori for finding all frequent sets, and then to test them for constraint satisfaction one by one. Our approach: Comprehensive analysis of the properties of constraints and try to push them as deeply as possible inside the frequent set computation.

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250 Anti-monotone and Monotone Constraints anti-monotone A constraint C a is anti-monotone iff. for any pattern S not satisfying C a, none of the super-patterns of S can satisfy C a monotone A constraint C m is monotone iff. for any pattern S satisfying C m, every super-pattern of S also satisfies it

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251 Succinct Constraint succinct set A subset of item I s is a succinct set, if it can be expressed as p (I) for some selection predicate p, where is a selection operator power set SP 2 I is a succinct power set, if there is a fixed number of succinct set I 1, …, I k I, s.t. SP can be expressed in terms of the strict power sets of I 1, …, I k using union and minus succinct A constraint C s is succinct provided SAT Cs (I) is a succinct power set

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252 Convertible Constraint Suppose all items in patterns are listed in a total order R convertible anti-monotone A constraint C is convertible anti-monotone iff a pattern S satisfying the constraint implies that each suffix of S w.r.t. R also satisfies C convertible monotone A constraint C is convertible monotone iff a pattern S satisfying the constraint implies that each pattern of which S is a suffix w.r.t. R also satisfies C

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253 Relationships Among Categories of Constraints Succinctness Anti-monotonicityMonotonicity Convertible constraints Inconvertible constraints

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254 Property of Constraints: Anti-Monotone Anti-monotonicity: If a set S violates the constraint, any superset of S violates the constraint. Examples: sum(S.Price) v is anti-monotone sum(S.Price) v is not anti-monotone sum(S.Price) = v is partly anti-monotone Application: Push “sum(S.price) 1000” deeply into iterative frequent set computation.

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255 Characterization of Anti-Monotonicity Constraints S v, { , , } v S S V S V S V min(S) v min(S) v min(S) v max(S) v max(S) v max(S) v count(S) v count(S) v count(S) v sum(S) v sum(S) v sum(S) v avg(S) v, { , , } (frequent constraint) yes no yes partly no yes partly yes no partly yes no partly yes no partly convertible (yes)

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256 Example of Convertible Constraints: Avg(S) V Let R be the value descending order over the set of items E.g. I={9, 8, 6, 4, 3, 1} Avg(S) v is convertible monotone w.r.t. R If S is a suffix of S 1, avg(S 1 ) avg(S) {8, 4, 3} is a suffix of {9, 8, 4, 3} avg({9, 8, 4, 3})=6 avg({8, 4, 3})=5 If S satisfies avg(S) v, so does S 1 {8, 4, 3} satisfies constraint avg(S) 4, so does {9, 8, 4, 3}

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257 Property of Constraints: Succinctness Succinctness: For any set S 1 and S 2 satisfying C, S 1 S 2 satisfies C Given A 1 is the sets of size 1 satisfying C, then any set S satisfying C are based on A 1, i.e., it contains a subset belongs to A 1, Example : sum(S.Price ) v is not succinct min(S.Price ) v is succinct Optimization: If C is succinct, then C is pre-counting prunable. The satisfaction of the constraint alone is not affected by the iterative support counting.

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258 Characterization of Constraints by Succinctness S v, { , , } v S S V S V S V min(S) v min(S) v min(S) v max(S) v max(S) v max(S) v count(S) v count(S) v count(S) v sum(S) v sum(S) v sum(S) v avg(S) v, { , , } (frequent constraint) Yes yes weakly no (no)

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259 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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260 Why Is the Big Pie Still There? More on constraint-based mining of associations Boolean vs. quantitative associations Association on discrete vs. continuous data From association to correlation and causal structure analysis. Association does not necessarily imply correlation or causal relationships From intra-trasanction association to inter-transaction associations E.g., break the barriers of transactions (Lu, et al. TOIS’99). From association analysis to classification and clustering analysis E.g, clustering association rules

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261 Chapter 6: Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary

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262 Summary Association rule mining probably the most significant contribution from the database community in KDD A large number of papers have been published Many interesting issues have been explored An interesting research direction Association analysis in other types of data: spatial data, multimedia data, time series data, etc.

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263 References R. Agarwal, C. Aggarwal, and V. V. V. Prasad. A tree projection algorithm for generation of frequent itemsets. In Journal of Parallel and Distributed Computing (Special Issue on High Performance Data Mining), 2000. R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. SIGMOD'93, 207-216, Washington, D.C. R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB'94 487-499, Santiago, Chile. R. Agrawal and R. Srikant. Mining sequential patterns. ICDE'95, 3-14, Taipei, Taiwan. R. J. Bayardo. Efficiently mining long patterns from databases. SIGMOD'98, 85-93, Seattle, Washington. S. Brin, R. Motwani, and C. Silverstein. Beyond market basket: Generalizing association rules to correlations. SIGMOD'97, 265-276, Tucson, Arizona. S. Brin, R. Motwani, J. D. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket analysis. SIGMOD'97, 255-264, Tucson, Arizona, May 1997. K. Beyer and R. Ramakrishnan. Bottom-up computation of sparse and iceberg cubes. SIGMOD'99, 359-370, Philadelphia, PA, June 1999. D.W. Cheung, J. Han, V. Ng, and C.Y. Wong. Maintenance of discovered association rules in large databases: An incremental updating technique. ICDE'96, 106-114, New Orleans, LA. M. Fang, N. Shivakumar, H. Garcia-Molina, R. Motwani, and J. D. Ullman. Computing iceberg queries efficiently. VLDB'98, 299-310, New York, NY, Aug. 1998.

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264 References (2) G. Grahne, L. Lakshmanan, and X. Wang. Efficient mining of constrained correlated sets. ICDE'00, 512-521, San Diego, CA, Feb. 2000. Y. Fu and J. Han. Meta-rule-guided mining of association rules in relational databases. KDOOD'95, 39-46, Singapore, Dec. 1995. T. Fukuda, Y. Morimoto, S. Morishita, and T. Tokuyama. Data mining using two-dimensional optimized association rules: Scheme, algorithms, and visualization. SIGMOD'96, 13-23, Montreal, Canada. E.-H. Han, G. Karypis, and V. Kumar. Scalable parallel data mining for association rules. SIGMOD'97, 277-288, Tucson, Arizona. J. Han, G. Dong, and Y. Yin. Efficient mining of partial periodic patterns in time series database. ICDE'99, Sydney, Australia. J. Han and Y. Fu. Discovery of multiple-level association rules from large databases. VLDB'95, 420-431, Zurich, Switzerland. J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. SIGMOD'00, 1-12, Dallas, TX, May 2000. T. Imielinski and H. Mannila. A database perspective on knowledge discovery. Communications of ACM, 39:58- 64, 1996. M. Kamber, J. Han, and J. Y. Chiang. Metarule-guided mining of multi-dimensional association rules using data cubes. KDD'97, 207-210, Newport Beach, California. M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, and A.I. Verkamo. Finding interesting rules from large sets of discovered association rules. CIKM'94, 401-408, Gaithersburg, Maryland.

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265 References (3) F. Korn, A. Labrinidis, Y. Kotidis, and C. Faloutsos. Ratio rules: A new paradigm for fast, quantifiable data mining. VLDB'98, 582-593, New York, NY. B. Lent, A. Swami, and J. Widom. Clustering association rules. ICDE'97, 220-231, Birmingham, England. H. Lu, J. Han, and L. Feng. Stock movement and n-dimensional inter-transaction association rules. SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery (DMKD'98), 12:1-12:7, Seattle, Washington. H. Mannila, H. Toivonen, and A. I. Verkamo. Efficient algorithms for discovering association rules. KDD'94, 181-192, Seattle, WA, July 1994. H. Mannila, H Toivonen, and A. I. Verkamo. Discovery of frequent episodes in event sequences. Data Mining and Knowledge Discovery, 1:259-289, 1997. R. Meo, G. Psaila, and S. Ceri. A new SQL-like operator for mining association rules. VLDB'96, 122-133, Bombay, India. R.J. Miller and Y. Yang. Association rules over interval data. SIGMOD'97, 452-461, Tucson, Arizona. R. Ng, L. V. S. Lakshmanan, J. Han, and A. Pang. Exploratory mining and pruning optimizations of constrained associations rules. SIGMOD'98, 13-24, Seattle, Washington. N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Discovering frequent closed itemsets for association rules. ICDT'99, 398-416, Jerusalem, Israel, Jan. 1999.

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266 References (4) J.S. Park, M.S. Chen, and P.S. Yu. An effective hash-based algorithm for mining association rules. SIGMOD'95, 175-186, San Jose, CA, May 1995. J. Pei, J. Han, and R. Mao. CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets. DMKD'00, Dallas, TX, 11-20, May 2000. J. Pei and J. Han. Can We Push More Constraints into Frequent Pattern Mining? KDD'00. Boston, MA. Aug. 2000. G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatetsky-Shapiro and W. J. Frawley, editors, Knowledge Discovery in Databases, 229-238. AAAI/MIT Press, 1991. B. Ozden, S. Ramaswamy, and A. Silberschatz. Cyclic association rules. ICDE'98, 412-421, Orlando, FL. J.S. Park, M.S. Chen, and P.S. Yu. An effective hash-based algorithm for mining association rules. SIGMOD'95, 175-186, San Jose, CA. S. Ramaswamy, S. Mahajan, and A. Silberschatz. On the discovery of interesting patterns in association rules. VLDB'98, 368-379, New York, NY.. S. Sarawagi, S. Thomas, and R. Agrawal. Integrating association rule mining with relational database systems: Alternatives and implications. SIGMOD'98, 343-354, Seattle, WA. A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association rules in large databases. VLDB'95, 432-443, Zurich, Switzerland. A. Savasere, E. Omiecinski, and S. Navathe. Mining for strong negative associations in a large database of customer transactions. ICDE'98, 494-502, Orlando, FL, Feb. 1998.

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267 References (5) C. Silverstein, S. Brin, R. Motwani, and J. Ullman. Scalable techniques for mining causal structures. VLDB'98, 594-605, New York, NY. R. Srikant and R. Agrawal. Mining generalized association rules. VLDB'95, 407-419, Zurich, Switzerland, Sept. 1995. R. Srikant and R. Agrawal. Mining quantitative association rules in large relational tables. SIGMOD'96, 1- 12, Montreal, Canada. R. Srikant, Q. Vu, and R. Agrawal. Mining association rules with item constraints. KDD'97, 67-73, Newport Beach, California. H. Toivonen. Sampling large databases for association rules. VLDB'96, 134-145, Bombay, India, Sept. 1996. D. Tsur, J. D. Ullman, S. Abitboul, C. Clifton, R. Motwani, and S. Nestorov. Query flocks: A generalization of association-rule mining. SIGMOD'98, 1-12, Seattle, Washington. K. Yoda, T. Fukuda, Y. Morimoto, S. Morishita, and T. Tokuyama. Computing optimized rectilinear regions for association rules. KDD'97, 96-103, Newport Beach, CA, Aug. 1997. M. J. Zaki, S. Parthasarathy, M. Ogihara, and W. Li. Parallel algorithm for discovery of association rules. Data Mining and Knowledge Discovery, 1:343-374, 1997. M. Zaki. Generating Non-Redundant Association Rules. KDD'00. Boston, MA. Aug. 2000. O. R. Zaiane, J. Han, and H. Zhu. Mining Recurrent Items in Multimedia with Progressive Resolution Refinement. ICDE'00, 461-470, San Diego, CA, Feb. 2000.

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268 http://www.cs.sfu.ca/~han/dmbook Thank you !!!

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Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 7 — ©Jiawei Han and Micheline Kamber Intelligent Database Systems Research Lab School of Computing Science Simon Fraser University, Canada http://www.cs.sfu.ca

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271 Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by backpropagation Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

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272 Classification: predicts categorical class labels classifies data (constructs a model) based on the training set and the values (class labels) in a classifying attribute and uses it in classifying new data Prediction: models continuous-valued functions, i.e., predicts unknown or missing values Typical Applications credit approval target marketing medical diagnosis treatment effectiveness analysis Classification vs. Prediction

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273 Classification—A Two-Step Process Model construction: describing a set of predetermined classes Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute The set of tuples used for model construction: training set The model is represented as classification rules, decision trees, or mathematical formulae Model usage: for classifying future or unknown objects Estimate accuracy of the model The known label of test sample is compared with the classified result from the model Accuracy rate is the percentage of test set samples that are correctly classified by the model Test set is independent of training set, otherwise over-fitting will occur

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274 Classification Process (1): Model Construction Training Data Classification Algorithms IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’ Classifier (Model)

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275 Classification Process (2): Use the Model in Prediction Classifier Testing Data Unseen Data (Jeff, Professor, 4) Tenured?

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276 Supervised vs. Unsupervised Learning Supervised learning (classification) Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations New data is classified based on the training set Unsupervised learning (clustering) The class labels of training data is unknown Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data

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277 Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by backpropagation Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

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278 Issues regarding classification and prediction (1): Data Preparation Data cleaning Preprocess data in order to reduce noise and handle missing values Relevance analysis (feature selection) Remove the irrelevant or redundant attributes Data transformation Generalize and/or normalize data

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279 Issues regarding classification and prediction (2): Evaluating Classification Methods Predictive accuracy Speed and scalability time to construct the model time to use the model Robustness handling noise and missing values Scalability efficiency in disk-resident databases Interpretability: understanding and insight provded by the model Goodness of rules decision tree size compactness of classification rules

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280 Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by backpropagation Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

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281 Classification by Decision Tree Induction Decision tree A flow-chart-like tree structure Internal node denotes a test on an attribute Branch represents an outcome of the test Leaf nodes represent class labels or class distribution Decision tree generation consists of two phases Tree construction At start, all the training examples are at the root Partition examples recursively based on selected attributes Tree pruning Identify and remove branches that reflect noise or outliers Use of decision tree: Classifying an unknown sample Test the attribute values of the sample against the decision tree

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282 Training Dataset This follows an example from Quinlan’s ID3

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283 Output: A Decision Tree for “buys_computer” age? overcast student?credit rating? noyes fair excellent <=30 >40 no yes 30..40

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284 Algorithm for Decision Tree Induction Basic algorithm (a greedy algorithm) Tree is constructed in a top-down recursive divide-and-conquer manner At start, all the training examples are at the root Attributes are categorical (if continuous-valued, they are discretized in advance) Examples are partitioned recursively based on selected attributes Test attributes are selected on the basis of a heuristic or statistical measure (e.g., information gain) Conditions for stopping partitioning All samples for a given node belong to the same class There are no remaining attributes for further partitioning – majority voting is employed for classifying the leaf There are no samples left

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285 Attribute Selection Measure Information gain (ID3/C4.5) All attributes are assumed to be categorical Can be modified for continuous-valued attributes Gini index (IBM IntelligentMiner) All attributes are assumed continuous-valued Assume there exist several possible split values for each attribute May need other tools, such as clustering, to get the possible split values Can be modified for categorical attributes

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286 Information Gain (ID3/C4.5) Select the attribute with the highest information gain Assume there are two classes, P and N Let the set of examples S contain p elements of class P and n elements of class N The amount of information, needed to decide if an arbitrary example in S belongs to P or N is defined as

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287 Information Gain in Decision Tree Induction Assume that using attribute A a set S will be partitioned into sets {S 1, S 2, …, S v } If S i contains p i examples of P and n i examples of N, the entropy, or the expected information needed to classify objects in all subtrees S i is The encoding information that would be gained by branching on A

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288 Attribute Selection by Information Gain Computation Class P: buys_computer = “yes” Class N: buys_computer = “no” I(p, n) = I(9, 5) =0.940 Compute the entropy for age: Hence Similarly

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289 Gini Index (IBM IntelligentMiner) If a data set T contains examples from n classes, gini index, gini(T) is defined as where p j is the relative frequency of class j in T. If a data set T is split into two subsets T 1 and T 2 with sizes N 1 and N 2 respectively, the gini index of the split data contains examples from n classes, the gini index gini(T) is defined as The attribute provides the smallest gini split (T) is chosen to split the node (need to enumerate all possible splitting points for each attribute).

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290 Extracting Classification Rules from Trees Represent the knowledge in the form of IF-THEN rules One rule is created for each path from the root to a leaf Each attribute-value pair along a path forms a conjunction The leaf node holds the class prediction Rules are easier for humans to understand Example IF age = “<=30” AND student = “no” THEN buys_computer = “no” IF age = “<=30” AND student = “yes” THEN buys_computer = “yes” IF age = “31…40” THEN buys_computer = “yes” IF age = “>40” AND credit_rating = “excellent” THEN buys_computer = “yes” IF age = “<=30” AND credit_rating = “fair” THEN buys_computer = “no”

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291 Avoid Overfitting in Classification The generated tree may overfit the training data Too many branches, some may reflect anomalies due to noise or outliers Result is in poor accuracy for unseen samples Two approaches to avoid overfitting Prepruning: Halt tree construction early—do not split a node if this would result in the goodness measure falling below a threshold Difficult to choose an appropriate threshold Postpruning: Remove branches from a “fully grown” tree—get a sequence of progressively pruned trees Use a set of data different from the training data to decide which is the “best pruned tree”

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292 Approaches to Determine the Final Tree Size Separate training (2/3) and testing (1/3) sets Use cross validation, e.g., 10-fold cross validation Use all the data for training but apply a statistical test (e.g., chi-square) to estimate whether expanding or pruning a node may improve the entire distribution Use minimum description length (MDL) principle: halting growth of the tree when the encoding is minimized

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293 Enhancements to basic decision tree induction Allow for continuous-valued attributes Dynamically define new discrete-valued attributes that partition the continuous attribute value into a discrete set of intervals Handle missing attribute values Assign the most common value of the attribute Assign probability to each of the possible values Attribute construction Create new attributes based on existing ones that are sparsely represented This reduces fragmentation, repetition, and replication

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294 Classification in Large Databases Classification—a classical problem extensively studied by statisticians and machine learning researchers Scalability: Classifying data sets with millions of examples and hundreds of attributes with reasonable speed Why decision tree induction in data mining? relatively faster learning speed (than other classification methods) convertible to simple and easy to understand classification rules can use SQL queries for accessing databases comparable classification accuracy with other methods

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295 Scalable Decision Tree Induction Methods in Data Mining Studies SLIQ (EDBT’96 — Mehta et al.) builds an index for each attribute and only class list and the current attribute list reside in memory SPRINT (VLDB’96 — J. Shafer et al.) constructs an attribute list data structure PUBLIC (VLDB’98 — Rastogi & Shim) integrates tree splitting and tree pruning: stop growing the tree earlier RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti) separates the scalability aspects from the criteria that determine the quality of the tree builds an AVC-list (attribute, value, class label)

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296 Data Cube-Based Decision-Tree Induction Integration of generalization with decision-tree induction (Kamber et al’97). Classification at primitive concept levels E.g., precise temperature, humidity, outlook, etc. Low-level concepts, scattered classes, bushy classification-trees Semantic interpretation problems. Cube-based multi-level classification Relevance analysis at multi-levels. Information-gain analysis with dimension + level.

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297 Presentation of Classification Results

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298 References (I) C. Apte and S. Weiss. Data mining with decision trees and decision rules. Future Generation Computer Systems, 13, 1997. L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Wadsworth International Group, 1984. P. K. Chan and S. J. Stolfo. Learning arbiter and combiner trees from partitioned data for scaling machine learning. In Proc. 1st Int. Conf. Knowledge Discovery and Data Mining (KDD'95), pages 39-44, Montreal, Canada, August 1995. U. M. Fayyad. Branching on attribute values in decision tree generation. In Proc. 1994 AAAI Conf., pages 601-606, AAAI Press, 1994. J. Gehrke, R. Ramakrishnan, and V. Ganti. Rainforest: A framework for fast decision tree construction of large datasets. In Proc. 1998 Int. Conf. Very Large Data Bases, pages 416-427, New York, NY, August 1998. M. Kamber, L. Winstone, W. Gong, S. Cheng, and J. Han. Generalization and decision tree induction: Efficient classification in data mining. In Proc. 1997 Int. Workshop Research Issues on Data Engineering (RIDE'97), pages 111-120, Birmingham, England, April 1997.

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299 References (II) J. Magidson. The Chaid approach to segmentation modeling: Chi-squared automatic interaction detection. In R. P. Bagozzi, editor, Advanced Methods of Marketing Research, pages 118-159. Blackwell Business, Cambridge Massechusetts, 1994. M. Mehta, R. Agrawal, and J. Rissanen. SLIQ : A fast scalable classifier for data mining. In Proc. 1996 Int. Conf. Extending Database Technology (EDBT'96), Avignon, France, March 1996. S. K. Murthy, Automatic Construction of Decision Trees from Data: A Multi-Diciplinary Survey, Data Mining and Knowledge Discovery 2(4): 345-389, 1998 J. R. Quinlan. Bagging, boosting, and c4.5. In Proc. 13th Natl. Conf. on Artificial Intelligence (AAAI'96), 725-730, Portland, OR, Aug. 1996. R. Rastogi and K. Shim. Public: A decision tree classifer that integrates building and pruning. In Proc. 1998 Int. Conf. Very Large Data Bases, 404-415, New York, NY, August 1998. J. Shafer, R. Agrawal, and M. Mehta. SPRINT : A scalable parallel classifier for data mining. In Proc. 1996 Int. Conf. Very Large Data Bases, 544-555, Bombay, India, Sept. 1996. S. M. Weiss and C. A. Kulikowski. Computer Systems that Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems. Morgan Kaufman, 1991.

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300 http://www.cs.sfu.ca/~han Thank you !!!

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August 18, 2009Data Mining: Concepts and Techniques 1 Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 4 — ©Jiawei Han and Micheline.

August 18, 2009Data Mining: Concepts and Techniques 1 Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 4 — ©Jiawei Han and Micheline.

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