1. Copyright Jiawei Han, modified by Charles Ling for CS411a
Course Outline
Introduction
Data warehousing and OLAP
Data preprocessing for mining and warehousing
Concept description: characterization and discrimination
Classification and prediction
Association analysis
Clustering analysis
Mining complex data and advanced mining techniques
Trends and research issues
Copyright Jiawei Han, modified by Charles Ling for CS411a

2. Data Mining and Warehousing: Session 7
Clustering Analysis
Copyright Jiawei Han, modified by Charles Ling for CS411a

3. Copyright Jiawei Han, modified by Charles Ling for CS411a
Clustering analysis
What is Clustering Analysis?
Clustering in Data Mining Applications
Handling Different Types of Variables
Major Clustering Techniques
Outlier Discovery
Problems and Challenges
Copyright Jiawei Han, modified by Charles Ling for CS411a

4. Copyright Jiawei Han, modified by Charles Ling for CS411a
What Is a Cluster?
a number of similar things growing together or of things or persons collected or grouped closely together: BUNCH
a group of buildings and esp. houses built close together on a sizable tract in order to preserve open spaces larger than the individual yard for common recreation
an aggregation of stars, galaxies, or super galaxies that appear close together in the sky and seem to have common properties (as distance)
Copyright Jiawei Han, modified by Charles Ling for CS411a

5. Copyright Jiawei Han, modified by Charles Ling for CS411a
What Is Clustering ?
Clustering is a process of partitioning a set of data (or objects) into a set of meaningful sub-classes, called clusters.
May help users understand the natural grouping or structure in a data set.
Cluster: a collection of data objects that are “similar” to one another and thus can be treated collectively as one group.
Clustering: unsupervised classification: no predefined classes.
Used either as a stand-alone tool to get insight into data distribution or as a preprocessing step for other algorithms.
Copyright Jiawei Han, modified by Charles Ling for CS411a

6. What Is Good Clustering?
A good clustering method will produce high quality clusters in which:
the intra-class (that is, intra-cluster) similarity is high.
the inter-class similarity is low.
The quality of a clustering result also depends on both the similarity measure used by the method and its implementation.
The quality of a clustering method is also measured by its ability to discover some or all of the hidden patterns.
Copyright Jiawei Han, modified by Charles Ling for CS411a

7. Requirements of Clustering in Data Mining
Scalability
Dealing with different types of attributes
Discovery of clusters with arbitrary shape
Able to deal with noise and outliers
Insensitive to order of input records
High dimensionality
Interpretability and usability.
Copyright Jiawei Han, modified by Charles Ling for CS411a

8. Copyright Jiawei Han, modified by Charles Ling for CS411a
Clustering analysis
What is Clustering Analysis?
Clustering in Data Mining Applications
Handling Different Types of Variables
Major Clustering Techniques
Outlier Discovery
Problems and Challenges
Copyright Jiawei Han, modified by Charles Ling for CS411a

9. Applications of Clustering
Clustering has wide applications in
Pattern Recognition
Spatial Data Analysis:
create thematic maps in GIS by clustering feature spaces
detect spatial clusters and explain them in spatial data mining.
Image Processing
Economic Science (especially market research)
WWW:
Document classification
Cluster Weblog data to discover groups of similar access patterns
Copyright Jiawei Han, modified by Charles Ling for CS411a

10. Examples of Clustering Applications
Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs.
Land use: Identification of areas of similar land use in an earth observation database.
Insurance: Identifying groups of motor insurance policy holders with a high average claim cost.
City-planning: Identifying groups of houses according to their house type, value, and geographical location.
Copyright Jiawei Han, modified by Charles Ling for CS411a

11. Copyright Jiawei Han, modified by Charles Ling for CS411a
Clustering analysis
What is Clustering Analysis?
Clustering in Data Mining Applications
Handling Different Types of Variables
Major Clustering Techniques
Outlier Discovery
Problems and Challenges
Copyright Jiawei Han, modified by Charles Ling for CS411a

12. Similarity and Dissimilarity Between Objects
Distances are normally used to measure the similarity or dissimilarity between two data objects.
Some popular ones include: Minkowski distance:
where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects, and q is a positive integer.
If q = 1, d is Manhattan distance.
If q = 2, d is Euclidean distance:
Copyright Jiawei Han, modified by Charles Ling for CS411a

13. Copyright Jiawei Han, modified by Charles Ling for CS411a
Measure Similarity
The definitions of distance functions are usually very different for interval-scaled, boolean, categorical, ordinal and ratio variables.
Values should be scaled (normalized to 0-1)
Weights should be associated with different variables based on applications and data semantics.
It is hard to define “similar enough” or “good enough”
the answer is typically highly subjective.
Copyright Jiawei Han, modified by Charles Ling for CS411a

14. Binary, Nominal, Continuous variables
Binary variable: d = 0 of x=y; d=0 otherwise
Nominal variables: > 2 states, e.g., red, yellow, blue, green.
Simple matching: u: # of matches, p: total # of variables.
Also, one can use a large number of binary variables.
Continuos variables: d = |x-y|
Scaling and normalization
Copyright Jiawei Han, modified by Charles Ling for CS411a

15. Copyright Jiawei Han, modified by Charles Ling for CS411a
Clustering analysis
What is Clustering Analysis?
Clustering in Data Mining Applications
Handling Different Types of Variables
Major Clustering Techniques
Outlier Discovery
Problems and Challenges
Copyright Jiawei Han, modified by Charles Ling for CS411a

16. Five Categories of Clustering Methods
Partitioning algorithms: Construct various partitions and then evaluate them by some criterion.
Hierarchy algorithms: Create a hierarchical decomposition of the set of data (or objects) using some criterion.
Density-based: based on connectivity and density functions
Grid-based: based on a multiple-level granularity structure
Model-based: A model is hypothesized for each of the clusters and the idea is to find the best fit of that model to each other.
Copyright Jiawei Han, modified by Charles Ling for CS411a

17. Partitioning Algorithms: Basic Concept
Partitioning method: Construct a partition of a database D of n objects into a set of k clusters
Given a k, find a partition of k clusters that optimizes the chosen partitioning criterion.
Global optimal: exhaustively enumerate all partitions.
Heuristic methods: k-means and k-medoids algorithms.
k-means (MacQueen’67): Each cluster is represented by the center of the cluster
k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster.
Copyright Jiawei Han, modified by Charles Ling for CS411a

18. The K-Means Clustering Method
Given k, the k-means algorithm is implemented in 4 steps:
Partition objects into k nonempty subsets
Compute seed points as the centroids of the clusters of the current partition. The centroid is the center (mean point) of the cluster.
Assign each object to the cluster with the nearest seed point.
Go back to Step 2, stop when no more new assignment.
Copyright Jiawei Han, modified by Charles Ling for CS411a

19. Comments on the K-Means Method
Strength of the k-means:
Relatively efficient: O(tkn), where n is # of objects, k is # of clusters, and t is # of iterations. Normally, k, t << n.
Often terminates at a local optimum.
Weakness of the k-means:
Applicable only when mean is defined, then what about categorical data?
Need to specify k, the number of clusters, in advance.
Unable to handle noisy data and outliers.
Not suitable to discover clusters with non-convex shapes.
Copyright Jiawei Han, modified by Charles Ling for CS411a

20. The K-Medoids Clustering Method
Find representative objects, called medoids, in clusters
To achieve this goal, only the definition of distance from any two objects is needed.
PAM (Partitioning Around Medoids, 1987)
starts from an initial set of medoids and iteratively replaces one of the medoids by one of the non-medoids if it improves the total distance of the resulting clustering.
PAM works effectively for small data sets, but does not scale well for large data sets.
Copyright Jiawei Han, modified by Charles Ling for CS411a

21. Two Types of Hierarchical Clustering Algorithms
Agglomerative (bottom-up): merge clusters iteratively.
start by placing each object in its own cluster
merge these atomic clusters into larger and larger clusters
until all objects are in a single cluster.
Most hierarchical methods belong to this category. They differ only in their definition of between-cluster similarity.
Divisive (top-down): split a cluster iteratively.
It does the reverse by starting with all objects in one cluster and subdividing them into smaller pieces.
Divisive methods are not generally available, and rarely have been applied.
Copyright Jiawei Han, modified by Charles Ling for CS411a

22. Hierarchical Clustering
Use distance matrix as clustering criteria. This method does not require the number of clusters k as an input, but needs a termination condition.
Step 0
Step 1
Step 2
Step 3
Step 4 b d c e a
a b
d e
c d e
a b c d e
agglomerative
(AGNES)
divisive
(DIANA)
Copyright Jiawei Han, modified by Charles Ling for CS411a

23. More on Hierarchical Clustering Methods
between-cluster similarity
Minimal distance
Maximal distance
Center distance
Major weakness of agglomerative clustering methods:
do not scale well: time complexity of at least O(n2), where n is the number of total objects
can never undo what was done previously.
Integration of hierarchical clustering with distance-based method:
Copyright Jiawei Han, modified by Charles Ling for CS411a

24. Copyright Jiawei Han, modified by Charles Ling for CS411a
Clustering analysis
What is Clustering Analysis?
Clustering in Data Mining Applications
Handling Different Types of Variables
Major Clustering Techniques
Outlier Discovery
Problems and Challenges
Copyright Jiawei Han, modified by Charles Ling for CS411a

25. What Is Outlier Discovery?
What are outliers?
The set of objects are considerably dissimilar from the remainder of the data
Example: Sports: Michael Jordon, Wayne Gretzky, ...
Problem
Given: Data points
Find top n outlier points
Applications:
Credit card fraud detection
Telecom fraud detection
Customer segmentation
Medical analysis
Copyright Jiawei Han, modified by Charles Ling for CS411a

26. Outlier Discovery Methods
Distance-based vs. statistics-based outlier analysis:
Most outlier analyses are univariate (single-var) and distribution-based (how do we know it is in a normal or gammar distribution?)
We need multi-dimensional analysis without knowing on data distribution.
Distance-based outlier:
An object O in a dataset T is a DB(p, D)-outlier if at least fraction p of the object in T lies greater than distance D from O.
Copyright Jiawei Han, modified by Charles Ling for CS411a

27. Copyright Jiawei Han, modified by Charles Ling for CS411a
Clustering analysis
What is Clustering Analysis?
Clustering in Data Mining Applications
Handling Different Types of Variables
Major Clustering Techniques
Outlier Discovery
Problems and Challenges
Copyright Jiawei Han, modified by Charles Ling for CS411a

28. Problems and Challenges
Considerable progress has been made in scalable clustering methods:
Partitioning: k-means, k-medoids, CLARANS
Hierarchical: BIRCH, CURE
Density-based: DBSCAN, CLIQUE, OPTICS
Grid-based: STING, WaveCluster.
Model-based: Autoclass, Denclue, Cobweb.
Current clustering techniques do not address all the requirements adequately.
Constraint-based clustering analysis: Constraints exists in data space (bridges and highways) or in user queries.
Copyright Jiawei Han, modified by Charles Ling for CS411a

29. Data Mining and Data Warehousing
Introduction
Data warehousing and OLAP
Data preprocessing for mining and warehousing
Concept description: characterization and discrimination
Classification and prediction
Association analysis
Clustering analysis
Mining complex data and advanced mining techniques
Trends and research issues
Copyright Jiawei Han, modified by Charles Ling for CS411a

30. Data Mining and Warehousing: Session 6
Association Analysis
Copyright Jiawei Han, modified by Charles Ling for CS411a

31. Session 6: Association Analysis
What is association analysis?
Mining single-dimensional Boolean association rules in transactional databases
Mining multi-level association rules
Copyright Jiawei Han, modified by Charles Ling for CS411a

32. What Is Association Mining?
Association rule mining:
Finding association, correlation, 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 ® Head [support, confidence]”.
buys(x, “diapers”) ® buys(x, “beers”) [0.5%, 60%]
major(x, “CS”) ^ takes(x, “DB”) ® grade(x, “A”) [1%, 75%]
Copyright Jiawei Han, modified by Charles Ling for CS411a

33. Session 6: Association Analysis
What is association analysis?
Mining single-dimensional Boolean association rules in transactional databases
Mining multi-level association rules
Copyright Jiawei Han, modified by Charles Ling for CS411a

34. What Is an Association Rule?
Given
A database of customer transactions
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
Example: 98% of people who purchase tires and auto accessories also get automotive services done
Any number of items in the consequent/antecedent of rule
Possible to specify constraints on rules (e.g., find only rules involving Home Laundry Appliances).
Copyright Jiawei Han, modified by Charles Ling for CS411a

35. Copyright Jiawei Han, modified by Charles Ling for CS411a
Application Examples
Market Basket Analysis
*  Maintenance Agreement
What the store should do to boost Maintenance Agreement sales
Home Electronics  *
What other products should the store stocks up on if the store has a sale on Home Electronics
Attached mailing in direct marketing
Detecting “ping-pong”ing of patients
transaction: patient
item: doctor/clinic visited by a patient
support of a rule: number of common patients
Copyright Jiawei Han, modified by Charles Ling for CS411a

36. Rule Measures: Support and Confidence
Customer
buys both
Customer
buys diaper
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.
Customer
buys beer
Let minimum support 50%, and minimum confidence 50%, we have
A  C (50%, 66.6%)
C  A (50%, 100%)
Copyright Jiawei Han, modified by Charles Ling for CS411a

37. Mining Association Rules -- Example
Min. support 50%
Min. confidence 50%
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.
Copyright Jiawei Han, modified by Charles Ling for CS411a

38. 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.
Copyright Jiawei Han, modified by Charles Ling for CS411a

39. Copyright Jiawei Han, modified by Charles Ling for CS411a
The Apriori Algorithm
Ck: Candidate itemset of size k
Lk : frequent itemset of size k
L1 = {frequent items};
for (k = 1; Lk !=; k++) do begin
Ck+1 = candidates generated from Lk;
for each transaction t in database do
increment the count of all candidates in Ck that are contained in t
Lk+1 = candidates in Ck+1 with min_support
end
return k Lk;
Copyright Jiawei Han, modified by Charles Ling for CS411a

40. The Apriori Algorithm -- Example
Database D L1 C1
Scan D C2 C2 L2
Scan D C3 L3
Scan D
Copyright Jiawei Han, modified by Charles Ling for CS411a

41. Generating Association Rules
A Naive Algorithm
for each frequent itemset F do
for each subset c of F do
if ( support(F)/support(F-c)  minconf ) then
output rule (F-c)  c,
with confidence = support(F)/support (F-c)
and support = support(F)
Copyright Jiawei Han, modified by Charles Ling for CS411a

42. Session 6: Association Analysis
What is association analysis?
Mining single-dimensional Boolean association rules in transactional databases
Mining multi-level association rules
Copyright Jiawei Han, modified by Charles Ling for CS411a

43. Multiple-Level Association Rules
Food
bread
milk
skim
Sunset
Fraser 2%
white
wheat
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
It is smart to explore shared multi-level mining (Han & Fu,VLDB’95).
Copyright Jiawei Han, modified by Charles Ling for CS411a

44. 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
Copyright Jiawei Han, modified by Charles Ling for CS411a

45. 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.
Copyright Jiawei Han, modified by Charles Ling for CS411a