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**Data Mining Techniques Association Rule**

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**What Is Association Mining?**

Association Rule Mining Finding frequent patterns, associations, correlations, or causal structures among item sets in transaction databases, relational databases, and other information repositories Applications Market basket analysis (marketing strategy: items to put on sale at reduced prices), cross-marketing, catalog design, shelf space layout design, etc Examples Rule form: Body ® Head [Support, Confidence]. buys(x, “Computer”) ® buys(x, “Software”) [2%, 60%] major(x, “CS”) ^ takes(x, “DB”) ® grade(x, “A”) [1%, 75%]

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**Market Basket Analysis**

Typically, association rules are considered interesting if they satisfy both a minimum support threshold and a minimum confidence threshold.

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**Rule Measures: Support and Confidence**

Let minimum support 50%, and minimum confidence 50%, we have A C [50%, 66.6%] C A [50%, 100%]

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Support & Confidence

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**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 Find all the rules A B with minimum confidence and support support, s, P(A B) confidence, c, P(B|A)

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**Terminologies Item Itemset 1-Itemset 2-Itemset I1, I2, I3, …**

A, B, C, … Itemset {I1}, {I1, I7}, {I2, I3, I5}, … {A}, {A, G}, {B, C, E}, … 1-Itemset {I1}, {I2}, {A}, … 2-Itemset {I1, I7}, {I3, I5}, {A, G}, …

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**Terminologies K-Itemset Frequent (Large) K-Itemset Association Rule**

If the length of the itemset is K Frequent (Large) K-Itemset If the length of the itemset is K and the itemset satisfies a minimum support threshold. Association Rule If a rule satisfies both a minimum support threshold and a minimum confidence threshold

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Analysis The number of itemsets of a given cardinality tends to grow exponentially

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**Fast Algorithms for Mining Association Rules**

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**Mining Association Rules: Apriori Principle**

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

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**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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**Example Database D 1 3 4 2 3 5 1 2 3 5 2 5 scan D count C1 C1 count**

2 5 scan D count C1 C1 count generate L1 L1 1 2 3 5 scan D count C2 C2 count generate L2 L2 13 23 25 35 C2 12 15 generate C2 scan D count C3 C3 count generate L3 L3 235 C3 generate C3

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**Example of Generating Candidates**

L3={abc, abd, acd, ace, bcd} Self-joining: L3*L3 abcd from abc and abd acde from acd and ace Pruning: acde is removed because ade is not in L3 C4={abcd}

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Example

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Apriori Algorithm

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Apriori Algorithm

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Apriori Algorithm

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Exercise 4 min-sup = 20% min-conf = 80%

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**Demo-IBM Intelligent Minner**

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Demo Database

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**Multi-Dimensional Association**

Single-Dimensional (Intra-Dimension) Rules: Single Dimension (Predicate) with Multiple Occurrences. buys(X, “milk”) buys(X, “bread”) Multi-Dimensional Rules: 2 Dimensions 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 (Nominal) Attributes finite number of possible values, no ordering among values Quantitative Attributes numeric, implicit ordering among values

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Exercise 5 min-sup = 20% min-conf = 80%

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**Research Topics Quantitative Association Rules**

buys (bread, 5) ® buys (milk, 3) Weighted Association Rules High Utility Association Rules Non-redundant Association Rule Constrained Association Rules Mining Multi-dimensional Association Rules Generalized Association Rules Negative Association Rules Incremental Mining Association Rules Data Stream Association Rule Mining Interactive Mining Association Rules

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LOGO Association Rule Lecturer: Dr. Bo Yuan

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