AssociationRule.pdf

AssociationRule.pdf

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  Association Analysis UE 141Spring 2013 1 Jing Gao SUNY Buffalo
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  Association Rule Mining •Given a set of transactions, find rules that will predict the occurrence of an item based on the occurrences of other items in the transaction Market-Basket transactions TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke Example of Association Rules {Diaper}  {Beer}, {Milk, Bread}  {Eggs,Coke}, {Beer, Bread}  {Milk}, Implication means co-occurrence, not causality!
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  Definition: Frequent Itemset •Itemset – A collection of one or more items • Example: {Milk, Bread, Diaper} – k-itemset • An itemset that contains k items • Support count () – Frequency of occurrence of an itemset – E.g. ({Milk, Bread,Diaper}) = 2 • Support – Fraction of transactions that contain an itemset – E.g. s({Milk, Bread, Diaper}) = 2/5 • Frequent Itemset – An itemset whose support is greater than or equal to a minsup threshold TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke
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  Definition: Association Rule Example: Beer } Diaper , Milk { 4 . 0 5 2 | T | ) Beer Diaper, , Milk (     s 67 . 0 3 2 ) Diaper , Milk ( ) Beer Diaper, Milk, (      c  Association Rule – An implication expression of the form X  Y, where X and Y are itemsets – Example: {Milk, Diaper}  {Beer}  Rule Evaluation Metrics – Support (s)  Fraction of transactions that contain both X and Y – Confidence (c)  Measures how often items in Y appear in transactions that contain X TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke
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  Association Rule MiningTask • Given a set of transactions T, the goal of association rule mining is to find all rules having – support ≥ minsup threshold – confidence ≥ minconf threshold • Brute-force approach: – List all possible association rules – Compute the support and confidence for each rule – Prune rules that fail the minsup and minconf thresholds  Computationally prohibitive!
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  Mining Association Rules Exampleof Rules: {Milk,Diaper}  {Beer} (s=0.4, c=0.67) {Milk,Beer}  {Diaper} (s=0.4, c=1.0) {Diaper,Beer}  {Milk} (s=0.4, c=0.67) {Beer}  {Milk,Diaper} (s=0.4, c=0.67) {Diaper}  {Milk,Beer} (s=0.4, c=0.5) {Milk}  {Diaper,Beer} (s=0.4, c=0.5) TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke Observations: • All the above rules are binary partitions of the same itemset: {Milk, Diaper, Beer} • Rules originating from the same itemset have identical support but can have different confidence • Thus, we may decouple the support and confidence requirements
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  Mining Association Rules •Two-step approach: 1. Frequent Itemset Generation – Generate all itemsets whose support  minsup 2. Rule Generation – Generate high confidence rules from each frequent itemset, where each rule is a binary partitioning of a frequent itemset • Frequent itemset generation is still computationally expensive
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  Frequent Itemset Generation null ABAC AD AE BC BD BE CD CE DE A B C D E ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE ABCD ABCE ABDE ACDE BCDE ABCDE Given d items, there are 2d possible candidate itemsets
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  Frequent Itemset Generation •Brute-force approach: – Each itemset in the lattice is a candidate frequent itemset – Count the support of each candidate by scanning the database – Match each transaction against every candidate TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke N Transactions List of Candidates M w
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  Reducing Number ofCandidates • Apriori principle: – If an itemset is frequent, then all of its subsets must also be frequent • Apriori principle holds due to the following property of the support measure: – Support of an itemset never exceeds the support of its subsets – This is known as the anti-monotone property of support ) ( ) ( ) ( : , Y s X s Y X Y X    
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  Found to be Infrequent null ABAC AD AE BC BD BE CD CE DE A B C D E ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE ABCD ABCE ABDE ACDE BCDE ABCDE Illustrating Apriori Principle null AB AC AD AE BC BD BE CD CE DE A B C D E ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE ABCD ABCE ABDE ACDE BCDE ABCDE Pruned supersets
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  12 The Apriori Algorithm—AnExample Database TDB 1st scan C1 L1 L2 C2 C2 2nd scan C3 L3 3rd scan Tid Items 10 A, C, D 20 B, C, E 30 A, B, C, E 40 B, E Itemset sup {A} 2 {B} 3 {C} 3 {D} 1 {E} 3 Itemset sup {A} 2 {B} 3 {C} 3 {E} 3 Itemset {A, B} {A, C} {A, E} {B, C} {B, E} {C, E} Itemset sup {A, B} 1 {A, C} 2 {A, E} 1 {B, C} 2 {B, E} 3 {C, E} 2 Itemset sup {A, C} 2 {B, C} 2 {B, E} 3 {C, E} 2 Itemset {B, C, E} Itemset sup {B, C, E} 2 Supmin = 2
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  Mining Association Rulesfrom Record Data Session Id Country Session Length (sec) Number of Web Pages viewed Gender Browser Type Buy 1 USA 982 8 Male IE No 2 China 811 10 Female Chrome No 3 USA 2125 45 Female Mozilla Yes 4 Germany 596 4 Male IE Yes 5 Australia 123 9 Male Mozilla No … … … … … … … 10 Example of Association Rule: {Number of Pages [5,10)  (Browser=Mozilla)}  {Buy = No} How to apply association analysis formulation to record data?
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  Handling Categorical Attributes •Transform categorical attribute into binary variables • Introduce a new “item” for each distinct attribute-value pair – Example: replace Browser Type attribute with • Browser Type = Internet Explorer • Browser Type = Mozilla • Browser Type = Chrome
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  Handling Categorical Attributes •Potential Issues – What if attribute has many possible values • Example: attribute country has more than 200 possible values • Many of the attribute values may have very low support – Potential solution: Aggregate the low-support attribute values – What if distribution of attribute values is highly skewed • Example: 95% of the visitors have Buy = No • Most of the items will be associated with (Buy=No) item – Potential solution: drop the highly frequent items
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  Handling Continuous Attributes •Different kinds of rules: – Age[21,35)  Salary[70k,120k)  Buy – Salary[70k,120k)  Buy  Age: =28, =4 • Different methods: – Discretization-based – Statistics-based
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  Question • Will associationanalysis help Wal-mart? – Start with the “beer and diaper” story – Discuss possible benefits and challenges in using association analysis for supermarkets 17