Frequent Pattern Mining

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1 Frequent Pattern Mining

2 How Many Words Is a Picture Worth? E. Aiden and J-B Michel: Uncharted. Reverhead Books, 2013 Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 2

3 Burnt or Burned? E. Aiden and J-B Michel: Uncharted. Reverhead Books, 2013 Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 3

4 Store Layout Design Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 4

5 Transaction Data Alphabet: a set of items Example: all products sold in a store A transaction: a set of items involved in an activity Example: the items purchased by a customer in a visit Other information is often associated Timestamp, price, salesperson, customer-id, store-id, Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 5

6 Examples of Transaction Data Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 6

7 How to Store Transaction Data? Transaction-id (t123, a, b, c) (t236, b, d) Relational storage Transaction-based storage Item-based (vertical) storage Item a:, t123, Item b:, t123,, t236, Tid t123 t123 t123 t236 t236 Item a b c b d Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 7

8 Transaction Data Analysis Transactions: customers purchases of commodities {bread, milk, cheese} if they are bought together Frequent patterns: product combinations that are frequently purchased together by customers Frequent patterns: patterns (set of items, sequence, etc.) that occur frequently in a database [AIS93] Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 8

9 Why Frequent Patterns? What products were often purchased together? What are the frequent subsequent purchases after buying a ipod? What kinds of genes are sensitive to this new drug? What key-word combinations are frequently associated with web pages about gameevaluation? Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 9

10 Why Frequent Pattern Mining? Foundation for many data mining tasks Association rules, correlation, causality, sequential patterns, spatial and multimedia patterns, associative classification, cluster analysis, iceberg cube, Broad applications Basket data analysis, cross-marketing, catalog design, sale campaign analysis, web log (click stream) analysis, Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 10

11 Frequent Itemsets Itemset: a set of items E.g., acm = {a, c, m} Support of itemsets Sup(acm) = 3 Given min_sup = 3, acm is a frequent pattern Frequent pattern mining: finding all frequent patterns in a database Transaction database TDB TID Items bought 100 f, a, c, d, g, I, m, p 200 a, b, c, f, l, m, o 300 b, f, h, j, o 400 b, c, k, s, p 500 a, f, c, e, l, p, m, n Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 11

12 A Naïve Attempt Generate all possible itemsets, test their supports against the database How to hold a large number of itemsets into main memory? 100 items à possible itemets How to test the supports of a huge number of itemsets against a large database, say containing 100 million transactions? A transaction of length 20 needs to update the support of = 1,048,575 itemsets Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 12

13 Transactions in Real Applications A large department store often carries more than 100 thousand different kinds of items Amazon.com carries more than 17,000 books relevant to data mining Walmart has more than 20 million transactions per day, AT&T produces more than 275 million calls per day Mining large transaction databases of many items is a real demand Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 13

14 How to Get an Efficient Method? Reducing the number of itemsets that need to be checked Checking the supports of selected itemsets efficiently Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 14

15 Candidate Generation & Test Any subset of a frequent itemset must also be frequent an anti-monotonic property A transaction containing {beer, diaper, nuts} also contains {beer, diaper} {beer, diaper, nuts} is frequent à {beer, diaper} must also be frequent In other words, any superset of an infrequent itemset must also be infrequent No superset of any infrequent itemset should be generated or tested Many item combinations can be pruned! Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 15

16 Apriori-Based Mining Generate length (k+1) candidate itemsets from length k frequent itemsets, and Test the candidates against DB Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 16

17 The Apriori Algorithm [AgSr94] Data base D TID Items 10 a, c, d 20 b, c, e 30 a, b, c, e 40 b, e Min_sup=2 Scan D Scan D 3-candidates Itemset bce Freq 3-itemsets Itemset Sup bce 2 1-candidates Itemset Sup a 2 b 3 c 3 d 1 e 3 Freq 2-itemsets Itemset Sup ac 2 bc 2 be 3 ce 2 Freq 1-itemsets Itemset Sup a 2 b 3 c 3 e 3 Counting Itemset Sup ab 1 ac 2 ae 1 bc 2 be 3 ce 2 2-candidates Itemset ab ac ae bc be ce Scan D Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 17

18 The Apriori Algorithm Level-wise, candidate generation and test C k : Candidate itemset of size k L k : frequent itemset of size k Candidate generation L 1 = {frequent items}; for (k = 1; L k!= ; k++) do C k+1 = candidates generated from L k ; for each transaction t in database do increment the Test count of all candidates in C k+1 that are contained in t L k+1 = candidates in C k+1 with min_support return k L k ; Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 18

19 Important Steps in Apriori How to find frequent 1- and 2-itemsets? How to generate candidates? Step 1: self-joining L k Step 2: pruning How to count supports of candidates? Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 19

20 Finding Frequent 1- & 2-itemsets Finding frequent 1-itemsets (i.e., frequent items) using a one dimensional array Initialize c[item]=0 for each item For each transaction T, for each item in T, c[item]++; If c[item]>=min_sup, item is frequent Finding frequent 2-itemsets using a 2- dimensional triangle matrix For items i, j (i<j), c[i, j] is the count of itemset ij Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 20

21 Counting Array A 2-dimensional triangle matrix can be implemented using a 1-dimensional array There are n items For items i, j (i>j), c[i,j] = c[(i-1)(2n-i)/2+j-i]; Example: c[3,5] =c[(3-1)*(2*5-3)/ 2+5-3]=c[9] Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 21

22 Example of Candidate-generation L 3 = {abc, abd, acd, ace, bcd} Self-joining: L 3 *L 3 abcd ß abc * abd acde ß acd * ace Pruning: acde is removed because ade is not in L 3 C 4 ={abcd} Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 22

23 How to Generate Candidates? Suppose the items in L k-1 are listed in an order Step 1: self-join 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 For each itemset c in C k do For each (k-1)-subsets s of c do if (s is not in L k-1 ) then delete c from C k Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 23

24 How to Count Supports? Why is 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 A 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 Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 24

25 Example: Counting Supports Subset function 3,6,9 1,4,7 2,5, Transaction: Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 25

26 Association Rules Rule c à am Support: 3 (i.e., the support of acm) Confidence: 75% (i.e., sup(acm) / sup(c)) Given a minimum support threshold and a minimum confidence threshold, find all association rules whose support and confidence passing the thresholds Transaction database TDB TID Items bought 100 f, a, c, d, g, I, m, p 200 a, b, c, f, l, m, o 300 b, f, h, j, o 400 b, c, k, s, p 500 a, f, c, e, l, p, m, n Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 26

27 To-Do List Read Sections 6.1, and in the textbook Understand the concept of frequent itemsets and association rules Understand algorithm Apriori Figure out how to use Weka to mine frequent itemsets Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 27

28 For Thesis-based Students Only Find out in the source code of Weka how transaction data are stored If you are asked to implement Apriori in SQL, what is the major bottleneck? How can you overcome it or why it cannot be overcome? Jian Pei: CMPT 741/459 Frequent Pattern Mining (1) 28

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