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CSE 634 Data Mining Concepts and Techniques Association Rule Mining

CSE 634 Data Mining Concepts and Techniques Association Rule Mining

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CSE 634 Data Mining Concepts and Techniques Association Rule Mining

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  1. CSE 634Data Mining Concepts and TechniquesAssociation Rule Mining Barbara Mucha Tania Irani Irem Incekoy Mikhail Bautin Course Instructor: Prof. Anita Wasilewska State University of New York, Stony Brook Group 6

  2. References • Data Mining: Concepts & Techniques by Jiawei Han and Micheline Kamber • Presentation Slides of Prateek Duble • Presentation Slides of the Course Book. • Mining Topic-Specific Concepts and Definitions on the Web • Effective Personalization Based on Association Rule Discovery from Web Usage Data

  3. Overview • Basic Concepts of Association Rule Mining • Association & Apriori Algorithm • Paper: Mining Topic-Specific Concepts and Definitions on the Web • Paper: Effective Personalization Based on Association Rule Discovery from Web Usage Data Barbara Mucha

  4. Outline • What is association rule mining? • Methods for association rule mining • Examples • Extensions of association rule Barbara Mucha

  5. What Is Association Rule Mining? • Frequent patterns: patterns (set of items, sequence, etc.) that occur frequently in a database • Frequent pattern mining: finding regularities in data • What products were often purchased together? • Beer and diapers?! • What are the subsequent purchases after buying a car? • Can we automatically profile customers? Barbara Mucha

  6. Basic Concepts of Association Rule Mining • 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 • * MaintenanceAgreement (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 Barbara Mucha

  7. Association Rule Definitions • Set of items: I={I1,I2,…,Im} • Transactions:D = {t1, t2,.., tn} be a set of transactions, where a transaction,t, is a set of items • Itemset: {Ii1,Ii2, …, Iik}  I • Support of an itemset: Percentage of transactions which contain that itemset. • Large (Frequent) itemset: Itemset whose number of occurrences is above a threshold. Barbara Mucha

  8. Rule Measures: Support & Confidence • An association rule is of the form : X  Y where X, Y are subsets of I, and X INTERSECT Y = EMPTY • Each rule has two measures of value, support, and confidence. • Support indicates the frequencies of the occurring patterns, and confidence denotes the strength of implication in the rule. • The support of the rule X  Y is support (X UNION Y) c is the CONFIDENCE of rule X  Y if c% of transactions that contain X also contain Y, which can be written as the radio: • support(X UNION Y)/support(X) Barbara Mucha

  9. Support & Confidence : An Example Let minimum support 50%, and minimum confidence 50%, then we have, • A  C (50%, 66.6%) • C  A (50%, 100%) Barbara Mucha

  10. Types of Association Rule Mining • Boolean vs. quantitative associations (Based on the types of values handled) • buys(x, “computer”)  buys(x, “financial software”) [.2%, 60%] • age(x, “30..39”) ^ income(x, “42..48K”) buys(x, “PC”) [1%, 75%] • Single dimension vs. multiple dimensional associations • buys(x, “computer”)  buys(x, “financial software”) [.2%, 60%] • age(x, “30..39”) ^ income(x, “42..48K”) buys(x, “PC”) [1%, 75%] Barbara Mucha

  11. Types of Association Rule Mining • 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 • Constraints enforced • E.g., small sales (sum < 100) trigger big buys (sum > 1,000)? Barbara Mucha

  12. Association Discovery • Given a user specified minimum support (called MINSUP) and minimum confidence (called MINCONF), an important • PROBLEM is to find all high confidence, large itemsets (frequent sets, sets with high support). (where support and confidence are larger than minsup and minconf). • This problem can be decomposed into two subproblems: • 1. Find all large itemsets: with support > minsup (frequent sets). • 2. For a large itemset, X and B X (or YX) , find those rules, X\{B} => B ( X-Y  Y) for which confidence > minconf. Barbara Mucha

  13. Basics • 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: find all frequent patterns in a database Transaction database TDB Barbara Mucha

  14. Mining Association Rules—An 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

  15. Rules from frequent sets • X = {mustard, sausage, beer}; frequency = 0.4 • Y = {mustard, sausage, beer, chips}; frequency = 0.2 • If the customer buys mustard, sausage, and beer, then the probability that he/she buys chips is 0.5 Barbara Mucha

  16. Applications • Mine: • Sequential patterns • find inter-transaction patterns such that the presence of a set of items is followed by another item in the time-stamp ordered transaction set. • Periodic patterns • It can be envisioned as a tool for forecasting and prediction of the future behavior of time-series data. • Structural Patterns • Structural patterns describe how classes and objects can be combined to form larger structures. Barbara Mucha

  17. Application Difficulties • Wal-Mart knows that customers who buy Barbie dolls have a 60% likelihood of buying one of three types of candy bars. • What does Wal-Mart do with information like that? 'I don't have a clue,' says Wal-Mart's chief of merchandising, Lee Scott www.kdnuggets.com/news/98/n01.html • Diapers and beer urban legend http://web.onetel.net.uk/~hibou/Beer%20and%20Nappies.html Barbara Mucha

  18. Thank You! Barbara Mucha

  19. CSE 634Data Mining Concepts and Techniques Association & Apriori Algorithm Tania Irani (105573836) Course Instructor: Prof. Anita Wasilewska State University of New York, Stony Brook

  20. References • Data Mining: Concepts & Techniques by Jiawei Han and Micheline Kamber • Presentation Slides of Prof. Anita Wasilewska

  21. Agenda • The Apriori Algorithm (Mining single-dimensional boolean association rules) • Frequent-Pattern Growth (FP-Growth) Method • Summary

  22. The Apriori Algorithm: Key Concepts • K-itemsets: An itemset having k items in it. • Support or Frequency: Number of transactions that contain a particular itemset. • Frequent Itemsets: An itemset that satisfies minimum support. (denoted by Lk for frequent k-itemset). • Apriori Property: All non-empty subsets of a frequent itemset must be frequent. • Join Operation: Ck, the set of candidate k-itemsets is generated by joining Lk-1 with itself. (L1: frequent 1-itemset, Lk: frequent k-itemset) • Prune Operation: Lk, the set of frequent k-itemsets is extracted from Ck by pruning it – getting rid of all the non-frequent k-itemsets in Ck Iterative level-wise approach: k-itemsets used to explore (k+1)-itemsets. The Apriori Algorithm finds frequent k-itemsets.

  23. How is the Apriori Property used in the Algorithm? • Mining single-dimensional Boolean association rules is a 2 step process: • Using the Apriori Property find the frequent itemsets: • Each iteration will generate Ck (candidate k-itemsets from Ck-1) and Lk (frequent k-itemsets) • Use the frequent k-itemsets to generate association rules.

  24. Finding frequent itemsets using the Apriori Algorithm: Example • Consider a database D, consisting of 9 transactions. • Each transaction is represented by an itemset. • Suppose min. support required is 2 (2 out of 9 = 2/9 =22 % ) • Say min. confidence required is 70%. • We have to first find out the frequent itemset using Apriori Algorithm. • Then, Association rules will be generated using min. support & min. confidence.

  25. Step 1: Generating candidate and frequent 1-itemsets with min. support = 2 Compare candidate support count with minimum support count Scan D for count of each candidate C1 L1 • In the first iteration of the algorithm, each item is a member of the set of candidates Ck along with its support count. • The set of frequent 1-itemsets L1, consists of the candidate 1-itemsets satisfying minimum support.

  26. Step 2: Generating candidate and frequent 2-itemsets with min. support = 2 Compare candidate support count with minimum support count Generate C2 candidates from L1 x L1 Scan D for count of each candidate L2 Note: We haven’t used Apriori Property yet! C2 C2

  27. Step 3: Generating candidate and frequent 3-itemsets with min. support = 2 Compare candidate support count with min support count Generate C3 candidates from L2 Scan D for count of each candidate L3 C3 Contains non-frequent (2-itemset) subsets C3 • The generation of the set of candidate 3-itemsets C3, involves use of the Apriori Property. • When Join step is complete, the Prune step will be used to reduce the size of C3. Prune step helps to avoid heavy computation due to large Ck.

  28. Step 4: Generating frequent 4-itemset • L3 Join L3C4 = {{I1, I2, I3, I5}} • This itemset is pruned since its subset {{I2, I3, I5}} is not frequent. • Thus, C4 = φ, and the algorithm terminates, having found all of the frequent items. • This completes our Apriori Algorithm. What’s Next ? • These frequent itemsets will be used to generate strong association rules (where strong association rules satisfy both minimum support & minimum confidence).

  29. Step 5: Generating Association Rules from frequent k-itemsets • Procedure: • For each frequent itemset l, generate all nonempty subsets of l • For every nonempty subset s of l, output the rule “s (l - s)” if support_count(l) / support_count(s) ≥ min_conf where min_conf is minimum confidence threshold. 70% in our case. • Back To Example: • Lets take l = {I1,I2,I5} • The nonempty subsets of Lets take l are {I1,I2}, {I1,I5}, {I2,I5}, {I1}, {I2}, {I5}

  30. Step 5: Generating Association Rules from frequent k-itemsets [Cont.] • The resulting association rules are: • R1: I1 ^ I2  I5 • Confidence = sc{I1,I2,I5} / sc{I1,I2} = 2/4 = 50% • R1 is Rejected. • R2: I1 ^ I5  I2 • Confidence = sc{I1,I2,I5} / sc{I1,I5} = 2/2 = 100% • R2 is Selected. • R3: I2 ^ I5  I1 • Confidence = sc{I1,I2,I5} / sc{I2,I5} = 2/2 = 100% • R3 is Selected.

  31. Step 5: Generating Association Rules from Frequent Itemsets [Cont.] • R4: I1  I2 ^ I5 • Confidence = sc{I1,I2,I5} / sc{I1} = 2/6 = 33% • R4 is Rejected. • R5: I2  I1 ^ I5 • Confidence = sc{I1,I2,I5} / {I2} = 2/7 = 29% • R5 is Rejected. • R6: I5  I1 ^ I2 • Confidence = sc{I1,I2,I5} / {I5} = 2/2 = 100% • R6 is Selected. We have found three strong association rules.

  32. Agenda • The Apriori Algorithm (Mining single dimensional boolean association rules) • Frequent-Pattern Growth (FP-Growth) Method • Summary

  33. 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: • Compress DB into FP-tree, retain itemset associations • Divide the new DB into a set of conditional DBs – each associated with one frequent item • Mine each such database seperately • Avoid candidate generation

  34. FP-Growth Method : An Example • Consider the previous example of a database D, consisting of 9 transactions. • Suppose min. support count required is 2 (i.e. min_sup = 2/9 = 22 % ) • The first scan of the database is same as Apriori, which derives the set of 1-itemsets & their support counts. • The set of frequent items is sorted in the order of descending support count. • The resulting set is denoted as L = {I2:7, I1:6, I3:6, I4:2, I5:2}

  35. FP-Growth Method: Construction of FP-Tree • First, create the root of the tree, labeled with “null”. • Scan the database D a second time (First time we scanned it to create 1-itemset and then L), this will generate the complete tree. • The items in each transaction are processed in L order (i.e. sorted order). • A branch is created for each transaction with items having their support count separated by colon. • Whenever the same node is encountered in another transaction, we just increment the support count of the common node or Prefix. • To facilitate tree traversal, an item header table is built so that each item points to its occurrences in the tree via a chain of node-links. • Now, The problem of mining frequent patterns in database is transformed to that of mining the FP-Tree.

  36. FP-Growth Method: Construction of FP-Tree null{} I2:7 I1:2 I1:4 I4:1 I3:2 I3:2 An FP-Tree that registers compressed, frequent pattern information I3:2 I4:1 I5:1 I5:1

  37. Mining the FP-Tree by Creating Conditional (sub) pattern bases • Start from each frequent length-1 pattern (as an initial suffix pattern). • Construct its conditional pattern base which consists of the set of prefix paths in the FP-Tree co-occurring with suffix pattern. • Then, construct its conditional FP-Tree & perform mining on this tree. • The pattern growth is achieved by concatenation of the suffix pattern with the frequent patterns generated from a conditional FP-Tree. • The union of all frequent patterns (generated by step 4) gives the required frequent itemset.

  38. FP-Tree Example Continued Now, following the above mentioned steps: • Lets start from I5. I5 is involved in 2 branches namely {I2 I1 I5: 1} and {I2 I1 I3 I5: 1}. • Therefore considering I5 as suffix, its 2 corresponding prefix paths would be {I2 I1: 1} and {I2 I1 I3: 1}, which forms its conditional pattern base. Mining the FP-Tree by creating conditional (sub) pattern bases

  39. FP-Tree Example Continued • Out of these, only I1 & I2 is selected in the conditional FP-Tree because I3 does not satisfy the minimum support count. For I1, support count in conditional pattern base = 1 + 1 = 2 For I2, support count in conditional pattern base = 1 + 1 = 2 For I3, support count in conditional pattern base = 1 Thus support count for I3 is less than required min_sup which is 2 here. • Now, we have a conditional FP-Tree with us. • All frequent pattern corresponding to suffix I5 are generated by considering all possible combinations of I5 and conditional FP-Tree. • The same procedure is applied to suffixes I4, I3 and I1. • Note: I2 is not taken into consideration for suffix because it doesn’t have any prefix at all.

  40. Why Frequent Pattern Growth Fast ? • Performance study shows • FP-growth is an order of magnitude faster than Apriori • Reasoning • No candidate generation, no candidate test • Use compact data structure • Eliminate repeated database scans • Basic operation is counting and FP-tree building

  41. Agenda • The Apriori Algorithm (Mining single dimensional boolean association rules) • Frequent-Pattern Growth (FP-Growth) Method • Summary

  42. Summary • Association rules are generated from frequent itemsets. • Frequent itemsets are mined using Apriori algorithm or Frequent-Pattern Growth method. • Apriori property states that all the subsets of frequent itemsets must also be frequent. • Apriori algorithm uses frequent itemsets, join & prune methods and Apriori property to derive strong association rules. • Frequent-Pattern Growth method avoids repeated database scanning of Apriori algorithm. • FP-Growth method is faster than Apriori algorithm.

  43. Thank You!

  44. Mining Topic-Specific Concepts and Definitions on the Web Irem Incekoy May 2003,  Proceedings of the 12th International conference on World Wide Web, ACM Press Bing Liu, University of Illinois at Chicago, 851 S. Morgan Street Chicago IL 60607-7053 Chee Wee Chin, Hwee Tou Ng, National University of Singapore 3 Science Drive 2 Singapore

  45. References • Agrawal, R. and Srikant, R. “Fast Algorithm for Mining Association Rules”, VLDB-94, 1994. • Anderson, C. and Horvitz, E. “Web Montage: A Dynamic Personalized Start Page”, WWW-02, 2002. • Brin, S. and Page, L. “The Anatomy of a Large-Scale Hypertextual Web Search Engine”, WWW7, 1998.

  46. Introduction • When one wants to learn about a topic, one reads a book or a survey paper. • One can read the research papers about the topic. • None of these is very practical. • Learning from web is convenient, intuitive, and diverse.

  47. Purpose of the Paper • This paper’s task is “mining topic-specific knowledge on the Web”. • The goal is to help people learn in-depth knowledge of a topic systematically on the Web.

  48. Learning about a New Topic • One needs to find definitions and descriptions of the topic. • One also needs to know the sub-topics and salient concepts of the topic. • Thus, one wants the knowledge as presented in a traditional book. • The task of this paper can be summarized as “compiling a book on the Web”.

  49. Proposed Technique • First, identify sub-topics or salient concepts of that specific topic. • Then, find and organize the informative pages containing definitions and descriptions of the topic and sub-topics.

  50. Why are the current search tecnhiques not sufficient? • For definitions and descriptions of the topic: Existing search engines rank web pages based on keyword matching and hyperlink structures. NOT very useful for measuring the informative value of the page. • For sub-topics and salient concepts of the topic: A single web page is unlikely to contain information about all the key concepts or sub-topics of the topic. Thus, sub-topics need to be discovered from multiple web pages. Current search engine systems do not perform this task.