1. © 2007 Cios / Pedrycz / Swiniarski / Kurgan Chapter 10 ASSOCIATION RULES Cios / Pedrycz / Swiniarski / Kurgan

2. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 2 Outline Introduction Association Rules and Transactional Data –Basic Concepts Mining Single Dimensional, Single-Level Boolean Association Rules –Naïve Algorithm –Apriori Algorithm –Generating Association Rules from Frequent Itemsets –Improving Efficiency of the Apriori Algorithm –Finding Interesting Association Rules

3. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 3 Introduction Association rules mining is another, after clustering, key unsupervised data mining method that finds interesting associations (relationships, dependencies) in large sets of data items.

4. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 4 Introduction AR are used to describe associations or correlations among a set of items in transaction databases, relational databases, and data warehouses –applications: basket data analysis, cross-marketing, catalog design, clustering, data preprocessing, genomics, etc. - rule format: LHS  RHS [support, confidence] Examples: buys(x, diapers)  buys(x, beers) [0.5%, 60%] major(x, CS) AND takes(x, Advanced Data Analysis)  level(x, PhD) [1%, 75%]

5. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 5 Rules Body ==> Consequent [ Support, Confidence ] Body: represents the examined data. Consequent: represents a discovered property for the examined data. Support: represents the percentage of the records satisfying the body or the consequent. Confidence: represents the percentage of the records satisfying both the body and the consequent to those satisfying only the body.

6. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 6 Introduction in this shopping basket customer bought tomatoes, carrots, bananas, bread, eggs, sup, milk, etc. how the demographical information affects what the customer buys? is bread usually bought with milk? does a specific milk brand make any difference? where we place the tomatoes in the store to maximize their sales? is the bread bought when both milk and eggs are bought together? what can be learned using association rules?

7. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 7 Introduction AR can be derived when data describes events that occur at the same time / in close proximity. They can be: –useful, when containing high quality, actionable information diapers  beer –trivial, when they are valid and supported by data, but useless since they describe well known facts milk  eggs –inexplicable, when they concern valid and new facts, but they cannot be utilized grocery store  milk is sold as often as bread

8. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 8 Introduction Some of the common applications: –planning store layouts we can place products that have a strong purchasing relationship close together OR we place such products far apart to increase traffic to purchase other items –planning bundling products and offering coupons knowing that buys(x, diapers)  buys(x, beers), discounts are not offered on both beer and diapers at the same time –we discount one to increase sales and make money on the other –designing direct marketing campaign mailing a camcorder promotion to people who bought VCR is best when it comes approximately two to three months after the VCR purchase –other applications will be discussed later…

9. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 9 Introduction How do we derive ARs: –techniques are based on probability and statistics –the process consists of 4 steps 1.prepare input data 2.choose items of interest… (itemset) 3.compute probabilities, joint probabilities, etc… 4.find (the most probable) association rules…

10. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 10 Transactional Data Data should be provided in transactional form –each record consists of transaction ID and information about all items that constitute the transaction Transaction ID Subset of all available items TIDTransaction (basket) 1000Beer, Diapers, Eggs …….

11. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 11 Transactional Data First look at the transactional data –example –rules (just by looking at the data) Beer  Eggs Apples  Celery TIDTransaction (basket) 1000Apples, Celery, Diapers 2000Beer, Celery, Eggs 3000Apples, Beer, Celery, Eggs 4000Beer, Eggs

12. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 12 Transactional Data Nominal data can also be transformed into transactions –transformed into transactional format Example Attributes Target Attribute BarFri/SatHungryRainEstimateWait? e1e1 No YesNo0-10Yes ………………… TIDTransaction (basket) 1Bar=No, Fri/Sat=No, Hungry=Yes, Rain=No, Estimate=0-10, Wait?=Yes …….

13. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 13 Association Rules What do we want to do? –given database of transactions, where each transaction is a list of items (purchased by a customer in a visit) –find all rules that correlate presence of one set of items with that of another set of items how many items do we consider in each set? how do we define correlation? –how strong the correlation should be? how do we extract useful rules? Let us answer these questions

14. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 14 Basic Definitions itemset transaction association rule dataset (set of transactions)

15. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 15 Basic Definitions How to measure interestingness of the rules? –each rule has two assigned measures support which indicates the frequencies of the occurring patterns –defined as ratio of # of transactions containing A and B to the total # of transactions confidence which denotes the strength of implication in the rule –defined as ratio of # of transactions containing A and B to the #of transactions containing A

16. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 16 Basic Definitions How to measure interestingness of the rules? –example: diapers  beer support confidence customer buys diapers customer buys both customer buys beer

17. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 17 Basic Definitions How to measure interestingness of the rules? let’s use a more complex rule and explain the concepts in terms of probabilities –find all the rules A and B  C with minimum confidence and support »support is probability that a transaction contains {A, B, C} »confidence is conditional probability that a transaction having {A, B}, also contains C A and B  C (support is 25%, confidence is 100%) if we decide to have minimum support of 50% and minimum confidence of 50%, we generate two rules from the data: A  C (support 50%, confidence 66.6%) C  A (support 50%, confidence 100%) TIDTransaction 1A, B, C 2A, C 3A, D 4B, E, F

18. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 18 Basic Definitions What is I? What is T for TID=2000? What is support(Beer  Eggs)? What is confidence(Beer  Eggs)? TIDTransaction (basket) 1000Apples, Celery, Diapers 2000Beer, Celery, Eggs 3000Apples, Beer, Celery, Eggs 4000Beer, Eggs

19. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 19 Basic Definitions What is I? Apples, Beer, Celery, Diapers, Eggsm (# of items) = 5 What is T for TID=2000? Beer, Celery, Eggs What is support(Beer  Eggs)? 3/4 = 75% What is confidence(Beer  Eggs)? 3/3 = 100% TIDTransaction (basket) 1000Apples, Celery, Diapers 2000Beer, Celery, Eggs 3000Apples, Beer, Celery, Eggs 4000Beer, Eggs

20. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 20 Basic Definitions Frequent itemsets –itemset is any set of items –k-itemset is an itemset containing k items –frequent itemset is an itemset that satisfies a minimum support level –the problem arises when we try to analyze dataset that contains m items how many itemsets are there? –many if m is large

21. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 21 Strong Association Rules Given an itemset it is easy to generate association rules Example itemset = {Beer, Diapers}:  Beer, Diapers Beer  Diapers Diapers  Beer Diapers, Beer  –we are interested only in strong rules those which satisfy minimum support and minimum confidence –these two are user-defined parameters

22. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 22 Strong Association Rules Given itemsets, it is easy to generate association rules –example itemsets: {Beer, Diapers} with support 40% {Beer, Diapers, Eggs} with support 20% –rule IF customer buys Beer and Diapers THEN the probability that (s)he buys Eggs is 50% can be inferred This provides simple descriptive pattern

23. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 23 Association Rules How to generate ARs? –two basic steps 1.Find all frequent itemsets –those that satisfy minimum support 2.Find all strong association rules –generate association rules from frequent itemsets –select and keep rules that satisfy minimum confidence

24. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 24 Naïve Algorithm How do we generate frequent itemsets (step 1)? –naïve algorithm n = |D| for each subset s of I { counter = 0 for each transaction T in D { if s is a subset of T counter = counter + 1 } if minimum support ≤ counter / n add s to frequent itemsets }

25. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 25 Frequent Itemsets Does the naïve algorithm work well? we have 2 m subsets of I we have to scan n transactions for each subset –thus we perform O(2 m n) tests –O(2 m n) complexity shows that the algorithm growth exponentially with the number of items m Thus we have to use some other approach!

26. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 26 Frequent Itemsets FIs support the apriori property –if A is not a frequent itemset, then any superset of A is not a frequent itemset we will use this property to speed up the computations Proof n is # of transactions suppose A is a subset of i transactions if A’  A, then A’ is a subset of i’  i transactions thus if i/n < minimum support, so is i’/n

27. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 27 Frequent Itemsets Using the apriori property –candidate k-itemsets are build from frequent (k-1)-itemsets find all frequent 1-itemsets extend (k-1)-itemsets to candidate k-itemsets prune candidate itemsets that do not meet the minimum support requirement

28. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 28 Apriori Algorithm Improved algorithm to generate frequent itemsets L 1 = {frequent 1-itemsets} for (k=2; L (k-1) is not empty; k++) { C k is generated as k-itemset candidate from L (k-1) for each transaction T in D { C t =subset(C k,T) // k-itemsets that are subsets of T for each k-itemset c in C t c.count++; } L k = {c in C k such that c.count ≥ minimum support} } the frequent itemsets are the union of the L k

29. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 29 Frequent Itemsets Apriori approach reduces number of considered itemsets (# of scans of D) –how do we generate k-itemset candidates? 1.for each item i that is not in a given frequent (k-1)-itemset, but in some other frequent (k-1) itemset in L k-1 –add i to the (k-1)-itemset to create a k-itemset candidate –remove duplicates »example frequent 1-itemsets {A}, {B}, {C} candidate 2-itemsets {A, B}, {A, C}, {B, A}, {B, C}, {C, A}, {C, B} eliminate duplicates {A, B}, {A, C}, {B, C} 2.joining together frequent (k-1)-itemsets –if frequent (k-1)-itemsets have (k-2)-items in common, create a k-itemset candidate by adding two different items to (k-2) common items »example { A, B, C} joined with {A, B, D} gives {A, B, C, D} L 1 = {frequent 1-itemsets} for (k=2; L (k-1) is not empty; k++) { C k is generated as k-itemset candidates from L (k-1) for each transaction T in D { C t =subset(C k,T) // candidates that are subsets of T for each candidate c in C t c.count++; } L k = {c in C k such that c.count ≥ minimum suport} } the frequent itemsets are the union of the L k

30. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 30 Association Rules 1.The frequent set is computed iteratively –1 st iteration large 1-candidate itemsets are found by scanning –k th iteration large k-candidate itemsets are generated by applying apriori-based generation to large (k-1)-itemsets apriori rule generates only those k-itemsets whose every (k-1)-itemset subset is frequent (above the threshold) 2.Generating rules –for each frequent itemset X output all rules Y  (X – Y) if s(X) / s(Y) > minimum confidence Y is a subset of X 1.Find all frequent itemsets –those that satisfy minimum support 2.Find all strong association rules –generate association rules from frequent itemsets –select and keep rules that satisfy minimum confidence

31. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 31 Example We will generate association rules from the transactional data given below: –minimum support = 50% the # of transactions above the minimum support is 4 x 50 % = 2 –minimum confidence = 60%  TIDTransaction 1000Apples, Celery, Diapers 2000Beer, Celery, Eggs 3000Apples, Beer, Celery, Eggs 4000Beer, Eggs TIDTransaction 1000A, C, D 2000B, C, E 3000A, B, C, E 4000B, E

32. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 32 Example item set support count A2 B3 C3 D1 E3 TIDTransaction 1000A, C, D 2000B, C, E 3000A, B, C, E 4000B, E generate candidate 1-itemsets generate frequent 2-itemsets item set support count A2 B3 C3 E3 delete candidates below minimum support generate candidate 2-itemsets item set support count A, B1 A, C2 A, E1 B, C2 B, E3 C, E2 generate frequent 1-itemsets item set support count A, C2 B, C2 B, E3 C, E2 generate frequent 3-itemsets generate candidate 3-itemsets itemsetsupport count B, C, E2 we do not use 3- itemsets with (A, B) and (A, E) they are below minimum support itemsetsupport count B, C, E2 C1C1 L1L1 C2C2 C3C3 L2L2 L3L3

33. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 33 Example Finally we derive association rules from generated frequent 3-itemset {B, C, E} with s = 50% –we need to satisfy minimum confidence of 60% B and C  E with support = 50% and confidence = 100% B and E  C with support = 50% and confidence = 66.7% C and E  B with support = 50% and confidence = 100% B  C and E with support = 50% and confidence = 66.7% C  B and E with support = 50% and confidence = 66.7% E  B and C with support = 50% and confidence = 66.7% TIDTransaction 1000A, C, D 2000B, C, E 3000A, B, C, E 4000B, E

34. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 34 Improving Efficiency of Apriori The Apriori algorithm can be modified to improve its efficiency (computational complexity) by: –hashing –removal of transactions that do not contain frequent itemsets –sampling of the data –partitioning of the data –mining frequent itemsets without generation of candidate itemsets

35. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 35 Improving efficiency: Hashing Hashing –is used to reduce the size of the candidate k-itemsets, i.e., itemsets that are generated from frequent itemsets from iteration k-1, C k, for k>1 for instance, when scanning D to generate L 1 from the candidate 1-temsets in C 1, we can at the same time generate all 2-itemsets for each transaction, hash (map) them into different buckets of the hash table structure and increase the corresponding bucket counts a 2-itemset, which corresponding bucket count is below the support threshold, cannot be frequent and thus we can remove it from the candidate set C 2. In this way we reduce the number of candidate 2-itemsets that must be examined to obtain L 2

36. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 36 Improving efficiency: Hashing To add itemset, start at root and go down until a leaf is reached At interior node at depth d, decide which branch to follow by applying hash function to the dth item of the itemset When # of items in a leaf node exceeds some threshold convert leaf node to an internal node

37. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 37 Improving efficiency: Hashing To find candidates contained in given transaction, t –Hash on every item in t at the root node to ensure that itemsets that start with an item not in t are ignored –At interior node reached by hashing the item i in the transaction hash on each item that comes after i in t

38. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 38 Improving efficiency: Hashing Let C 3 = {{1 2 3}, {1 2 4}, {1 3 4}, {1 3 5}, {2 3 4}} C t = subset(C 3, {1 0 1 1 0}) First build hash-tree with candidate itemsets Then determine which of those itemsets are actually in the given transaction

39. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 39 Hash-Tree Hash Table {2 3 4} ROOT {1 3 4} {1 3 5} {1 2 3} {1 2 4} 1 23 C t = {1 3 4} d = 2 Hash on the next item in t: 3, ignore itemsets with 2 since not in t. 2 t = {1 0 1 1 0} At root (d=1), hash on items in t: 1, 3, 4. 3, 4 return nothing since no itemsets start with 3 or 4. 2 Is ignored since not in t. Check which are in t. Those that are get added to C t as output from subset function. Manually verify that of the 5 itemsets in C 3 only {1 3 4} was actually present in the transaction

40. © 2007 Cios / Pedrycz / Swiniarski / Kurgan Direct Hashing and Pruning(DHP) 40

41. © 2007 Cios / Pedrycz / Swiniarski / Kurgan DHP 41

42. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 42 Improving Efficiency of Apriori Removal of transactions that do not contain frequent itemsets –we remove transactions that do not contain frequent itemsets –In general, if a transaction does not contain any frequent k-itemsets, it cannot contain any frequent (k+1) itemsets, and thus can be removed from computation of any frequent t-itemsets, where t > k

43. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 43 Improving Efficiency of Apriori Sampling of the data –we generate association rules based on a sampled subset of transactions in D a randomly selected subset S of D is used to search for the frequent itemsets generation of frequent itemsets from S is more efficient (faster) but some of the rules that would have been generated from D may be missing, and some rules generated from S may not be present in D

44. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 44 Improving Efficiency of Apriori Partitioning of the data –partitioning generates frequent itemsets by finding frequent itemsets in subsets (partition) of D

45. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 45 Improving Efficiency of Apriori Mining frequent itemsets without generation of candidate itemsets –one of the main limiting aspects of the Apriori is that it can generate very large number of candidate itemsets for instance, for 10,000 1-itemsets, the Apriori algorithm generates approximately 10,000,000 candidate 2-itemsets –other limiting aspect is that the Apriori may need to repeatedly scan the data set D –to address these issues, a divide-and-conquer method, which decomposes the overall problem into a set of smaller tasks, is used the method, referred to as frequent-pattern growth (FP-growth) compresses the set of frequent (individual) items from D into a frequent pattern tree (FP-tree)

46. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 46 General Algorithm to be improved 1.In the first pass, the support of each individual item is counted, and the large ones are determined 2.In each subsequent pass, the frequent itemsets determined in the previous pass is used to generate new itemsets called candidate itemsets. 3.The support of each candidate itemset is counted, and the frequent ones are determined. 4.This process continues until no new large itemsets are found.

47. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 47 AIS Algorithm Candidate itemsets are generated and counted on- the-fly as the database is scanned. 1.For each transaction, it is determined which of the frequent itemsets of the previous pass are contained in this transaction. 2.New candidate itemsets are generated by extending these frequent itemsets with other items in this transaction. The disadvantage is that this results in unnecessarily generating and counting too many candidate itemsets that turn out to be small.

48. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 48 Example TIDItems 1001 3 4 2002 3 5 3001 2 3 5 4002 5 Database ItemsetSupport {1}2 {2}3 {3}3 {5}3 L1L1 ItemsetSupport {1 3}*2 {1 4}1 {3 4}1 {2 3}*2 {2 5}*3 {3 5}*2 {1 2}1 {1 5}1 C2C2 ItemsetSupport {1 3 4}1 {2 3 5}*2 {1 3 5}1 C3C3

49. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 49 SETM Algorithm Candidate itemsets are generated on-the-fly as the database is scanned, but counted at the end of the pass. 1.New candidate itemsets are generated the same way as in AIS algorithm, but the TID of the generating transaction is saved with the candidate itemset in a sequential structure. 2.At the end of the pass, the support count of candidate itemsets is determined by aggregating this sequential structure It has the same disadvantage of the AIS algorithm. Another disadvantage is that for each candidate itemset, there are as many entries as its support value.

50. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 50 Example TIDItems 1001 3 4 2002 3 5 3001 2 3 5 4002 5 Database ItemsetSupport {1}2 {2}3 {3}3 {5}3 L1L1 ItemsetTID {1 3}100 {1 4}100 {3 4}100 {2 3}200 {2 5}200 {3 5}200 {1 2}300 {1 3}300 {1 5}300 {2 3}300 {2 5}300 {3 5}300 {2 5}400 C2C2 ItemsetTID {1 3 4}100 {2 3 5}200 {1 3 5}300 {2 3 5}300 C3C3

51. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 51 Apriori Algorithm Candidate itemsets are generated using only the frequent itemsets of the previous pass without considering the transactions in the database. 1.The frequent itemset of the previous pass is joined with itself to generate all itemsets whose size is higher by 1. 2.Each generated itemset, that has a subset which is not frequent, is deleted. The remaining itemsets are the candidate ones.

52. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 52 Example TIDItems 1001 3 4 2002 3 5 3001 2 3 5 4002 5 Database ItemsetSupport {1}2 {2}3 {3}3 {5}3 L1L1 ItemsetSupport {1 2}1 {1 3}*2 {1 5}1 {2 3}*2 {2 5}*3 {3 5}*2 C2C2 ItemsetSupport {2 3 5}*2 C3C3 {1 2 3} {1 3 5} {2 3 5}

53. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 53 AprioriTid Algorithm The database is not used at all for counting the support of candidate itemsets after the first pass. 1.The candidate itemsets are generated the same way as in Apriori algorithm. 2.Another set C’ is generated of which each member has the TID of each transaction and the large itemsets present in this transaction. This set is used to count the support of each candidate itemset. The advantage is that the number of entries in C’ may be smaller than the number of transactions in the database, especially in the later passes.

54. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 54 Example TIDItems 1001 3 4 2002 3 5 3001 2 3 5 4002 5 Database ItemsetSupport {1}2 {2}3 {3}3 {5}3 L1L1 ItemsetSupport {1 2}1 {1 3}*2 {1 5}1 {2 3}*2 {2 5}*3 {3 5}*2 C2C2 ItemsetSupport {2 3 5}*2 C3C3 100{1 3} 200{2 3}, {2 5}, {3 5} 300{1 2}, {1 3}, {1 5}, {2 3}, {2 5}, {3 5} 400{2 5} C’ 2 200{2 3 5} 300{2 3 5} C’ 3

55. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 55 Performance Analysis

56. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 56 AprioriHybrid Algorithm Performance Analysis shows that: 1.Apriori does better than AprioriTid in the earlier passes. 2.AprioriTid does better than Apriori in the later passes. Hence, a hybrid algorithm can be designed that uses Apriori in the initial passes and switches to AprioriTid when it expects that the set C’ will fit in memory.

57. © 2007 Cios / Pedrycz / Swiniarski / Kurgan RARM and FOLDARM Both the techniques use a data structure SOTrieIT (Support ordered Trie Itemset) –Trie: position in the tree defines the key it is associated with –Support-ordered: most frequent on left-most branch This trie-like tree structure stores the support counts of all 1-itemsets and 2-itemsets in the database. –This structure is then sorted according to the support counts of each node in descending order Unlike RARM, FOLDARM allows transactions and unique transactional items to be added and removed without the need to destroy the current SOTrieIT and rebuild it. 57

58. © 2007 Cios / Pedrycz / Swiniarski / Kurgan FP-Growth Algorithm 58

59. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 59 Finding Interesting Association Rules Depending on the minimum support and confidence values the user may generate a large number of rules to analyze and assess How to filter out the rules that are potentially the most interesting? –whenever a rule is interesting (or not) can be evaluated either objectively or subjectively the ultimate but subjective user’s evaluation cannot be quantified or anticipated; they are different for different users that is why objective interestingness measures, based on the statistical information present in D are used

60. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 60 Finding Interesting Association Rules The subjective evaluation of association rules often boils down to checking if a given rule is unexpected (i.e., surprises the user) and actionable (i.e., the user can use it for something useful) –useful, when they provide high quality actionable information e.g. diapers  beers –trivial, when they are valid and supported by data but useless since they confirm well known facts e.g. milk  bread –inexplicable, when they contain valid new facts but cannot be utilized e.g. grocery_store  milk_is_sold_as_often_as_bread

61. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 61 Finding Interesting Association Rules In most cases, confidence and support values associated with each rule are used as the objective measure to select the most interesting rules –rules that have these values higher with respect to other rules are preferred –although this simple approach works in many cases, we will show that sometimes rules with high confidence and support may be uninteresting or even misleading

62. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 62 Objective interestingness measures –example let us assume that transactional data contains milk and bread as the frequent items 2,000 transactions were recorded –in 1,200 customers bought milk –in 1,650 customers bought bread –in 900 customers bought both milk and bread milknot milktotal bread9007501650 not bread30050350 total12008002000 Finding Interesting Association Rules

63. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 63 Objective interestingness measures –Example given the minimum support threshold of 40% and minimum confidence threshold of 70% rule “milk  bread [45%, 75%]” would be generated on the other hand, due to low support and confidence values the rule “milk  not bread [15%, 25%]” would not be generated the latter rule is by far more “accurate” while the first may be misleading Finding Interesting Association Rules

64. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 64 Objective interestingness measures –example “milk  bread [45%, 75%]” rule –probability of buying bread is 82.5%, while confidence of milk  bread is lower and equals 75% –bread and milk are negatively associated, i.e., buying one decreases buying the other –obviously using this rule would not be a wise decision Finding Interesting Association Rules milknot milktotal bread9007501650 not bread30050350 total12008002000

65. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 65 Finding Interesting Association Rules Objective interestingness measures –alternative approach to evaluate interestingness of association rules is to use measures based on correlation –for A  B rule, the itemset A is independent of the occurrence of the itemset B if P(A  B) = P(A)P(B). Otherwise, itemsets A and B are dependent and correlated as events. –correlation measure (also referred to as lift and interest), is defined between itemsets A and B as

66. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 66 Finding Interesting Association Rules Objective interestingness measures –correlation measure if the correlation value is less than 1, then the occurrence of A is negatively correlated (inhibits) the occurrence of B if the value is greater than 1, then A and B are positively correlated, which means that occurrence of one promotes occurrence of the other if correlation equals 1, then A and B are independent, i.e., there is no correlation between these itemsets –correlation value for the rule milk  bread is 0.45 / (0.6*0.825) = 0.45 / 0.495 = 0.91

67. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 67 Other measures for association rule Objective interestingness measures –All-confidence –Collective strength –Coverage: It measures how often a rule X -> Y is applicable in a database similar to support –Conviction: the frequency at which the rule makes an incorrect prediction –Succinctness: characterized by clear, precise expression in few words –Leverage: Leverage measures the difference of X and Y appearing together in the data set and what would be expected if X and Y where statistically dependent. –Lift: Leverage measures the difference of X and Y appearing together in the data set and what would be expected if X and Y where statistically dependent.

68. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 68 Applications Web Personalization –personalization and recommendation systems for browsing web pages e.g. Amazon’s recommended books Mobasher, et al., Effective Personalization Based on Association Rule Discovery from Web Usage Data, ACM Workshop on Web Information and Data Management, 2001 Genomic Data –mining to find associations in genomic data Satou, K., et al., Finding Association Rules on Heterogeneous Genome Data, Proceedings of the Pacific Symposium on Biocomputing, pp.397-408, pp.1997

69. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 69 Genomic Data Summary of results –182,388 association rules were generated with minimum support = 5% minimum confidence = 65% –post processing of the generated rules selected rules with maximum support of 30 final number of generated rules was 381 –they were corroborated by biological data »common substructures in serine endopeptidases were found

70. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 70 References R. Agrawal, T. Imielinski, and A. Swami, Mining Association Rules Between Sets of Items in Large Databases, Proceedings of the ACM SIGMOD Conference on Management of Data, pp. 207-216, 1993 R. Agrawal, and R. Srikant, Fast Algorithms for Mining Association Rules, Proceedings of the 20th VLDB Conference, pp. 487-499, 1994 J. Han, M. Kamber, Data Mining, Morgan Kaufmann, 2001 Jong Soo Park, Member, Ming-Syan Chen and Philip S. Yu, Using a Hash- Based Method with Transaction Trimming for Mining Association Rules, IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 9, NO. 5, SEPTEMBER/OCTOBER 1997 Slides 5, 46 – 56 from Mohamed G. Elfeky, Purdue University Slide 58, Florian Verhein, School of Information Technologies,The University of Sydney,Australia

71. © 2007 Cios / Pedrycz / Swiniarski / Kurgan 71 References Amitabha Das, Wee-Keong Ng, Yew-Kwong Woon, Rapid association rule mining, CIKM '01: Proceedings of the tenth international conference on Information and knowledge management, Oct 2001 Yew-Kwong Woon Wee-Keong Ng Amitabha Das, Fast Online Dynamic Association Rule Mining, Web Information Systems Engineering, 2001. Proceedings of the Second International Conference, 2001