Feequent Item Mining - Data Mining - Pattern Mining
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The document provides an overview of frequent itemset mining in data mining, explaining concepts such as itemsets, support counts, and the apriori principle. It discusses various methods for generating frequent itemsets, challenges faced in frequent itemset mining, and presents alternative techniques like Eclat and FP-Growth. The document emphasizes the significance of frequent pattern mining across different application domains, highlighting its utility in association rule mining, classification, and clustering.
Feequent Item Mining - Data Mining - Pattern Mining
- 2. What is data mining? • Pattern Mining • What patterns • Why are they useful
- 3. 3 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
- 4. Frequent Itemsets Mining TID Transactions 100 { A, B, E } 200 { B, D } 300 { A, B, E } 400 { A, C } 500 { B, C } 600 { A, C } 700 { A, B } 800 { A, B, C, E } 900 { A, B, C } 1000 { A, C, E } • Minimum support level 50% – {A},{B},{C},{A,B}, {A,C} • How to link this to Data Cube?
- 5. Three Different Views of FIM • Transactional Database – How we do store a transactional database? • Horizontal, Vertical, Transaction-Item Pair • Binary Matrix • Bipartite Graph • How does the FIM formulated in these different settings? 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
- 6. 6 Frequent Itemset Generation 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 Given d items, there are 2d possible candidate itemsets
- 7. 7 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 – Complexity ~ O(NMw) => Expensive since M = 2d !!! 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
- 8. 8 Reducing Number of Candidates • 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
- 9. 9 Illustrating Apriori Principle Found to be Infrequent 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 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
- 10. 10 Illustrating Apriori Principle Item Count Bread 4 Coke 2 Milk 4 Beer 3 Diaper 4 Eggs 1 Itemset Count {Bread,Milk} 3 {Bread,Beer} 2 {Bread,Diaper} 3 {Milk,Beer} 2 {Milk,Diaper} 3 {Beer,Diaper} 3 Itemset Count {Bread,Milk,Diaper} 3 Items (1-itemsets) Pairs (2-itemsets) (No need to generate candidates involving Coke or Eggs) Triplets (3-itemsets) Minimum Support = 3 If every subset is considered, 6C1 + 6C2 + 6C3 = 41 With support-based pruning, 6 + 6 + 1 = 13
- 11. Apriori R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB, 487-499, 1994
- 13. 13 How to Generate Candidates? • Suppose the items in Lk-1 are listed in an order • Step 1: self-joining Lk-1 insert into Ck select p.item1, p.item2, …, p.itemk-1, q.itemk-1 from Lk-1 p, Lk-1 q where p.item1=q.item1, …, p.itemk-2=q.itemk-2, p.itemk-1 < q.itemk-1 • Step 2: pruning forall itemsets c in Ck do forall (k-1)-subsets s of c do if (s is not in Lk-1) then delete c from Ck
- 14. 14 Challenges of Frequent Itemset Mining • Challenges – Multiple scans of transaction database – Huge number of candidates – Tedious workload of support counting for candidates • Improving Apriori: general ideas – Reduce passes of transaction database scans – Shrink number of candidates – Facilitate support counting of candidates
- 15. 15 Alternative Methods for Frequent Itemset Generation • Representation of Database – horizontal vs vertical data layout TID Items 1 A,B,E 2 B,C,D 3 C,E 4 A,C,D 5 A,B,C,D 6 A,E 7 A,B 8 A,B,C 9 A,C,D 10 B Horizontal Data Layout A B C D E 1 1 2 2 1 4 2 3 4 3 5 5 4 5 6 6 7 8 9 7 8 9 8 10 9 Vertical Data Layout
- 16. 16 ECLAT • For each item, store a list of transaction ids (tids) TID Items 1 A,B,E 2 B,C,D 3 C,E 4 A,C,D 5 A,B,C,D 6 A,E 7 A,B 8 A,B,C 9 A,C,D 10 B Horizontal Data Layout A B C D E 1 1 2 2 1 4 2 3 4 3 5 5 4 5 6 6 7 8 9 7 8 9 8 10 9 Vertical Data Layout TID-list
- 17. 17 ECLAT • Determine support of any k-itemset by intersecting tid-lists of two of its (k-1) subsets. • 3 traversal approaches: – top-down, bottom-up and hybrid • Advantage: very fast support counting • Disadvantage: intermediate tid-lists may become too large for memory A 1 4 5 6 7 8 9 B 1 2 5 7 8 10 AB 1 5 7 8
- 20. 20 FP-growth Algorithm • Use a compressed representation of the database using an FP-tree • Once an FP-tree has been constructed, it uses a recursive divide-and-conquer approach to mine the frequent itemsets
- 21. 21 FP-tree construction TID Items 1 {A,B} 2 {B,C,D} 3 {A,C,D,E} 4 {A,D,E} 5 {A,B,C} 6 {A,B,C,D} 7 {B,C} 8 {A,B,C} 9 {A,B,D} 10 {B,C,E} null A:1 B:1 null A:1 B:1 B:1 C:1 D:1 After reading TID=1: After reading TID=2:
- 22. 22 FP-Tree Construction null A:7 B:5 B:3 C:3 D:1 C:1 D:1 C:3 D:1 D:1 E:1 E:1 TID Items 1 {A,B} 2 {B,C,D} 3 {A,C,D,E} 4 {A,D,E} 5 {A,B,C} 6 {A,B,C,D} 7 {B,C} 8 {A,B,C} 9 {A,B,D} 10 {B,C,E} Pointers are used to assist frequent itemset generation D:1 E:1 Transaction Database Item Pointer A B C D E Header table
- 23. 23 FP-growth null A:7 B:5 B:1 C:1 D:1 C:1 D:1 C:3 D:1 D:1 Conditional Pattern base for D: P = {(A:1,B:1,C:1), (A:1,B:1), (A:1,C:1), (A:1), (B:1,C:1)} Recursively apply FP- growth on P Frequent Itemsets found (with sup > 1): AD, BD, CD, ACD, BCD D:1
- 25. 25 Compact Representation of Frequent Itemsets • Some itemsets are redundant because they have identical support as their supersets • Number of frequent itemsets • Need a compact representation TID A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 10 1 10 3 k k
- 26. 26 Maximal Frequent Itemset 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 ABCD E Border Infrequent Itemsets Maximal Itemsets An itemset is maximal frequent if none of its immediate supersets is frequent
- 27. 27 Closed Itemset • An itemset is closed if none of its immediate supersets has the same support as the itemset TID Items 1 {A,B} 2 {B,C,D} 3 {A,B,C,D} 4 {A,B,D} 5 {A,B,C,D} Itemset Support {A} 4 {B} 5 {C} 3 {D} 4 {A,B} 4 {A,C} 2 {A,D} 3 {B,C} 3 {B,D} 4 {C,D} 3 Itemset Support {A,B,C} 2 {A,B,D} 3 {A,C,D} 2 {B,C,D} 3 {A,B,C,D} 2
- 28. 28 Maximal vs Closed Itemsets TID Items 1 ABC 2 ABCD 3 BCE 4 ACDE 5 DE 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 124 123 1234 245 345 12 124 24 4 123 2 3 24 34 45 12 2 24 4 4 2 3 4 2 4 Transaction Ids Not supported by any transactions
- 29. 29 Maximal vs Closed Frequent Itemsets 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 124 123 1234 245 345 12 124 24 4 123 2 3 24 34 45 12 2 24 4 4 2 3 4 2 4 Minimum support = 2 # Closed = 9 # Maximal = 4 Closed and maximal Closed but not maximal
- 30. 30 Maximal vs Closed Itemsets Frequent Itemsets Closed Frequent Itemsets Maximal Frequent Itemsets
- 31. Beyond Itemsets • Sequence Mining – Finding frequent subsequences from a collection of sequences • Graph Mining – Finding frequent (connected) subgraphs from a collection of graphs • Tree Mining – Finding frequent (embedded) subtrees from a set of trees/graphs • Geometric Structure Mining – Finding frequent substructures from 3-D or 2-D geometric graphs • Among others…
- 32. Frequent Pattern Mining B A E A B C C F B D F F D E A B A C A E D C F D A B A C E A D A B D C A A B B D D C C A B D C
- 33. Why Frequent Pattern Mining is So Important? • Application Domains – Business, biology, chemistry, WWW, computer/networing security, … • Summarizing the underlying datasets, providing key insights • Basic tools for other data mining tasks – Assocation rule mining – Classification – Clustering – Change Detection – etc…
- 34. Network motifs: recurring patterns that occur significantly more than in randomized nets • Do motifs have specific roles in the network? • Many possible distinct subgraphs
- 35. The 13 three-node connected subgraphs
- 36. 199 4-node directed connected subgraphs And it grows fast for larger subgraphs : 9364 5-node subgraphs, 1,530,843 6-node…
- 37. Finding network motifs – an overview • Generation of a suitable random ensemble (reference networks) • Network motifs detection process: Count how many times each subgraph appears Compute statistical significance for each subgraph – probability of appearing in random as much as in real network (P-val or Z-score)
- 38. Real = 5 Rand=0.5±0.6 Zscore (#Standard Deviations)=7.5 Ensemble of networks
- 39. 39 References • R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. SIGMOD, 207-216, 1993. • R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB, 487-499, 1994. • R. J. Bayardo. Efficiently mining long patterns from databases. SIGMOD, 85-93, 1998.
- 40. References: • Christian Borgelt, Efficient Implementations of Apriori and Eclat, FIMI’03 • Ferenc Bodon, A fast APRIORI implementation, FIMI’03 • Ferenc Bodon, A Survey on Frequent Itemset Mining, Technical Report, Budapest University of Technology and Economic, 2006
- 41. Important websites: • FIMI workshop – Not only Apriori and FIM • FP-tree, ECLAT, Closed, Maximal – http://fimi.cs.helsinki.fi/ • Christian Borgelt’s website – http://www.borgelt.net/software.html • Ferenc Bodon’s website – http://www.cs.bme.hu/~bodon/en/apriori/