1. Mining Frequent patterns without candidate generation Jiawei Han, Jian Pei and Yiwen Yin

2. Problem : Mining Frequent Pattern I={a 1, a 1, …, a m } is a set of items. DB={T 1, T 1, …, T n } is the database of transactions where each transaction is a non empty subset of I. A pattern is also a subset of I. A pattern is frequent if it is contained in (supported by) more than a fixed number (ξ) of transactions.

3. Previous work : Apriori It may need to generate a huge number of candidate itemsets. To discover a frequent pattern of size k it needs to generate more than 2 k candidates in total. It may need to scan the database repeatedly and check for the frequencies of the candidates.

4. FP-growth FP-growth mines frequent patterns without generating the candidate sets. It grows the patterns from fragments. It builds an extended prefix tree (FP-tree) for the transaction database. This tree is a compressed representation of the database. It saves repeated scan of the database.

5. FP-tree TIDItems Bought Frequent Items 100 f,a,c,d,g,i,m,pf,c,a,m,p 200 a,b,c,f,l,m,of,c,a,b,m 300 b,f,h,j,of,b 400 b,c,k,s,pc,b,p 500 a,f,c,e,l,p,m,nf,c,a,m,p sorted in descending order of the freq. root c:1 m:1 b:1 p:2 m:2 c:3 a:3 f:4 b:1 p:1 Item Head of node-links f c a b m p Minimum support (ξ) = 3

6. Conditional FP-tree of p Items Bought Frequent Items f,c,a,mc c c,bc Conditional pattern base for p root c:3 Conditional FP-tree of p Minimum support (ξ) = 3 The set of frequent patterns containing p is{ cp, p }{ p }

7. Frequent patterns containing m Items Bought Frequent Items f,c,a f,c,a, f,c,a,bf,c,a Conditional pattern base for m root c:3 a:3 f:3 Conditional FP-tree of m Items Freq. Items f,c Conditional pattern base for am root c:3 f:3 Conditional FP-tree of am root f:3 Items Freq. Items ff ff ff The set of frequent patterns containing m is { m }{ m, am }{ m, am, cam }{ m, am, cam, fcam } Conditional FP-tree of cam root c:3 a:3 f:3 { m, am, cam, fcam, fam } pattern base for cam root c:3 f:3 { m, am, cam, fcam, fam, cm, fcm } root c:3 a:3 f:3 { m, am, cam, fcam, fam, cm, fcm, fm }

8. Complete Frequent Pattern set facpm fc b apfmfacaamcm camfcafcmfam fcam Generated by conditional FP tree of m which is a single Path A single path generates each combination of its nodes as frequent pattern Supports for a pattern is equal to the minimum support of a node in it. root c:3 a:3 f:3

9. Pseudocode Procedure FP-growth(Tree,α) if Tree contains a single path P for each combination (β) of the nodes in P Generate pattern βUα with support = minimum support of a node in β else for each a i in the header of Tree do Generate pattern β= αUa i with support = a i.support. Construct β’s conditional pattern base and conditional FP-tree Tree β if Tree β ≠ Ø Call FP-growth(Tree β, β)

10. Implementation issues For different support thresholds (ξ) there are different FP-trees. We may chose ξ=20 if 98% of the queries have ξ≥20. Updating the FP-tree after each new transaction may be costly. We may count the occurrence frequency of every items and update the tree if relative frequency of an item gets a large change.

11. New Challenges FP-growth may output a large number of frequent patterns for small (ξ) and very small number of frequent patterns for large (ξ). We may not know the (ξ) for our purpose. Which frequent patterns are good instances for generating interesting association rules?

12. Top-K frequent closed patterns Closed pattern is a pattern whose support is larger than any of its super pattern. TIDItems Bought Frequent Items 100 f,a,c,d,g,i,m,pf,c,a,m,p 200 a,b,c,f,l,m,of,c,a,b,m 300 b,f,h,j,of,b 400 b,c,k,s,pf,c,b,p 500 a,f,c,e,l,p,m,nf,c,a,m,p f:5a:3c:4p:3m:3 fc:4 b:3 ap:3fm:3fa:3ca:3am:3cm:3 cam:3fca:3fcm:3fam:3 fcam:3 fp:3fb:3 We can also specify the minimum length of the patterns. Top-2 frequent closed patterns with length ≥ 2 is fc and fcam

13. Mining Top-K closed FP The algorithm starts with an FP-tree having 0 support threshold. While building the tree, it prunes the smaller patterns with length < min_length. After the tree is built, it prunes the relatively infrequent patterns by raising the support threshold. Mining is performed on the final pruned FP-tree.

14. Compressed Frequent Pattern FP-growth may end up with a large set of patterns. We can compress the set of frequent patterns by clustering it minimally and selecting a representative pattern from each cluster. facpm fc b apfmfacaamcm camfcafcmfam fcam {fcam, cam, ap, b}

15. Clustering Criterion For each cluster there must be a representative pattern P r. D(P,P r ) ≤ δ for all patterns inside the cluster of P r. D(P 1,P 2 ) = 1- |T(P 1 )∩T(P 2 )| |T(P 1 )UT(P 2 )| T(P) is the set of transactions that support P. D is a metric for closed patterns.

16. Summary FP-tree is an extended prefix tree that summarizes the database in a compressed form. FP-growth is an algorithm for mining frequent patterns using FP-tree. FP-tree can also be used to mine Top-K frequent closed patterns and Compressed frequent patterns.

17. References Mining Frequent Patterns without Candidate Generation –Jiawei Han, Jian Pei and Yiwen Yin Mining Top-K Frequent Closed Patterns without Minimum Support –Jiawei Han, Jianyong Wang, Ying Lu and Petre Tzetkov Mining Compressed Frequent-Pattern Sets –Dong Xin, Jiawei Han, Xipheng Yan and Hong Cheng

18. Thank You