Web. The Discovery Method of Multiple Web Communities with Markov Cluster Algorithm

Transcription

1 Markov Cluster Algorithm Web Web Web Kleinberg HITS Web Web HITS Web Markov Cluster Algorithm ( ) Web The Discovery Method of Multiple Web Communities with Markov Cluster Algorithm Kazutami KATO and Hiroshi MATSUO A web community is a set of web pages created by individuals or associations with a common interest on a topic. Kleinberg s HITS algorithm find a web community on a query topic by link analysis. For multiple meanings of query terms, there might be multiple web communities related to the query topic. However, HITS algorithm can t always extract web community which users would expect or prefer, because it can only extract single community on a query topic.in this paper, we propose a method for discovering web communities on a query topic, using Markov Cluster Algorithm. 1. Web Web Web Web (Web ) Web Web Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology Web Web Web Kleinberg HITS(Hyperlink-Induced Topic Search) 1) Web 2),3) Kleinberg HITS Web HITS 4) 6) apple Apple Computer apple 1

2 Web HITS Markov Cluster Algorithm (MCL) ( ) Web HITS Markov Cluster Algorithm Web 2. HITS HITS Web Web HITS authority hub Web authority hub authority p authority hub auth(p) = hub(q) (1) hub(p) = q,q p q,p q auth(q) (2) authority hub authority hub hub authority HITS authority hub Web authority hub Web HITS 1. σ Yahoo 8) Web t root (R σ) 2. root p p d backward 3. root p p forward 4. backward forward root n base (S σ) 5. base (G σ) 6. G σ n n A A T 7. A T A µ 1 x AA T λ 1 y ( x, y authority, hub ) 8. M authority hub Web 2.1 HITS apple Apple Computer apple σ base G σ Web 1 9) apple base G σ ( ) () apple base Web HITS G σ Web authority hub Web 2

3 3.1 Markov Cluster Algorithm MCL G MCL 1 Fig. 1 apple Web Web graph of the topic apple 1. G 2. M = M G (M G G ) 3. Do (a) M = M 2 (b) M =Γ rm While (M 2 M) 4. M H H 1 C = {C 1,C 2,..., C N}(N: ) G σ Web HITS Web 3. HITS σ base G σ Web G σ Web Web G σ Markov Cluster Algorithm(MCL) 7) G σ HITS Web G M G M G (M G) pq q p k M G k (MG) k (MG) 2 pq p q MCL expansion inflation M expansion M = M 2 M R k l inflation Γ r k (Γ rm) pq =(M pq) r / (M iq) r (3) i=1 r inflation r >1 r =2 MCL ( ) 2 MCL C C1 = { 1, 6, 7, 10 } C2 = { 2, 3, 5 } C3 = { 4, 8, 9, 11, 12 } 7 C MCL Fig. 2 Example of graph clustering with MCL 4 C3 3

4 3.2 Web authority hub 1. σ base G σ (base HITS ) 2. G σ G σ MCL G σ C = {C 1,C 2,..., C N }(N: ) 3. G σ C 1,C 2,..., C N G 1,G 2,..., G N 4. G i HITS G i Web authority hub 5. G i M authority hub Web 4. apple, amazon, motor company Web HITS 4.1 base HITS 10,000 base HITS MCL base Web n 3 HITS 6) base Web base k =2 HITS base 1 Table 1 Parameters for the proposed method Yahoo! root t 200 backward d 50 base k 2 inflation r 1.4 M HITS [ apple ] 2 HITS apple authority 5 (authority ) 3 apple authority 5 ( 1st, 2nd, 3rd,... ) 2 HITS apple Table 2 An experimental result of apple by HITS algorithm top 5 authorities apple Table 3 An experimental result of apple by proposed method top 5 authorities (1st cluster) top 5 authorities (2nd cluster) top 5 authorities (3rd cluster) HITS authority 4

5 Apple Computer Apple Computer HITS Apple Computer authority Apple Computer authority apple Apple Computer appleii authority appleii HITS Apple Computer Apple Computer, apple, appleii MCL appleii Web [ amazon ] 4 HITS amazon authority 5 (authority ) 5 amazon authority 5 4 HITS amazon Table 4 An experimental result of amazon by HITS algorithm top 5 authorities HITS amazon 5 amazon Table 5 An experimental result of amazon by proposed method top 5 authorities (1st cluster) top 5 authorities (2nd cluster) top 5 authorities (3rd cluster) top 5 authorities (6th cluster) amazonswarrior ryci.htm amazon-connection.html authority HITS topic drift 4) Amazon.com authority Amazon.com authority authority amazon HITS amazon authority amazon Jupitermedia authority Amazon.com authority Amazon.com 5

6 ( ) authority Amazon HITS topic drift amazon Web amazon Amazon.com, amazon, Amazon base Web [ motor company ] 6 HITS motor company authority 5 (authority ) 7 motor company authority 5 6 HITS motor company Table 6 An experimental result of motor company by HITS algorithm top 5 authorities HITS authority authority motor car company HITS authority motor car company authority motorcycle company Vintage Chesil 7 Table 7 motor company An experimental result of motor company by proposed method top 5 authorities (1st cluster) top 5 authorities (2nd cluster) top 5 authorities (3rd cluster) Scamp authority kit car company HITS motor car company motor car company, motorcycle company, kit car company motor company HITS motor company 5. Web HITS Markov Cluster Algorithm(MCL) Web Web 6

7 Web base root Web 1 Web base 2 1) J. Kleinberg, Authoritative Sources in a Hyperlinked Environment, In Proceedings ACM- SIAM Symposium on Discrete Algorithms, pp (1998) 2), Web,, Vol.16, No.3, pp (2001) 3), Web,, Vol.17, No.3, pp (2002) 4) K. Bharat, M. Henzinger, Improved Algorithms for Topic Distillation in a Hyperlinked Environment, In Proceedings ACM SIGIR Conference, pp (1998) 5) S. Chakrabarti, B. Dom, P. Raghavan, S. Rajagopalan, D. Gibson, J. Kleinberg, Automatic resource compilation by analyzing hyperlink structure and associated text, In Proceedings of the 7th International World Wide Web Conference (1998) 6),,,, WEB HITS, D-I, Vol.J85- D-I, No.8, pp (2002) 7) Stijn van Dongen, Graph Clustering by Flow Simulation, PhD thesis, University of Utrecht (2000) 8) 9),,, CoPE,, NC-2004 (2005/03) () 7E