Discovering Interesting Patterns in Large Graph Cubes

Transcription

1 Discovering Interesting Patterns in Large Graph Cubes 07 BigGraphs Workshop at IEEE BigData'7 Florian Demesmaeker, NOVA

2 Discovering Interesting Patterns in Large Graph Cubes Florian Demesmaeker, Amine Ghrab, Prof. Siegfried Nijssen & Sabri Skhiri

3 Agenda. Objectives. Interesting Itemset Mining Approach 3. Graph Cube Based Approach 4. Experiments 5. Conclusion

4 Agenda. Objectives. Interesting Itemset Mining Approach 3. Graph Cube Based Approach 4. Experiments 5. Conclusion

5 Objectives Exploratory data analysis Networks Surprising features associations (Gender, Location, Profession) Friends (M, US, Law) (F, US, Eng) (F, BE, Law) (M, UK, Eng) (M, UK, Law) (F, UK, Eng) (M, BE, Tea) (F, UK, Law) (F, US, Law) 5

6 Agenda. Objectives. Interesting Itemset Mining Approach 3. Graph Cube Based Approach 4. Experiments 5. Conclusion

7 Pattern Mining with Itemsets (F, US) (M, BE) Edge Transactions (F, US)-(M, BE) { (F,M), (US,BE) } { (M,F), (BE,US) } (F, BE)-(M, BE) { (F,M), (BE,BE) } { (M,F), (BE,BE) } (F, BE) (F, US)-(F, BE) { (F,F), (US,BE) } { (F,F), (BE,US) } 7

8 Interesting Itemsets The independence between nodes as null model Under the null model, compute the probability of support(i) Number of occurrences of I support(i) ~ B(n, p) Number of transactions Probability of I under the null model Arianna Gallo, Tijl De Bie, and Nello Cristianini. Mini: Mining informative non-redundant itemsets. In European Conference on Principles of Data Mining and Knowledge Discovery, pages Springer, 007 8

9 Agenda. Objectives. Interesting Itemset Mining Approach 3. Graph Cube Based Approach 4. Experiments 5. Conclusion

10 The Search Space The graph cube as a search structure (M, US, Law) (F, US, Eng) (M, UK, Law) (F, BE, Law) (M, UK, Eng) (BE) 4 3 (F, UK, Eng) (F, UK, Law) (F, US, Law) 4 (UK) 4 (US) (M, BE, Tea) Original network Aggregate network w.r.t. (Location) Peixiang Zhao, Xiaolei Li, Dong Xin, and Jiawei Han. Graph cube: on warehousing and olap multidimensional networks. In Proceedings of the 0 ACM SIGMOD International Conference on Management of data, pages ACM, 0. 0

11 Interesting Patterns The independence model P = ((F, US), (M, UK)) P = ((F), (M)) (F) (M) (M, UK) (F, BE) (M, US) (F, UK) (F, US) (M, BE)

12 Interesting Patterns The support probability P = ((F, US), (M, UK)) P = ((F), (M)) (F) (M) supp(p ) (M, UK) (F, BE) (M, US) (F, UK) (F, US) (M, BE) Number of occurrences of P Pr(P P )

13 The Graph Cube Lattice Represents the search space Apex (Profession) (Location) (Gender) (Gender, Profession) (Gender, Location) (Profession, Location) Base Peixiang Zhao, Xiaolei Li, Dong Xin, and Jiawei Han. Graph cube: on warehousing and olap multidimensional networks. In Proceedings of the 0 ACM SIGMOD International Conference on Management of data, pages ACM, 0. 3

14 The Graph Cube Lattice Represents the search space Apex (BE) (Profession) (Location) (Gender) 4 4 (UK) 4 3 (US) (Gender, Profession) (Gender, Location) (Profession, Location) Base Peixiang Zhao, Xiaolei Li, Dong Xin, and Jiawei Han. Graph cube: on warehousing and olap multidimensional networks. In Proceedings of the 0 ACM SIGMOD International Conference on Management of data, pages ACM, 0. 4

15 Search Uses the lattice Apex (Profession) (Location) (Gender) Null model data (Gender, Profession) (Gender, Location) (Profession, Location) Pattern lies in this network Base 5

16 Agenda. Objectives. Interesting Itemset Mining Approach 3. Graph Cube Based Approach 4. Experiments 5. Conclusion

17 Experiments Extended MovieLens dataset: categorical data MINI: a greedy approach Graph cube mining: an exhaustive approach Cuboid Pattern p-value Critic (Good)-(Very good) 3.67 x 0-94 Critic (Good)-(Very bad) 4.9 x 0-34 Critic (Very good)-(very good) 4.9 x 0-30 Country (USA)-(USA) 5.3 x 0-7 Cuboid Pattern p-value Country, Critic (USA, Good)-(USA, Good) 8.85 x 0 - Critic (Good)-(Very good) 0.74 Critic (Very good)-(good) 0.74 Decade (000)-(000) 0.74 Critic (Average)-(Very bad) 9.5 x 0-06 Decade (000)-(990) 0.74 Top 5 by graph cube miner Top 5 by MINI 7

18 Agenda. Objectives. Interesting Itemset Mining Approach 3. Graph Cube Based Approach 4. Experiments 5. Conclusion

19 Conclusion A data exploratory analysis technique in networks Searching for surprising features associations A statistical approach Compute the probability of observing a pattern property under the null model An itemset mining approach A graph cube based approach Perspectives Perform experiments on synthetic data Handle numerical attributes 9

20 Q/A time

21 Frequent Itemset Mining (FIM) Transaction ID Items Bread, Milk Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke Size Size Size 3 Size 4 Diaper Bread, Diaper Bread, Diaper, Coke Eggs, Coke, Beer, Milk Milk Diaper, Eggs Diaper, Milk, Coke Bread, Milk, Diaper, Coke

22 Search Apex (Profession) (Location) (Gender) Null model data (Gender, Profession) (Gender, Location) (Profession, Location) Pattern lies in this network Base

23 Pattern Mining with Itemsets Edge Transactions (F, US) (M, BE) (F, US)-(M, BE) { (F,M), (US,BE) } { (M,F), (BE,US) } (F, BE)-(M, BE) { (F,M), (BE,BE) } { (M,F), (BE,BE) } (M, US) (F, BE) (F, US)-(F, BE) { (F,F), (US,BE) } { (F,F), (BE,US) } (F, US)-(M, US) { (F,M), (US,US) } { (M,F), (US,US) } (F, US)-(F, BE) { (F,F), (US,BE) } { (F,F), (BE,US) } 3

24 Datasets statistics 4

25 Search time Cutoff Movielens Extended Movielens p < 3 sec 3 sec p < sec.5 sec 5

26 Bibliography Arianna Gallo, Tijl De Bie, and Nello Cristianini. Mini: Mining informative non-redundant itemsets. In European Conference on Principles of Data Mining and Knowledge Discovery, pages Springer, 007 Peixiang Zhao, Xiaolei Li, Dong Xin, and Jiawei Han. Graph cube: on warehousing and olap multidimensional networks. In Proceedings of the 0 ACM SIGMOD International Conference on Management of data, pages ACM, 0. I. Cantador, P. Brusilovsky, and T. Kuflik, nd workshop on information heterogeneity and fusion in recommender systems (hetrec 0), in Proceedings of the 5th ACM conference on Recommender systems, ser. RecSys 0. New York, NY, USA: ACM, 0. 6