1. Association Mining via Co-clustering of Sparse Matrices Brian Thompson *, Linda Ness †, David Shallcross †, Devasis Bassu † *†

2. Definitions Association Mining via Co-clustering of Sparse Matrices

3. Motivation Matrices can represent: binary relations, objects and attributes, terms and documents, gene expression, recommender systems,... Dense biclusters indicate strong associations Association Mining via Co-clustering of Sparse Matrices

4. Motivation Matrices can represent: binary relations, objects and attributes, terms and documents, gene expression, recommender systems,... Dense biclusters indicate strong associations Association Mining via Co-clustering of Sparse Matrices

5. Co-Clustering Co-clustering: Given a matrix, cluster the rows and columns to form large, dense biclusters Challenges: Don’t know the number or sizes of clusters a priori Want solution to be efficient and scalable Matrix may be sparse Association Mining via Co-clustering of Sparse Matrices R1R1 R2R2 R3R3 C1C1 C2C2 C3C3

6. Our Approach Association Mining via Co-clustering of Sparse Matrices

7. The CC-MACS Algorithm Association Mining via Co-clustering of Sparse Matrices

8. The CC-MACS Algorithm

14. Experiments: Synthetic Data Association Mining via Co-clustering of Sparse Matrices

15. Experiments: Real-World Data Matrices from domains of finite element modeling and quantum chemistry [src: NIST Matrix Market repository] Association Mining via Co-clustering of Sparse Matrices DatasetOriginal Matrix Cross- Association

16. Concluding Thoughts Association Mining via Co-clustering of Sparse Matrices

17. Acknowledgements/Disclaimer This research was supported by the Intelligence Advanced Research Projects Activity (IARPA) via Air Force Research Laboratory (AFRL) contract number FA8650-10-C-706. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, AFRL, or the U.S. Government. Any misinformation, mistakes, or misunderstanding resulting from this talk are solely the fault of the speaker. Association Mining via Co-clustering of Sparse Matrices

19. Example Matrices Spectral methods, which try to rearrange rows and columns to form a diagonal block matrix, would not perform well on this matrix. The dashed lines suggest a good co-clustering. Association Mining via Co-clustering of Sparse Matrices