1. Bi-Clustering

2. 2 Data Mining: Clustering Where K-means clustering minimizes

3. 3 Clustering by Pattern Similarity (p-Clustering) The micro-array “raw” data shows 3 genes and their values in a multi-dimensional space  Parallel Coordinates Plots  Difficult to find their patterns “non-traditional” clustering

4. 4 Clusters Are Clear After Projection

5. 5 Motivation E-Commerce: collaborative filtering Movie 1 Movie 2 Movie 3 Movie 4 Movie 5 Movie 6 Movie 7 Viewer 112435 Viewer 24671 Viewer 323463 Viewer 43457 Viewer 55534

6. 6 Motivation

7. 7 Movie 1 Movie 2 Movie 3 Movie 4 Movie 5 Movie 6 Movie 7 Viewer 112435 Viewer 24671 Viewer 323463 Viewer 43457 Viewer 55534

8. 8 Motivation

9. 9 DNA microarray analysis CH1ICH1BCH1DCH2ICH2B CTFC343922844108280228 VPS8401281120275298 EFB131828037277215 SSA1401292109580238 FUN1428572852576271226 SP0722829048285224 MDM10538272266277236 CYS332228841278219 DEP131227240273232 NTG132929633274228

10. 10 Motivation

11. 11 Motivation Strong coherence exhibits by the selected objects on the selected attributes.  They are not necessarily close to each other but rather bear a constant shift.  Object/attribute bias bi-cluster

12. 12 Challenges The set of objects and the set of attributes are usually unknown. Different objects/attributes may possess different biases and such biases  may be local to the set of selected objects/attributes  are usually unknown in advance May have many unspecified entries

13. 13 Previous Work Subspace clustering  Identifying a set of objects and a set of attributes such that the set of objects are physically close to each other on the subspace formed by the set of attributes. Collaborative filtering: Pearson R  Only considers global offset of each object/attribute.

14. 14 bi-cluster Consists of a (sub)set of objects and a (sub)set of attributes  Corresponds to a submatrix  Occupancy threshold   Each object/attribute has to be filled by a certain percentage.  Volume: number of specified entries in the submatrix  Base: average value of each object/attribute (in the bi-cluster)

15. 15 bi-cluster CH1ICH1BCH1DCH2ICH2BObj base CTFC3 VPS8401120298273 EFB131837215190 SSA1 FUN14 SP07 MDM10 CYS332241219194 DEP1 NTG1 Attr base34766244219

16. 16 bi-cluster Perfect  -cluster Imperfect  -cluster  Residue: d IJ d Ij d iJ d ij

17. 17 bi-cluster The smaller the average residue, the stronger the coherence. Objective: identify  -clusters with residue smaller than a given threshold

18. 18 Cheng-Church Algorithm Find one bi-cluster. Replace the data in the first bi-cluster with random data Find the second bi-cluster, and go on. The quality of the bi-cluster degrades (smaller volume, higher residue) due to the insertion of random data.

19. 19 The FLOC algorithm Generating initial clusters Determine the best action for each row and each column Perform the best action of each row and column sequentially Improved? Y N

20. 20 The FLOC algorithm Action: the change of membership of a row(or column) with respect to a cluster 34 4 13 22 3 2 2 04 column row 1 3 2 1 234 M+N actions are Performed at each iteration N=3 M=4

21. 21 The FLOC algorithm Gain of an action: the residue reduction incurred by performing the action Order of action:  Fixed order  Random order  Weighted random order Complexity: O((M+N)MNkp) 

22. 22 The FLOC algorithm Additional features  Maximum allowed overlap among clusters  Minimum coverage of clusters  Minimum volume of each cluster Can be enforced by “temporarily blocking” certain action during the mining process if such action would violate some constraint.

23. 23 Performance Microarray data: 2884 genes, 17 conditions  100 bi-clusters with smallest residue were returned.  Average residue = 10.34  The average residue of clusters found via the state of the art method in computational biology field is 12.54  The average volume is 25% bigger  The response time is an order of magnitude faster

24. 24 Conclusion Remark The model of bi-cluster is proposed to capture coherent objects with incomplete data set.  base  residue Many additional features can be accommodated (nearly for free).