1. Efficient Semi-supervised Spectral Co-clustering with Constraints
Xiaoxiao Shi, Wei Fan, Philip S. Yu

2. Motivation Co-clustering with constraints Document-word co-clustering
How to use?
Co-clustering
Network
Clustering
Doc 1 (ICNP)
Doc 2 (ICDM)
Doc 3 (AAAI) C
Doc 4 (KDD)

3. Motivation Co-clustering with constraints
Author-conference co-clustering
Collaborators
Collaborators
John
Mary
Jack
Tom
Cathy
How to use?
ICDM 07
ICDM 08
ICDM 09
AAAI 08
AAAI 09
ICDM
AAAI

4. Straightforward solution I: transform constraints as edges, and solve global graph partition problem
Keyword-conference co-clustering
ICDM
ICDM
Co-clustering
Co-clustering
Cut I
KDD
KDD
Clustering
Clustering
AAAI
AAAI
Cut II
Network
Network
ICNP
ICNP

5. Straightforward solution II: transform constraints as nodes, and solve bipartite graph partition problem in a larger graph
Pseudo node
Pseudo node
ICDM
Co-clustering
ICDM
Co-clustering
Cut I
KDD
KDD
Clustering
Clustering
AAAI
Cut II
AAAI
Network
Network
ICNP
ICNP

6. Problems of the two straightforward solutions
Not efficient
more edges are added; more nodes are included
(10 to 80 times slower than the original co-clustering without constraint)
Not effective
The graph becomes more complicated, of which the optimal partition is more difficult to find
(In some cases, the Normalized Mutual Information drops 30% compared with the original co-clustering without constraint)

7. Formulate the problem as an optimization problem
The solution can be directly obtained via the left and right eigenvectors of the following matrix (more details in Theorem 2 of the paper):
Minimize the number of inter-group edges
Maximize the number of satisfied constraints
Graph Laplacian

8. Algorithm Flow

9. Experiments
Document-word co-clustering

10. Experiments
Graph-pattern co-clustering

11. Results

12. Conclusions
For many applications, some prior knowledge exists about the relationship among rows and columns for co-clustering applications. Problem: how to use the knowledge (constraints) to find better co-clusters?
Two straightforward solutions
Model the constraints as linkages
Model the constraints as additional pseudo nodes
Problem: not efficient; not effective
Proposed method: model the problem as an optimization problem, and solve it with the selected eigenvectors

13. Related Work Traditional Co-clustering without constraint
Information based co-clustering
Information-theoretic co-clustering (Dhillon, etc 2003)
Partition based co-clustering
Spectral co-clustering (Dhillon, etc 2001)
Previous constraint-based co-clustering models
Co-clustering with row constraint (Chen, etc 2008)
Co-clustering with order based constraint (suitable for a specific type of constraint, not comparable with the proposed model; Pensa. Etc 2008)
Straightforward modifications of traditional co-clustering models to use constraints:
Link-based constraint co-clustering
Node-based constraint co-clustering