# ML Wiki

## Co-Clustering

Co-clustering is a set of techniques in Cluster Analysis

Co-clustering is also called bi-clustering

• let $A$ be $m \times n$ matrix,
• goal is to generate biclusters/co-clusters: a subset of rows which exhibit similar behavior across a subset of columns, or vice versa.

Co-clustering is defined as two map functions:

• rows -> row cluster indexes
• columns -> column cluster indexes
• these map functions are learned simultaneously
• Unlike Two-Phase Document Clustering where we first cluster columns and then we use this to cluster rows

### Subspace Clustering

Can use subspace clustering for co-clustering

• subspace clustering $\approx$ local feature selection

## Non-Negative Matrix Factorization

One way of doing Co-Clustering is via NMF:

• let $A = UV^T$ where $U$ is $m \times k$ and $V$ is $n \times k$
• then rows of $U$ may correspond to clusters of rows, and rows of $V$ to clusters of columns

## References

• Dhillon, Inderjit S. "Co-clustering documents and words using bipartite spectral graph partitioning." 2001. [1]
• Dhillon, Inderjit S., Subramanyam Mallela, and Dharmendra S. Modha. "Information-theoretic co-clustering." 2003. [2]
• Li, Tao, Sheng Ma, and Mitsunori Ogihara. "Document clustering via adaptive subspace iteration." 2004. [3]