Coclustering

Coclustering, also called co-clustering or biclustering, is the simultaneous partitioning of the rows and columns of a data matrix into corresponding row and column clusters. The goal is to identify submatrices, or blocks, that display coherent patterns across their contained rows and columns. This approach captures local structures that may be invisible to global clustering.

Common methods include spectral co-clustering, which uses eigenvectors of the data or a derived similarity matrix to partition rows and columns; information-theoretic co-clustering, which optimizes mutual information between the row and column partitions; probabilistic models such as latent block models; and matrix factorization approaches like nonnegative matrix factorization with alternating updates. Some implementations perform hard clustering on one dimension while updating the other, enabling scalable iterative refinement.

Applications span several domains. In bioinformatics, coclustering identifies groups of genes co-expressed under specific conditions. In text mining, it discovers blocks of documents and terms that co-occur together. In recommender systems, it reveals user and item groups with similar interaction patterns. Other uses include market analysis, collaboration networks, and sensor or time-series data where patterns depend on particular subsets of features and observations.

Advantages include the ability to reveal local, interpretable patterns that global methods miss. Challenges involve selecting the numbers of row and column clusters, handling noise and sparsity, and ensuring scalable computation for large data sets. Evaluation can be difficult due to the lack of universal ground truth, and results often require careful interpretation in the context of the application.