Coclustered

Co-clustered (or coclustering) refers to a data-analysis approach in which both rows and columns of a data matrix are partitioned simultaneously into clusters, producing a grid of blocks that each exhibits a shared pattern. This stands in contrast to traditional clustering, which typically clusters a single dimension. In a data matrix X with n rows and m columns, coclustering seeks to divide the rows into K clusters and the columns into L clusters so that the submatrices X[R_i, C_j] reveal coherent structure, such as similar values across the entries or consistent relationships between the corresponding row and column groups.

Models may assume blocks are homogeneous or follow simple probabilistic distributions. Objective functions vary; common goals include minimizing within-block dispersion, maximizing between-block separation, or maximizing likelihood under a block-structured model.

Algorithms include: Cheng and Church biclustering, which searches for submatrices with coherent patterns in gene expression data; spectral co-clustering, which uses a bipartite graph representation and spectral partitioning to partition rows and columns simultaneously; information-theoretic co-clustering, which minimizes divergence between the empirical distribution and a block-model distribution. These methods differ in assumptions, scalability, and suitability for continuous versus binary data.

Applications are widespread in bioinformatics, text mining, and market analysis. For example, in gene expression, coclustering can reveal groups of genes and experimental conditions with similar expression patterns; in document-term data, it can reveal topics and associated terms. The term coclustered may describe data or results that have been organized into such row and column clusters.