An Approximation Ratio for Biclustering

The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+ √ 2 under L1-norm for 0–1 valued matrices, and of 2 under L2-norm for real valued matrices.