An Approximation Ratio for Biclustering

TL;DR

This paper presents approximation algorithms for biclustering, providing worst-case ratios for 0-1 and real-valued matrices, improving understanding of biclustering's computational complexity.

Contribution

It introduces a simple approximation method for biclustering using independent one-way clusterings and establishes worst-case approximation ratios.

Findings

Approximation ratio of 1+sqrt(2) for 0-1 matrices under L1-norm

Approximation ratio of 2 for real-valued matrices under L2-norm

Method offers a theoretical bound on biclustering quality

Abstract

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+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2 under L2-norm for real valued matrices.