An approximation ratio for biclustering

Authors:
Kai Puolamäki;Sami Hanhijärvi;Gemma C. Garriga
Affiliations:
Helsinki Institute for Information Technology, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland;Helsinki Institute for Information Technology, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland;Helsinki Institute for Information Technology, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland
Venue:
Information Processing Letters
Year:
2008

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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+2 under L"1-norm for 0-1 valued matrices, and of 2 under L"2-norm for real valued matrices.