DMTCS Proceedings, 2005 International Conference on Analysis of Algorithms

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DMTCS Conference vol AD (2005), pp. 267-274


2005 International Conference on Analysis of Algorithms

Conrado Martínez (ed.)

DMTCS Conference Volume AD (2005), pp. 267-274

author: Gahyun Park and Wojciech Szpankowski
title: Analysis of biclusters with applications to gene expression data
keywords: Random matrix, two-dimensional patterns, bicluster, microarray data, biclique.
abstract: For a given matrix of size
n × m
over a finite alphabet
, a bicluster is a submatrix composed of selected columns and rows satisfying a certain property. In microarrays analysis one searches for largest biclusters in which selected rows constitute the same string (pattern); in another formulation of the problem one tries to find a maximally dense submatrix. In a conceptually similar problem, namely the bipartite clique problem on graphs, one looks for the largest binary submatrix with all `
'. In this paper, we assume that the original matrix is generated by a memoryless source over a finite alphabet
. We first consider the case where the selected biclusters are square submatrices and prove that with high probability (whp) the largest (square) bicluster having the same row-pattern is of size
n m
is the (largest) probability of a symbol. We observe, however, that when we consider any submatrices (not just square submatrices), then the largest area of a bicluster jumps to
A n
(whp) where
is an explicitly computable constant. These findings complete some recent results concerning maximal biclusters and maximum balanced bicliques for random bipartite graphs.
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reference: Gahyun Park and Wojciech Szpankowski (2005), Analysis of biclusters with applications to gene expression data , in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 267-274
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