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
, 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 `
1
'. In this paper, we assume that the original matrix
is generated by a memoryless source over a finite alphabet
A
. 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
log
where
Q
2
n m
Q
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
-1
A n
(whp) where
A
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 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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