Analysis of biclusters with applications to gene expression data †
نویسندگان
چکیده
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 alphabetA. 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 log2Q nm where Q −1
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