Possibilistic biclustering algorithm for discovering value-coherent overlapping δ-biclusters

Abstract

One of the important tools for analyzing gene expression data is biclustering method. It focuses on finding a subset of genes and a subset of experimental conditions that together exhibit coherent behavior. However, most of the existing biclustering algorithms find exclusive biclusters, which is inappropriate in the context of biology. Since biological processes are not independent of each other, many genes may participate in multiple different processes. Hence, nonexclusive biclustering algorithms are required for finding overlapping biclusters. In this regard, a novel possibilistic biclustering algorithm is presented here to find highly overlapping biclusters of larger volume with mean squared residue lower than a predefined threshold. It judiciously incorporates the concept of possibilistic clustering algorithm into biclustering framework. The integration enables efficient selection of highly overlapping coherent biclusters with mean squared residue lower than a given threshold. The detailed formulation of the proposed possibilistic biclustering algorithm, along with a mathematical analysis on the convergence property, is presented. Some quantitative indices are introduced for evaluating the quality of generated biclusters. The effectiveness of the algorithm, along with a comparison with other algorithms, is demonstrated both qualitatively and quantitatively on yeast gene expression data set. In general, the proposed algorithm shows excellent performance at finding patterns in gene expression data.