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.
This basic algorithmic problem and several variations were initially presented in @cite_9 with the name of direct clustering. The same problem and its variations have also been referred to as two-way clustering, co-clustering or subspace clustering. In practice, finding highly homogeneous biclusters has important applications in biological data analysis (see @cite_7 for review and references), where a bicluster may, for example, correspond to an activation pattern common to a group of genes only under specific experimental conditions.
@cite_9 @cite_7
2036328877 2144544802
Abstract Clustering algorithms are now in widespread use for sorting heterogeneous data into homogeneous blocks. If the data consist of a number of variables taking values over a number of cases, these algorithms may be used either to construct clusters of variables (using, say, correlation as a measure of distance between variables) or clusters of cases. This article presents a model, and a technique, for clustering cases and variables simultaneously. The principal advantage in this approach is the direct interpretation of the clusters on the data. A large number of clustering approaches have been proposed for the analysis of gene expression data obtained from microarray experiments. However, the results from the application of standard clustering methods to genes are limited. This limitation is imposed by the existence of a number of experimental conditions where the activity of genes is uncorrelated. A similar limitation exists when clustering of conditions is performed. For this reason, a number of algorithms that perform simultaneous clustering on the row and column dimensions of the data matrix has been proposed. The goal is to find submatrices, that is, subgroups of genes and subgroups of conditions, where the genes exhibit highly correlated activities for every condition. In this paper, we refer to this class of algorithms as biclustering. Biclustering is also referred in the literature as coclustering and direct clustering, among others names, and has also been used in fields such as information retrieval and data mining. In this comprehensive survey, we analyze a large number of existing approaches to biclustering, and classify them in accordance with the type of biclusters they can find, the patterns of biclusters that are discovered, the methods used to perform the search, the approaches used to evaluate the solution, and the target applications.