Models and Issues in Consistent Biclustering

Biclustering is a methodology allowing simultaneous partitioning of a set of samples and their features into classes. Samples and features classified together are supposed to have a high relevance to each other which can be observed by intensity of their expressions. The notion of consistency for biclustering is defined using interrelation between centroids of sample and feature classes. Consistent biclustering also implies separability of the classes by convex cones (see [Busygin et al. (2005)]). Previous works on biclustering concentrated on unsupervised learning and did not consider employing a training set, whose classification is given. However, with the introduction of consistent biclustering, significant progress has been made in supervised learning as well. A dataset (e.g., from microarray experiments) is normally given as a rectangular m× n matrix A, where each column represents a data sample (e.g., patient) and each row represents a feature (e.g., gene)