Constraint-driven co-clustering of 0/1 data

We investigate a co-clustering framework (i.e., a method that provides a partition of objects and a linked partition of features) for binary data sets. So far, constrained co-clustering has been seldomly explored. First, we consider straightforward extensions of the classical instance level constraints (Must-link, Cannot-link) to express relationships on both objects and features. Furthermore, we study constraints that exploit sequential orders on objects and/or features. The idea is that we can specify whether the extracted co-clusters should involve or not contiguous elements (Interval and non-Interval constraints). Instead of designing constraint processing integration within a co-clustering scheme, we propose a Local-to-Global (L2G) framework. It consists in postprocessing a collection of (constrained) local patterns that have been computed beforehand (e.g., closed feature sets and their supporting sets of objects) to build a global pattern like a co-clustering. Roughly speaking, the algorithmic scheme is a k-means-like approach that groups the local patterns. We show that it is possible to push local counterparts of the global constraints on the co-clusters during the local pattern mining phase itself. A large part of the chapter is dedicated to experiments that demonstrate the added-value of our approach. Considering both synthetic data and real gene expression data sets, we discuss the use of constraints to get not only more stable but also more relevant co-clusters.