R. Porreca and G. Ferrari-Trecate. Identification of piecewise affine models of genetic regulatory networks: the data classification problem. Technical Report 143/07, Universita' degli Studi di Pavia, 2007.
In this paper we consider the identification of PieceWise Affine (PWA) models of Genetic Regulatory Networks (GRNs) and focus on data classification that is a task of the whole identification process. By assuming that gene expression profiles have been split into segments generated by a single affine mode, data classification amounts to group together segments that have been produced by the same mode. In particular, this operation must be performed in a noisy setting and without using any knowledge on the number of modes excited in the experiment. At a mathematical level, classification amounts to find all partitions of the set of segments that verify a statistical criterion and as such it has a combinatorial nature. In order to minimize the computational complexity we propose a pruning strategy for reducing the dimension of the search space. In particular, our approach hinges on a new algorithm for generating in an effcient way all partitions of a finite set that verify a bound on a monotone cost function.