R. Porreca and G. Ferrari-Trecate. Identification of piecewise affine models of genetic regulatory networks: the data classification problem. 17th IFAC World Congress on Automatic Control , 2008. Seoul, Korea, 6-11 July.
In this paper we consider the identification of PieceWise Affine(PWA) models of Genetic Regulatory Networks (GRNs) and focus on dataclassification that is a task of the whole identification process.By assuming that gene expression profiles have been split intosegments generated by a single affine mode, data classificationamounts to group together segments that have been produced by thesame mode. In particular, this operation must be performed in anoisy setting and without using any knowledge on the number of modesexcited in the experiment. At a mathematical level, classificationamounts to find all partitions of the set of segments that verify astatistical criterion and as such it has a combinatorial nature. Inorder to minimize the computational complexity we propose a pruningstrategy for reducing the dimension of the search space. Inparticular, our approach hinges on a new algorithm for generating inan efficient way all partitions of a finite set that verify a boundon a monotone cost function.