A Unified Framework for Data Visualization and Coclustering

We propose a new theoretical framework for data visualization. This framework is based on iterative procedure looking up an appropriate approximation of the data matrix  by using two stochastic similarity matrices from the set of rows and the set of columns. This process converges to a steady state where the approximated data  is composed of g similar rows and l similar columns. Reordering A according to the first left and right singular vectors involves an optimal data reorganization revealing homogeneous block clusters. Furthermore, we show that our approach is related to a Markov chain model, to the double k-means with g × l block clusters and to a spectral coclustering. Numerical experiments on simulated and real data sets show the interest of our approach.