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 A 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.