Generalized topographic block model

Co-clustering leads to parsimony in data visualisation with a number of parameters dramatically reduced in comparison to the dimensions of the data sample. Herein, we propose a new generalized approach for nonlinear mapping by a re-parameterization of the latent block mixture model. The densities modeling the blocks are in an exponential family such that the Gaussian, Bernoulli and Poisson laws are particular cases. The inference of the parameters is derived from the block expectation-maximization algorithm with a Newton-Raphson procedure at the maximization step. Empirical experiments with textual data validate the interest of our generalized model. The authors have very carefully revised the document by following every comments from the editors and the two anonymous reviewers. It has been tried every possible effort to solve each remark that has been addressed. Below a detailed summary of the updates is provided. We would like to thank the editors and the reviewers for their constructive comments on this manuscript and positive support. To Editors: Once more, we would very much like to invite you to revise your paper, seriously taking into account the comments of the reviewers, and to resubmit your revised version by 02/25/2015 (mm/dd/yy). Any revision received after that may be treated as a new submission. Authors' response: The paper has been revised according to the comments and suggestions of reviewer 2. 2) To Reviewer #1: The revised manuscript is sufficient to Neurocomputing publication standards, and I suggest accepting this manuscript. Authors' response: Thanks for the positive comments and the opportunity of publishing the document in Neurocomputing. 3) To Reviewer #2: Q1. I thank the authors for the revised version of their manuscript. Authors' response: Thanks for the positive comments. Q2. They open the abstract with the statement: "Parametric methods for data visualisation are most of the time founded on an usual mixture model framework." Even a light-hearted revision of existing parametric methods for multivariate data visualization (See, for instance, Lee & Verleysen, 2007) would reveal that this is not the case. Therefore, I think this statement should be either removed or revised. Authors' response: Thanks for this suggestion. Indeed, the term « parametric methods » was meaning « probabilistic methods » or « parametric model » in a statistical framework and could have been read as any methods with parameters on the contrary to svd for instance. This sentence has been removed, and the summary updated for complying with other comments in the review. Q3. Co(Bi)-clustering in general and co(bi)-clustering with visualization-oriented self-organizing models are more adequately introduced in the new version. Authors' response: Thanks for this remark. Q4. I am a bit puzzled by the new introduction "storyline", though. It roughly goes like this: Revision Notes