1. Generalized topographic block model
- Author
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Gérard Govaert, Mohamed Nadif, Rodolphe Priam, Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, Laboratoire d'Informatique Paris Descartes (LIPADE - EA 2517), Université Paris Descartes - Paris 5 (UPD5), Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), University of Southampton [Southampton], Laboratoire d'Informatique Paris Descartes ( LIPADE - EA 2517 ), Université Paris Descartes - Paris 5 ( UPD5 ), Heuristique et Diagnostic des Systèmes Complexes [Compiègne] ( Heudiasyc ), and Université de Technologie de Compiègne ( UTC ) -Centre National de la Recherche Scientifique ( CNRS )
- Subjects
0301 basic medicine ,Cognitive Neuroscience ,Gaussian ,Inference ,02 engineering and technology ,Machine learning ,computer.software_genre ,Poisson distribution ,03 medical and health sciences ,symbols.namesake ,Bernoulli's principle ,Exponential family ,Artificial Intelligence ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST] ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Block (data storage) ,business.industry ,Maximization ,Mixture model ,Computer Science Applications ,030104 developmental biology ,symbols ,020201 artificial intelligence & image processing ,Artificial intelligence ,business ,computer - Abstract
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.
- Published
- 2016