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The topographic organization and visualization of binary data using multivariate-Bernoulli latent variable models

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1 Author(s)
Girolami, M. ; Div. of Comput. & Inf. Syst., Univ. of Paisley, UK

A nonlinear latent variable model for the topographic organization and subsequent visualization of multivariate binary data is presented. The generative topographic mapping (GTM) is a nonlinear factor analysis model for continuous data which assumes an isotropic Gaussian noise model and performs uniform sampling from a two-dimensional (2-D) latent space. Despite the, success of the GTM when applied to continuous data the development of a similar model for discrete binary data has been hindered due, in part, to the nonlinear link function inherent in the binomial distribution which yields a log-likelihood that is nonlinear in the model parameters. The paper presents an effective method for the parameter estimation of a binary latent variable model-a binary version of the GTM-by adopting a variational approximation to the binomial likelihood. This approximation thus provides a log-likelihood which is quadratic in the model parameters and so obviates the necessity of an iterative M-step in the expectation maximization (EM) algorithm. The power of this method is demonstrated on two significant application domains, handwritten digit recognition and the topographic organization of semantically similar text-based documents

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Neural Networks, IEEE Transactions on  (Volume:12 ,  Issue: 6 )