A Generative Model for Sparse Discrete Binary ... - Semantic Scholar
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A Generative Model for Sparse Discrete. Binary Data with Non-Uniform. Categorical Priors. Mark Girolami. Applied computational Intelligence Research Unit.
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A Generative Model for Sparse Discrete Binary Data with Non-Uniform Categorical Priors
Mark Girolami Applied Computational Intelligence Research Unit Department of Computing and Information Systems University of Paisley P aisley PA1 2BE Scotland Abstract. The Generative T opographic Mapping (GTM)was developed and introduced as a principle d alternativ eto the Self-Organising Map for, principally, visualising high dimensional continuous data. There are many cases where the observation data is ordinal and discrete and the application of methods developed speci cally for continuous data is inappropriate. Based on the continuous GTM data model a non-linear latent variable model for modeling sparse high dimensional binary data is presen ted. The primary motivation forthis w ork is the requirement for a dense and low dimensional representation of sparse binary vector space models of text documents based on the multiv ariate Bernoulli event model. The method is however applicable to binary data in general.
1.
Introduction
Generative laten t variable models have recen tly been proposed as tools for the visualisation and analysis of high dimensional data [1, 5]. The Generative T opographic Mapping (GTM) [5] was proposed as a means of visualising high dimensional continuous data on a tw o-dimensional grid.The GTM is essentially based on a nonlinear mapping from an L = 2 dimensional uniform grid of points in latent space x 2
