Two papers available on-line

[C.M. Bishop]

	           Two Papers Available Online:


      PROBABILISTIC PRINCIPAL COMPONENT ANALYSIS (NCRG/97/010)

           Michael E. Tipping and Christopher M. Bishop
     
	         Neural Computing Research Group
            Aston University, Birmingham B4 7ET, U.K.. 
     
   http://neural-server.aston.ac.uk/Papers/postscript/NCRG_97_010.ps.Z


Abstract: 

Principal component analysis (PCA) is a ubiquitous technique for data
analysis and processing, but one which is not based upon a probability
model. In this paper we demonstrate how the principal axes of a set of
observed data vectors may be determined through maximum-likelihood
estimation of parameters in a latent variable model closely related to
factor analysis. We consider the properties of the associated
likelihood function, giving an EM algorithm for estimating the
principal subspace iteratively, and discuss the advantages conveyed by
the definition of a probability density function for PCA.


       MIXTURES OF PRINCIPAL COMPONENT ANALYSERS (NCRG/97/003)

           Michael E. Tipping and Christopher M. Bishop
     
	         Neural Computing Research Group
            Aston University, Birmingham B4 7ET, U.K.. 

   http://neural-server.aston.ac.uk/Papers/postscript/NCRG_97_003.ps.Z
     
Abstract: 

Principal component analysis (PCA) is one of the most popular
techniques for processing, compressing and visualising data, although
its effectiveness is limited by its global linearity. While nonlinear
variants of PCA have been proposed, an alternative paradigm is to
capture data complexity by a combination of local linear PCA
projections. However, conventional PCA does not correspond to a
probability density, and so there is no unique way to combine PCA
models. Previous attempts to formulate mixture models for PCA have
therefore to some extent been ad hoc. In this paper, PCA is formulated
within a maximum-likelihood framework, based on a specific form of
Gaussian latent variable model. This leads to a well-defined mixture
model for probabilistic principal component analysers, whose
parameters can be determined using an EM algorithm. We discuss the
advantages of this model in the context of clustering, density
modelling and local dimensionality reduction, and we demonstrate its
application to image compression and handwritten digit recognition.

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