Hidden Markov Bayesian Principal Component Analysis Hidden Markov Bayesian Principal Component Analysis

Probabilistic Principal Component Analysis is a reformulation of the common multivariate analysis technique known as Principal Component Analysis. It employs a latent variable model framework similar to factor analysis allowing to establish a maximum likelihood solution for the parameters that comprise the model. One of the main assumptions of Probabilistic Principal Component Analysis is that observed data is independent and identically distributed. This assumption is inadequate for many applications, in particular, for modeling sequential data. In this paper, the authors introduce a temporal version of Probabilistic Principal Component Analysis by using a hidden Markov model in order to obtain optimized representations of observed data through time. Combining Probabilistic Principal Component Analyzers with a hidden Markov model, it is possible to enhance the capabilities of transformation and reduction of time series vectors. In order to find automatically the dimensionality of the principal subspace associated with these Probabilistic Principal Component Analyzers through time, a Bayesian treatment of the Principal Component model is introduced as well.