A Unified Framework for Probabilistic Component Analysis

In this paper, we present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood via the prior, thus providing an elegant and principled framework for creating novel component analysis models. Under our framework, we unify many very popular and well-studied component analysis algorithms, such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Locality Preserving Projections (LPP) and Slow Feature Analysis (SFA). We firstly show that the projection directions produced by all the aforementioned methods are also produced by the Maximum Likelihood (ML) solution of a single joint probability density function (PDF) just by choosing an appropriate prior over the latent space in our framework. Subsequently, we propose novel Expectation Maximization (EM) algorithms utilising the proposed joint PDF. Theoretical analysis and experiments show the usefulness of the proposed framework.