Latent Variable Models for Dimensionality Reduction

Zhihua Zhang, Michael I. Jordan

Abstract: Principal coordinate analysis (PCO), as a duality of principal component analysis (PCA), is also a classical method for explanatory data analysis. In this paper we propose a probabilistic PCO by using a normal latent variable model in which maximum likelihood estimation and an expectation-maximization algorithm are respectively devised to calculate the configurations of objects in a low-dimensional Euclidean space. We also devise probabilistic formulations for kernel PCA which is a nonlinear extension of PCA.