Laplace Exponential Family PCA

摘要

Considering numerous types of data, this paper discusses application of PCA to exponential family distributions. Reviewing the probabilistic basis of PCA, we propose a model using Laplace approximation, which was widely used in classification context, Laplace exponential family PCA (LePCA). The proposed approach provides a more probabilistic solution compared with numerous models before. Standard EM algorithm can be applied to this model, while only a degraded form of EM is applicable on previous exponential PCA models. LePCA absorbs probabilistic PCA, as well as the traditional PCA as its specialization by taking the Gaussian assumption for granted.