A Dual Formulation for Probabilistic Principal Component Analysis

TL;DR

This paper introduces a dual formulation for Probabilistic PCA in Hilbert spaces, enabling a generative kernel framework that unifies Kernel PCA and demonstrates practical applications on datasets.

Contribution

It develops a dual space representation for Probabilistic PCA, facilitating a new generative kernel method that unifies and extends existing PCA techniques.

Findings

The dual formulation characterizes Probabilistic PCA in Hilbert spaces.

The framework unifies Kernel PCA and probabilistic approaches.

Demonstrated on toy and real datasets.

Abstract

In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods. Furthermore, we show how it englobes Kernel Principal Component Analysis and illustrate its working on a toy and a real dataset.