Bayesian Nonlinear Principal Component Analysis Using Random Fields

TL;DR

This paper introduces a probabilistic nonlinear dimension reduction model that employs location-specific transformations smoothed by a Markov random field prior, leveraging recent sampling techniques for efficient computation.

Contribution

It presents a novel nonlinear PCA framework using Markov random fields to model spatially varying transformations, enhancing flexibility over traditional linear PCA.

Findings

Effective nonlinear dimension reduction demonstrated

Utilizes Markov random fields for smooth transformation modeling

Employs advanced sampling methods for feasible computation

Abstract

We propose a novel model for nonlinear dimension reduction motivated by the probabilistic formulation of principal component analysis. Nonlinearity is achieved by specifying different transformation matrices at different locations of the latent space and smoothing the transformation using a Markov random field type prior. The computation is made feasible by the recent advances in sampling from von Mises-Fisher distributions.