Probabilistic Auto-Associative Models and Semi-Linear PCA

TL;DR

This paper introduces a probabilistic semi-linear auto-associative model that generalizes PCA, demonstrating its effectiveness through simulations and an astronomical application.

Contribution

It proposes a new probabilistic semi-linear auto-associative model extending PCA, with theoretical properties and practical validation.

Findings

Model generalizes PCA to semi-linear case

Numerical experiments validate the approach

Effective in astronomical data analysis

Abstract

Auto-Associative models cover a large class of methods used in data analysis. In this paper, we describe the generals properties of these models when the projection component is linear and we propose and test an easy to implement Probabilistic Semi-Linear Auto- Associative model in a Gaussian setting. We show it is a generalization of the PCA model to the semi-linear case. Numerical experiments on simulated datasets and a real astronomical application highlight the interest of this approach