An Information Geometric Framework for Dimensionality Reduction

TL;DR

This paper introduces an information geometric framework for reducing dimensionality of data represented on statistical manifolds, addressing limitations of Euclidean-based methods for high-dimensional probability distributions.

Contribution

It proposes a novel approach that leverages information geometry for both reconstructing statistical manifolds and performing dimensionality reduction directly in the data domain.

Findings

Framework effectively reduces dimensions on statistical manifolds.

Applicable to high-dimensional signals without Euclidean representation.

Enhances learning tasks like classification and visualization.

Abstract

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these methods have focused primarily on Riemannian manifolds in Euclidean space. While sufficient for many applications, there are many high-dimensional signals which have no straightforward and meaningful Euclidean representation. In these cases, signals may be more appropriately represented as a realization of some distribution lying on a statistical manifold, or a manifold of probability density functions (PDFs). We present a framework for dimensionality reduction that uses information geometry for both statistical manifold reconstruction as well as dimensionality reduction in the data domain.