An Information Geometric Framework for Dimensionality Reduction

09/29/2008
by   Kevin M. Carter, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/27/2020

Nested Grassmanns for Dimensionality Reduction

Grassmann manifolds have been widely used to represent the geometry of f...
research
06/14/2016

Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction

We reframe linear dimensionality reduction as a problem of Bayesian infe...
research
06/28/2018

Grassmannian Discriminant Maps (GDM) for Manifold Dimensionality Reduction with Application to Image Set Classification

In image set classification, a considerable progress has been made by re...
research
02/11/2019

Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold

Dictionary leaning (DL) and dimensionality reduction (DR) are powerful t...
research
08/16/2020

Geometric Foundations of Data Reduction

The purpose of this paper is to write a complete survey of the (spectral...
research
12/18/2018

Deep Variational Sufficient Dimensionality Reduction

We consider the problem of sufficient dimensionality reduction (SDR), wh...
research
07/21/2010

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learni...

Please sign up or login with your details

Forgot password? Click here to reset