Communications Inspired Linear Discriminant Analysis

TL;DR

This paper introduces a supervised linear dimensionality reduction method that maximizes mutual information between projected data and class labels using gradient descent, offering a novel information-theoretic approach.

Contribution

It presents a new method for linear discriminant analysis based on mutual information maximization and gradient descent, with theoretical analysis and empirical validation.

Findings

Achieves promising results on real datasets

Outperforms traditional LDA and IDA methods

Effectively utilizes Shannon and Renyi entropy for mutual information

Abstract

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods (Linear Discriminant Analysis and Information Discriminant Analysis), and comparisons are also made with a method in which Renyi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets.