Grassmann Iterative Linear Discriminant Analysis with Proxy Matrix Optimization

TL;DR

This paper introduces GILDA, a novel Grassmann Iterative LDA method utilizing Proxy Matrix Optimization with automatic differentiation and SGD, which outperforms existing manifold optimization techniques in dimensionality reduction tasks.

Contribution

The paper presents a new GILDA method based on PMO, combining automatic differentiation and SGD on the Grassmann manifold, improving over existing manifold optimization approaches.

Findings

GILDA outperforms existing manifold optimization methods.

The use of PMO enhances the efficiency of LDA.

Automatic differentiation facilitates the optimization process.

Abstract

Linear Discriminant Analysis (LDA) is commonly used for dimensionality reduction in pattern recognition and statistics. It is a supervised method that aims to find the most discriminant space of reduced dimension that can be further used for classification. In this work, we present a Grassmann Iterative LDA method (GILDA) that is based on Proxy Matrix Optimization (PMO). PMO makes use of automatic differentiation and stochastic gradient descent (SGD) on the Grassmann manifold to arrive at the optimal projection matrix. Our results show that GILDAoutperforms the prevailing manifold optimization method.