Two-dimensional Bhattacharyya bound linear discriminant analysis with its applications

TL;DR

This paper extends L2-norm linear discriminant analysis to two-dimensional data, specifically images, by developing 2DBLDA which maximizes inter-class distances and minimizes intra-class distances, improving robustness and avoiding small sample size issues.

Contribution

The paper introduces 2DBLDA, a novel 2D extension of L2BLDA that considers intrinsic image structure and adaptively optimizes the Bhattacharyya bound for better feature extraction.

Findings

Effective in image recognition tasks

Improves face image reconstruction quality

Avoids small sample size problem

Abstract

Recently proposed L2-norm linear discriminant analysis criterion via the Bhattacharyya error bound estimation (L2BLDA) is an effective improvement of linear discriminant analysis (LDA) for feature extraction. However, L2BLDA is only proposed to cope with vector input samples. When facing with two-dimensional (2D) inputs, such as images, it will lose some useful information, since it does not consider intrinsic structure of images. In this paper, we extend L2BLDA to a two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance which is measured by the weighted pairwise distances of class means and meanwhile minimizes the matrix-based within-class distance. The weighting constant between the between-class and within-class terms is determined by the involved data that makes the proposed 2DBLDA adaptive. In addition, the criterion of 2DBLDA is equivalent to optimizing an upper bound of the Bhattacharyya error. The construction of 2DBLDA makes it avoid the small sample size problem while also possess robustness, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of the proposed methods.