Classification of Hyperspectral Images With Regularized Linear Discriminant Analysis

TLDR

Hyperspectral image classification with linear discriminant analysis is ill‑posed when training samples are few relative to spectral features, requiring regularization that is highly sensitive to parameter tuning. The authors propose an efficient variant of regularized LDA to address these ill‑posed problems in remote sensing. They compare several LDA‑based classifiers—including penalized, orthogonal, and uncorrelated LDA—to standard LDA and the proposed RLDA, illustrating differences with toy examples and testing them exhaustively on multiple ill‑posed hyperspectral classification tasks. Experiments confirm the effectiveness of the proposed RLDA and highlight the key properties of the other LDA techniques in critical ill‑posed hyperspectral image classification scenarios.

Abstract

This paper analyzes the classification of hyperspectral remote sensing images with linear discriminant analysis (LDA) in the presence of a small ratio between the number of training samples and the number of spectral features. In these particular ill-posed problems, a reliable LDA requires one to introduce regularization for problem solving. Nonetheless, in such a challenging scenario, the resulting regularized LDA (RLDA) is highly sensitive to the tuning of the regularization parameter. In this context, we introduce in the remote sensing community an efficient version of the RLDA recently presented by Ye to cope with critical ill-posed problems. In addition, several LDA-based classifiers (i.e., penalized LDA, orthogonal LDA, and uncorrelated LDA) are compared theoretically and experimentally with the standard LDA and the RLDA. Method differences are highlighted through toy examples and are exhaustively tested on several ill-posed problems related to the classification of hyperspectral remote sensing images. Experimental results confirm the effectiveness of the presented RLDA technique and point out the main properties of other analyzed LDA techniques in critical ill-posed hyperspectral image classification problems.