An Evaluation of Low-Rank Mahalanobis Metric Learning Techniques for Hyperspectral Image Classification

We provide a comparative study of several state-of-the-art Mahalanobis metric learning algorithms evaluated on three well-studied, high-dimensional hyperspectral images captured by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) instrument. We focus on the problem of low-rankMahalanobis metric learning, where our objective is to learn an
${\mbi{n}}\ {\mmb \times}\ {\mbi{m}}$
projection matrix
${\bf A}$
, where
${\mbi{m}}\ {\mmb \ll}\ {\mbi{n}}$
. Low-rank metrics offer a “plug-in” enhancement to similarity-based classifiers that can reduce computation time and improve classification accuracy with fewer training samples, enabling operations in resource-constrained environments such as onboard spacecraft. Our results indicate that applying a simple shrinkage-based regularization procedure to multiclass Linear Discriminant Analysis (LDA) produces comparable or better classification accuracies than the low-rank extensions of several widely used Mahalanobis metric learning algorithms, at considerably lower computational cost.