Riemannian-based Discriminant Analysis for Feature Extraction and Classification

Discriminant analysis, as a widely used approach in machine learning to extract low-dimensional features from the high-dimensional data, applies the Fisher discriminant criterion to find the orthogonal discriminant projection subspace. But most of the Euclidean-based algorithms for discriminant analysis are easily convergent to a spurious local minima and hardly obtain an unique solution. To address such problem, in this study we propose a novel method named Riemannian-based Discriminant Analysis (RDA), which transforms the traditional Euclidean-based methods to the Riemannian manifold space. In RDA, the second-order geometry of trust-region methods is utilized to learn the discriminant bases. To validate the efficiency and effectiveness of RDA, we conduct a variety of experiments on image classification tasks. The numerical results suggest that RDA can extract statistically significant features and robustly outperform state-of-the-art algorithms in classification tasks.