Riemannian-based Discriminant Analysis for Feature Extraction and Classification

• URL: http://arxiv.org/abs/2101.08032v2
• Date: Tue, 26 Jan 2021 07:17:29 GMT
• Title: Riemannian-based Discriminant Analysis for Feature Extraction and Classification
• Authors: Wanguang Yin, Zhengming Ma, Quanying Liu
• Abstract summary: Discriminant analysis is a widely used approach in machine learning to extract low-dimensional features from the high-dimensional data. Traditional Euclidean-based algorithms for discriminant analysis are easily convergent to a spurious local minima. We propose a novel method named Riemannian-based Discriminant Analysis (RDA), which transforms the traditional Euclidean-based methods to the Riemannian manifold space.
• Score: 2.1485350418225244
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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