Discriminative subspace learning via optimization on Riemannian manifold

Abstract

Discriminative subspace learning is an important problem in machine learning, which aims to find the maximum separable decision subspace. Traditional Euclidean-based methods usually use Fisher discriminant criterion for finding an optimal linear mapping from a high-dimensional data space to a lower-dimensional subspace, which hardly guarantee a quadratic rate of global convergence and suffers from the singularity problem. Here, we propose the manifold optimization-based discriminant analysis (MODA) which is constructed by using the latent subspace alignment and the geometry of objective function with orthogonality constraint. MODA is solved by using Riemannian version of trust-region algorithm. Experimental results on various image datasets and electroencephalogram (EEG) datasets show that MODA achieves the best separability and is significantly superior to the competing algorithms. Especially for the time series of EEG signals, the accuracy of MODA is 20–30% higher than existing algorithms. The code for MODA is available at https://github.com/ncclabsustech/MODA-algorithm.