  Linear discriminant analysis (LDA) is a widely used algorithm in machine
learning to extract a low-dimensional representation of high-dimensional data,
it features to find the orthogonal discriminant projection subspace by using
the Fisher discriminant criterion. However, the traditional Euclidean-based
methods for solving LDA are easily convergent to spurious local minima and
hardly obtain an optimal solution. To address such a problem, in this paper, we
propose a novel algorithm namely Riemannian-based discriminant analysis (RDA)
for subspace learning. In order to obtain an explicit solution, we transform
the traditional Euclidean-based methods to the Riemannian manifold space and
use the trust-region method to learn the discriminant projection subspace. We
compare the proposed algorithm to existing variants of LDA, as well as the
unsupervised tensor decomposition methods on image classification tasks. The
numerical results suggest that RDA achieves state-of-the-art performance in
classification accuracy.
