Distance Preserving Projection Space of Symmetric Positive Definite Manifolds

Recent advances in computer vision suggest that encoding images through Symmetric Positive Definite (SPD) matrices can lead to increased classification performance. Taking into account manifold geometry is typically done via embedding the manifolds in tangent spaces, or Reproducing Kernel Hilbert Spaces (RKHS). Recently it was shown that projecting such manifolds into a kernel-based random projection space (RPS) leads to higher classification performance. In this paper, we propose to learn an optimized projection, based on building local and global sparse similarity graphs that encode the association of data points to the underlying subspace of each point. To this end, we project SPD matrices into an optimized distance preserving projection space (DPS), which can be followed by any Euclidean-based classification algorithm. Further, we adopt the concept of dictionary learning and sparse coding, and discriminative analysis, for the learned DPS on SPD manifolds. Experiments on face recognition, texture classification, person re-identification, and virus classification demonstrate that the proposed methods outperform state-of-the-art methods on such manifolds