Riemannian Coding and Dictionary Learning: Kernels to the Rescue Supplementary Material

This supplementary material is organized into following sections: • Derivation of the solution of intrinsic locality constrained coding (Section 2.1 of the main paper). • Proof of Theorem 3.1 (Section 3.1 of the main paper). • Derivation of the solution of kernel locality constrained coding (Section 3.2 of the main paper). • Pseudo-code of our kernel-based supervised dictionary learning algorithm (Section 4.2 of the main paper). • Recognition curves for the experiments on SPD manifolds (Section 6.1 of the main paper). • Recognition curves for the experiments on Grassmann manifolds (Section 6.2 of the main paper). • Additional experiments on the shape manifold. 1. Intrinsic Locality Constrained Coding Here, we provide a closed-form solution for our Intrinsic Locality Constrained Coding (int-LCC) method (Section 2.1 of the main paper). Given a Riemannian manifold M and a dictionary D = {di}Ni=1, di ∈ M, we define intrinsic Locality Constrained Coding (int-LCC) as the solution of min α N