Fast and accurate Nearest Neighbor search in the manifolds of symmetric positive definite matrices

In this paper, we present a fast and accurate Nearest Neighbor (NN) search method in the Riemannian manifolds formed by a kind of structured data - symmetric positive definite (SPD) matrices. We use an ensemble of vocabulary trees based on hierarchical k-means clustering and query these trees to find the NN candidates in sub-linear time. As generating these vocabulary trees with widely used affine-invariant Riemannian metric (AIRM) will be very time-demanding, we propose to use the second-order approximation to AIRM (SOA-AIRM). We evaluate the proposed NN search algorithm in the application scenario of near-duplicate image detection in a large database. Experimental results demonstrate that the proposed method significantly outperforms state of the art techniques in terms of both accuracy and speed.