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

Abstract

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 affineinvariant Riemannian metric (AIRM) will be very timedemanding, 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. Index Terms—near duplicate image detection, nearest neighbor search, Riemannian manifold, vocabulary forest.