Isometric Mapping Hashing

Hashing is a popular solution to Approximate Nearest Neighbor (ANN) problems. Many hashing schemes aim at preserving the Euclidean distance of the original data. However, it is the geodesic distance rather than the Euclidean distance that more accurately characterizes the semantic similarity of data, especially in a high dimensional space. Consequently, manifold based hashing methods have achieved higher accuracy than conventional hashing schemes. To compute the geodesic distance, one should construct a nearest neighbor graph and invoke the shortest path algorithm, which is too expensive for a retrieval task. In this paper, we present a hashing scheme that preserves the geodesic distance and use a feasible out-of-sample method to generate the binary codes efficiently. The experiments show that our method outperforms several alternative hashing methods.