Sparse Isotropic Hashing

Abstract

This paper address the problem of binary coding of real vectors for efficient similarity computations. It has been argued that orthogonal transformation of center-subtracted vectors followed by sign function produces binary codes which well preserve similarities in the original space, especially when orthogonally transformed vectors have covariance matrix with equal diagonal elements. We propose a simple hashing algorithm that can orthogonally transform an arbitrary covariance matrix to the one with equal diagonal elements. We further expand this method to make the projection matrix sparse, which yield faster coding. It is demonstrated that proposed methods have comparable level of similarity preservation to the existing methods.