Yui Noma

Markov Chain Monte Carlo for Arrangement of Hyperplanes in Locality-Sensitive Hashing

Since Hamming distances can be calculated by bitwise computations, they can be calculated with less computational load than L2 distances. Similarity searches can therefore be performed faster in Hamming distance space. The elements of Hamming distance space are bit strings. On the other hand, the arrangement of hyperplanes induce the transformation from the feature vectors into feature bit strings. This transformation method is a type of locality-sensitive hashing that has been attracting attention as a way of performing approximate similarity searches at high speed. Supervised learning of hyperplane arrangements allows us to obtain a method that transforms them into feature bit strings reflecting the information of labels applied to higher-dimensional feature vectors. In this p aper, we propose a supervised learning method for hyperplane arrangements in feature space that uses a Markov chain Monte Carlo (MCMC) method. We consider the probability density functions used during learning, and evaluate their performance. We also consider the sampling method for learning data pairs needed in learning, and we evaluate its performance. We confirm that the accuracy of this learning method when using a suitable probability density function and sampling method is greater than the accuracy of existing learning methods.

Inverse Stereographic Projecting Hashing for Fast Similarity Search

Fast similarity searches that use high-dimensional feature vectors for a vast amount of multi-media data have recently become increasingly important. However, ordinary similarity searches are slow because they require a large number of floating-point operations that are proportional to the number of record data. Many studies have been done recently that propose to speed up similarity searches by converting feature vectors to bit vectors. Such similarity searches are regarded as approximations of the similarity searches over the original data. However, some of those approximations are not theoretically guaranteed since no direct approximate relations between the Euclidean and Hamming distances are given. We propose a novel hashing method that utilizes inverse-stereographic projection and gives a direct approximate relation between the Euclidean and Hamming distances in a closed-form expression. Although some studies have discussed the relationship between the two distances, to the best of our knowledge, our hashing method is the first one to give a direct approximate relation between the two distances. We also propose parameter values that are needed for our proposal method. Furthermore, we show through experiments that the proposed method has more accurate approximation than the existing random projection-based and Hamming distance-based methods for many datasets.