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

概要

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Since Hamming distances can be calculated by bitwise computations, they can be calculated with a lighter computational load than L2 distances. Similarity searches can therefore be performed faster in Hamming distance space. On the other hand, the arrangement of hyperplanes induces a transformation from the feature vectors into feature bit strings, which are elements of the Hamming distance space. This transformation 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 enables us to devise a method that transforms the higher-dimensional feature vectors into feature bit strings that reflect the information about the labels applied to feature vectors. In this paper, 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 data pairs needed in learning and evaluate its performance. The performance evaluations indicate that the accuracy of this learning method, when using a suitable probability density function and sampling method, is greater than those of existing learning methods.
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