Markov Chain Monte Carlo for Arrangement of Hyperplanes in Locality-Sensitive Hashing
This work addresses the need for faster and more accurate approximate similarity searches in machine learning, though it appears incremental as it builds on existing supervised learning methods for hyperplane arrangements.
The paper tackles the problem of supervised learning for hyperplane arrangements in locality-sensitive hashing to improve similarity search accuracy, and it confirms that using a suitable probability density function and sampling method yields greater accuracy than existing methods.
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.