  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.
