Conditional High-Order Boltzmann Machine: A Supervised Learning Model for Relation Learning

Relation learning is a fundamental operation in many computer vision tasks. Recently, high-order Boltzmann machine and its variants have exhibited the great power of modelling various data relation. However, most of them are unsupervised learning models which are not very discriminative and thus cannot server as a standalone solution to relation learning tasks. In this paper, we explore supervised learning algorithms and propose a new model named Conditional High-order Boltzmann Machine (CHBM), which can be directly used as a bilinear classifier to assign similarity scores for pairwise images. Then, to better deal with complex data relation, we propose a gated version of CHBM which untangles factors of variation by exploiting a set of latent variables to gate classification. We perform four-order tensor factorization for parameter reduction, and present two efficient supervised learning algorithms from the perspectives of being generative and discriminative, respectively. The experimental results of image transformation visualization, binary-way classification and face verification demonstrate that, by performing supervised learning, our models can greatly improve the performance.