Joint distance and similarity measure learning based on triplet-based constraints

Distance and similarity measures usually are complementary to pattern classification. With pairwise constraints, several approaches have been proposed to combine distance and similarity measures. However, it remains less investigated to use triplets of samples for joint learning of distance and similarity measures. Moreover, the kernel extension of triplet-based model is also nontrivial and computationally expensive. In this paper, we propose a novel method to learn a combined distance and similarity measure (CDSM). By incorporating with the max-margin model, we suggest a triplet-based CDSM learning model with a unified regularizer of the Frobenius norm. A support vector machine (SVM)-based algorithm is then adopted to solve the optimization problem. Furthermore, we extend CDSM for learning nonlinear measures via the kernel trick. Two effective strategies are adopted to speed up training and testing of kernelized CDSM. Experiments on the UCI, handwritten digits and person re-identification datasets demonstrate that CDSM and kernelized CDSM outperform several state-of-the-art metric learning methods.