Semi-supervised metric learning via topology preserving multiple semi-supervised assumptions

Learning an appropriate distance metric is a critical problem in pattern recognition. This paper addresses the problem of semi-supervised metric learning. We propose a new regularized semi-supervised metric learning (RSSML) method using local topology and triplet constraints. Our regularizer is designed and developed based on local topology, which is represented by local neighbors from the local smoothness, cluster (low density) and manifold information point of view. The regularizer is then combined with the large margin hinge loss on the triplet constraints. In other words, we keep a large margin between different labeled samples, and in the meanwhile, we use the unlabeled samples to regularize it. Then the semi-supervised metric learning method is developed. We have performed experiments on classification using publicly available databases to evaluate the proposed method. To our best knowledge, this is the only method satisfying all the three semi-supervised assumptions, namely smoothness, cluster (low density) and manifold. Experimental results have shown that the proposed method outperforms state-of-the-art semi-supervised distance metric learning algorithms.