An efficient multi-metric learning method by partitioning the metric space

Abstract

Metric learning has attracted significant attention due to its high effectiveness and efficiency for pattern recognition task. Traditional supervised metric learning algorithms attempt to seek a global distance metric with labeled samples. When data are represented with multimodal and only limited supervision information is available, these approaches are insufficient to obtain satisfactory results. In this paper, we develop a robust semi-supervised multi-metric learning method (RSMM) to improve classification performance. The proposed RSMM learns multiple local metrics and a background metric instead of a single global metric. Specifically, we divide the metric space into influential regions and background region, and then regulate the effectiveness of each local metric to be within the related regions. Simultaneously, a geometrically interpretable, symmetric distance is defined with local metrics and background metric. Based on the resultant learning bounds, we obtain the regularization term to improve the classifier’s generalization ability. Moreover, the manifold regularization term is introduced to preserve the supervision information as well as geometry structure. The substantial unlabeled samples may cause potential threats and large uncertainties, so the logarithmic loss function is utilized to enhance the robustness. An efficient gradient descent algorithm is exploited to solve the non-convex challenging problem. To further understand the proposed algorithm, we theoretically derive its robustness and generalization error bounds. Finally, numerical experiments on UCI datasets and image datasets demonstrate the feasibility and validity of the RSMM.