Distance metric learning based on the class center and nearest neighbor relationship

Distance metric learning has been a promising technology to improve the performance of algorithms related to distance metrics. The existing distance metric learning methods are either based on the class center or the nearest neighbor relationship. In this work, we propose a new distance metric learning method based on the class center and nearest neighbor relationship (DMLCN). Specifically, when centers of different classes overlap, DMLCN first splits each class into several clusters and uses one center to represent one cluster. Then, a distance metric is learned such that each example is close to the corresponding cluster center and the nearest neighbor relationship is kept for each receptive field. Therefore, while characterizing the local structure of data, the proposed method leads to intra-class compactness and inter-class dispersion simultaneously. Further, to better process complex data, we introduce multiple metrics into DMLCN (MMLCN) by learning a local metric for each center. Following that, a new classification decision rule is designed based on the proposed methods. Moreover, we develop an iterative algorithm to optimize the proposed methods. The convergence and complexity are analyzed theoretically. Experiments on different types of data sets including artificial data sets, benchmark data sets and noise data sets show the feasibility and effectiveness of the proposed methods.