An efficient method for clustered multi-metric learning

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.

Asymmetric Weighted Logistic Metric Learning for Hyperspectral Target Detection

Traditional target detection methods assume that the background spectrum is subject to the Gaussian distribution, which may only perform well under certain conditions. In addition, traditional target detection methods suffer from the problem of the unbalanced number of target and background samples. To solve these problems, this study presents a novel target detection method based on asymmetric weighted logistic metric learning (AWLML). We first construct a logistic metric-learning approach as an objective function with a positive semidefinite constraint to learn the metric matrix from a set of labeled samples. Then, an asymmetric weighted strategy is provided to emphasize the unbalance between the number of target and background samples. Finally, an accelerated proximal gradient method is applied to identify the global minimum value. Extensive experiments on three challenging hyperspectral datasets demonstrate that the proposed AWLML algorithm improves the state-of-the-art target detection performance.

A multi-birth metric learning framework based on binary constraints

Multi-metric learning plays a significant role in improving the generalization of algorithms related to distance metrics since using a single metric is sometimes insufficient to handle complex data. Metric learning can adjust automatically the distance between samples to make the intra-class samples compact while making the inter-class distance as far as possible. To implement this intention better,in this work, we propose a novel multi-metric learning framework based on the pair constraints instead of triple constraints to reduce computational burden. To solve effectively the problem, we first propose a multi-birth metric learning model (termed MBML), where for each class sample, the global metric and a local metric are jointly trained. Both global and local structural information are adapted to better depict sample information. Then two alternating iterative algorithms are developed to optimize the MBML. The convergence of the proposed algorithm and complexity are analyzed theoretically. Moreover, a fast diagonal multi-metric learning method is proposed based on binary constraints, and problem can be reformulated a linear programming, with fast training speed, low the computational burden and the global optimal solutions. Numerical experiments are carried out on different scales and different types of datasets including an artificial data, benchmark datasets and an image database from binary class and multi-class problems. Experiment results confirm the feasibility and effectiveness of the proposed methods.