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.