Broad Metric Learning: A Fast and Efficient Discriminative Metric Learning Model

Metric learning aims to learn a discriminative metric space, where samples of the same class stay close, and those of different classes far apart. Existing classical metric learning methods based on linear transformation have limited learning performance due to the low representation capability. Although deep metric learning learns nonlinear mappings, the training may come across convergence issues and be unstable. Additionally, many classical metric learning algorithms suffer from long computational time for iterative optimization especially when data dimension is high. Deep metric learning also requires high training cost. To learn a metric space more efficiently and effectively, this article proposes a novel broad metric learning (BML) model, which learns the data transformation by training a broad network. BML maps input data to a broad feature space by fast and convenient nonlinear feature mapping based on random weights, and learns a linear transformation to a discriminative output space. Intraclass distance is reduced by minimizing the distance between data and their class-specific reference points in the target space. The hard-triplet distance learning (HDL) is proposed to learn the distance of hard positive and negative sample pairs, which enhances the intraclass compactness and interclass separation. Closed-form solutions are adopted to solve the optimization problems efficiently when learning the linear transformation. Experiments are conducted on nine datasets to verify the efficiency and effectiveness of BML. BML learns fast and achieves high classification and clustering accuracies in the learned data space.