Discriminative distance metric learning via class-center guidance

Distance metric learning is a technique of great importance to machine learning and data processing, which can effectively improve the generalization performance of algorithms related to distance metrics. The method projects the original data to the metric space through a transformation to realize the automatic adjustment of the distance between samples, so as to achieve the increase of the between-class distance and the decrease of the within-class distance. To better achieve this goal, we propose a discriminative distance metric learning via class-center guidance (DML-CG). The proposed DML-CG learns a novel discriminative distance metric by maximizing the trace ratio of between-class covariance to within-class covariance, and at the same time transforms the trace ratio problem into a ratio-trace problem to find the global optimal solution. In addition, this method selects k nearest neighbors for each training sample to generate sample pairs, and jointly uses local metrics learned from multiple class-center guidance and a global metric to guide samples of the same class closer to the class center, and samples of different class farther away from the sample class center. This achieves both the distance metric and captures the discriminative structure of the data. Meanwhile, global regularization is introduced to improve the generalization performance and control overfitting. We design an alternating iteration algorithm to optimally solve the proposed method and theoretically analyze the convergence and complexity. Finally, the effectiveness of the proposed algorithm is demonstrated on structured artificial datasets and UCI datasets as well as unstructured image recognition datasets. Most of the results show that the proposed algorithm outperforms other state-of-the-art distance metric learning methods.