Metric learning with geometric mean for similarities measurement

Abstract

Distance metric learning aims to find an appropriate method to measure similarities between samples. An excellent distance metric can greatly improve the performance of many machine learning algorithms. Most previous methods in this area have focused on finding metrics which utilize large-margin criterion to optimize compactness and separability simultaneously. One major shortcoming of these methods is their failure to balance all between-class scatters when the distributions of samples are extremely unbalanced. Large-margin criterion tends to maintain bigger scatters while abandoning those smaller ones to make the total scatters maximized. In this paper, we introduce a regularized metric learning framework, metric learning with geometric mean which obtains a distance metric using geometric mean. The novel method balances all between-class scatters and separates samples from different classes simultaneously. Various experiments on benchmark datasets show the good performance of the novel method.