A Scalable Algorithm for Learning a Mahalanobis Distance Metric

In this work, we propose a scalable and fast algorithm to learn a Mahalanobis distance metric. The key issue in this task is to learn an optimal Mahalanobis matrix in this distance metric. It has been shown in the statistical learning theory [?] that increasing the margin between different classes helps to reduce the generalization error. Hence, our algorithm formulates the Mahalanobis matrix as a variable of the margin and optimizes it via margin maximization. By doing so, the learned Mahalanobis distance metric can achieve sufficient separation at the boundaries between different classes. More importantly, we address the scalability problem of learning a Mahalanobis distance in the presence of high-dimensional feature vectors, which is a critical issue of distance metric learning.