Distance Metric Learning Revisited

The success of many machine learning algorithms (e.g. the nearest neighborhood classification and k-means clustering) depends on the representation of the data as elements in a metric space. Learning an appropriate distance metric from data is usually superior to the default Euclidean distance. In this paper, we revisit the original model proposed by Xing et al. [25] and propose a general formulation of learning a Mahalanobis distance from data. We prove that this novel formulation is equivalent to a convex optimization problem over the spectrahedron. Then, a gradient-based optimization algorithm is proposed to obtain the optimal solution which only needs the computation of the largest eigenvalue of a matrix per iteration. Finally, experiments on various UCI datasets and a benchmark face verification dataset called Labeled Faces in the Wild (LFW) demonstrate that the proposed method compares competitively to those state-of-the-art methods.