Semi-supervised Distance Metric Learning in High-Dimensional Spaces by Using Equivalence Constraints

Abstract. This paper introduces a semi-supervised distance metric learning al-gorithm which uses pairwise equivalence (similarity and dissimilarity) constraints to discover the desired groups within high-dimensional data. In contrast to the tra-ditional full rank distance metric learning algorithms, the proposed method can learn nonsquare projection matrices that yield low rank distance metrics. This brings additional benefits such as visualization of data samples and reducing the storage cost, and it is more robust to overfitting since the number of estimated parameters is greatly reduced. The proposed method works in both the input and kernel induced-feature space, and the distance metric is found by a gradient de-scent procedure that involves an eigen-decomposition in each step. Experimental results on high-dimensional visual object classification problems show that the computed distance metric improves the performances of the subsequent classifi-cation and clustering algorithms.