This paper describes a semi-supervised distance metric learning algorithm which uses pairwise equivalence (similarity and dissimilarity) constraints to discover the desired groups within high-dimensional data. As opposed to the traditional 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. Our method works in both the input and kernel induced-feature space, and the distance metric is found by a gradient descent 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 performance of the subsequent clustering algorithm.