Distance metric learning has been successfully incorporated in many machine learning applications. The main challenge arises from the positive semidefiniteness constraint on the Mahalanobis matrix, which results in a high computational cost. In this paper, we develop a novel approach to reduce this computational burden. We first map each training example into a new space by an orthonormal transformation. Then, in the transformed space, we simply learn a diagonal matrix. This two-phase approach is thus much easier and less costly than learning a full Mahalanobis matrix in one phase as is commonly done
