Asymmetric Local Metric Learning with PSD Constraint for Person Re-identification

Person re-identification is one of the key issues in both machine learning and video monitor application. In particular, defining an appropriate distance metric between the person images is very important. Existing metric learning approaches used in person re-identification either learn a single measure, or ignore the positive semi-definite (PSD) of measurement matrix, at the same time, since the number of negative sample pairs largely exceeds the number of positive sample pairs, some metric learning methods are largely influenced by the sample imbalance. Considering the above issues, we propose a new adaptive local metric learning method with positive semi-definite (PSD) constraint. Unlike existing metric learning methods which learn a single distance metric, we use an approximation error bound of a smooth metric matrix function over the data manifold to learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. Besides, we develop an efficient two stage algorithm that first learns the anchor points and the linear combinations of each instance, then learns the metric matrices of the anchor points. We employ the fast iterative shrinkage-thresholding algorithm which is a fast first-order optimization algorithm in the learning process of the linear combinations as well as the basis metrics of the anchor points. Our metric learning method has excellent performance. We firstly apply the proposed method on 5 UCI databases, which are widely used in machine learning, to test and evaluate the effectiveness of the proposed method. Then the proposed approach is applied for person re-identification, achieving better performance on three challenging databases (GRID, VIPeR, CUHK01) than the existing methods. The experimental results show that the proposed method can prvide the theoretical and practical support for the person re-identification problem.