Scalable Metric Learning via Weighted Approximate Rank Component Analysis

Our goal is to learn a Mahalanobis distance by minimizing a loss defined on the weighted sum of the precision at different ranks. Our core motivation is that minimizing a weighted rank loss is a natural criterion for many problems in computer vision such as person re-identification. We propose a novel metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). We then derive a scalable stochastic gradient descent algorithm for the resulting learning problem. We also derive an efficient non-linear extension of WARCA by using the kernel trick. Kernel space embedding decouples the training and prediction costs from the data dimension and enables us to plug inarbitrary distance measures which are more natural for the features. We also address a more general problem of matrix rank degeneration & non-isolated minima in the low-rank matrix optimization by using new type of regularizer which approximately enforces the orthonormality of the learned matrix very efficiently. We validate this new method on nine standard person re-identification datasets including two large scale Market1501 and CUHK03 datasets and show that we improve upon the current state-of-the-art methods on all of them.