Similarity learning on an explicit polynomial kernel feature map for person re-identification

In this paper, we address the person re-identification problem, discovering the correct matches for a probe person image from a set of gallery person images. We follow the learning-to-rank methodology and learn a similarity function to maximize the difference between the similarity scores of matched and unmatched images for a same person. We introduce at least three contributions to person re-identification. First, we present an explicit polynomial kernel feature map, which is capable of characterizing the similarity information of all pairs of patches between two images, called soft-patch-matching, instead of greedily keeping only the best matched patch, and thus more robust. Second, we introduce a mixture of linear similarity functions that is able to discover different soft-patch-matching patterns. Last, we introduce a negative semi-definite regularization over a subset of the weights in the similarity function, which is motivated by the connection between explicit polynomial kernel feature map and the Mahalanobis distance, as well as the sparsity constraint over the parameters to avoid over-fitting. Experimental results over three public benchmarks demonstrate the superiority of our approach.