For better describing pedestrian’s appearance, the feature representations used in person re-identification are usually of high dimension - typically amounting to thousands or even higher. However, this incurs the typical Small Sample Size (SSS) problem, i.e., the number of training samples in most re-identification datasets is much smaller than the feature dimension. Although some dimension reduction techniques or metric regularization could be applied to alleviate this problem, they may result in the loss of discriminative power.

In this work, we propose to overcome SSS problem by embedding training samples into a discriminative null space based on Marginal Fisher Analysis (MFA). In such a null space, the within-class distribution of the images of the same pedestrian will shrink to a single point, resulting the extreme fisher analysis criterion. We theoretically analyze the subspace where the discriminant vectors lie on and derive a closed-form solution. Furthermore, we also extend the proposed method to nonlinear domain via the kernel trick. Experiments on VIPeR, PRID450S and 3DPes benchmark datasets show that our method achieves 56.30%, 76.80% and 66.88% rank-1 matching rates respectively, outperforming the state-of-the-art results by 2.74%, 15.38% and 9.59%.