Learning Kernel for Conditional Moment-Matching Discrepancy-based Image Classification

Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does not work well on complex distributions, especially when the kernel function fails to correctly characterize the difference between intra-class similarity and inter-class similarity. In this paper, a new kernel learning method is proposed to improve the discrimination performance of CMMD. It can be operated with deep network features iteratively and thus denoted as KLN for abbreviation. The CMMD loss and an auto-encoder (AE) are used to learn an injective function. By considering the compound kernel, i.e., the injective function with a characteristic kernel, the effectiveness of CMMD for data category description is enhanced. KLN can simultaneously learn a more expressive kernel and label prediction distribution, thus, it can be used to improve the classification performance in both supervised and semi-supervised learning scenarios. In particular, the kernel-based similarities are iteratively learned on the deep network features, and the algorithm can be implemented in an end-to-end manner. Extensive experiments are conducted on four benchmark datasets, including MNIST, SVHN, CIFAR-10 and CIFAR-100. The results indicate that KLN achieves state-of-the-art classification performance.