  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.
