  Asymmetric kernels naturally exist in real life, e.g., for conditional
probability and directed graphs. However, most of the existing kernel-based
learning methods require kernels to be symmetric, which prevents the use of
asymmetric kernels. This paper addresses the asymmetric kernel-based learning
in the framework of the least squares support vector machine named AsK-LS,
resulting in the first classification method that can utilize asymmetric
kernels directly. We will show that AsK-LS can learn with asymmetric features,
namely source and target features, while the kernel trick remains applicable,
i.e., the source and target features exist but are not necessarily known.
Besides, the computational burden of AsK-LS is as cheap as dealing with
symmetric kernels. Experimental results on the Corel database, directed graphs,
and the UCI database will show that in the case asymmetric information is
crucial, the proposed AsK-LS can learn with asymmetric kernels and performs
much better than the existing kernel methods that have to do symmetrization to
accommodate asymmetric kernels.
