Learning With Asymmetric Kernels: Least Squares and Feature Interpretation

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 various tasks, including Corel, PASCAL VOC, Satellite, directed graphs, and UCI database, all 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 rely on symmetrization to accommodate asymmetric kernels.