Learning kernels from labels with ideal regularization

In this paper, we propose a new form of regularization that is able to utilize the label information of a data set for learning kernels. We first present the definition of extended ideal kernel for both labeled and unlabeled data of multiple classes. Based on this extended ideal kernel, we propose an ideal regularization which is a linear function of the kernel matrix to be learned. The ideal regularization allows us to develop effective algorithms to exploit labels. Two applications of the ideal regularization are considered. Empirical results show the ideal regularization exploits the labels effectively.