Learning Translation Invariant Kernels for Classification

Appropriate selection of the kernel function, which implicitly defines the feature space of an algorithm, has a crucial role in the success of kernel methods. In this paper, we consider the problem of optimizing a kernel function over the class of translation invariant kernels for the task of binary classification. The learning capacity of this class is invariant with respect to rotation and scaling of the features and it encompasses the set of radial kernels. We show that how translation invariant kernel functions can be embedded in a nested set of sub-classes and consider the kernel learning problem over one of these sub-classes. This allows the choice of an appropriate sub-class based on the problem at hand. We use the criterion proposed by Lanckriet et al. (2004) to obtain a functional formulation for the problem. It will be proven that the optimal kernel is a finite mixture of cosine functions. The kernel learning problem is then formulated as a semi-infinite programming (SIP) pr...

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Sayed Kamaledin Ghiasi Shirazi, Reza Safabakhsh, Mostafa Shamsi
• Keywords: Cosine Kernels, JMLR 2010, Kernel Functions, Translation Invariant Kernel