Classification with Invariant Distance Substitution Kernels

Kernel methods offer a flexible toolbox for pattern analysis and machine learning. A general class of kernel functions which incorporates known pattern invariances are invariant distance substitution (IDS) kernels. Instances such as tangent distance or dynamic timewarping kernels have demonstrated the real world applicability. This motivates the demand for investigating the elementary properties of the general IDS-kernels. In this paper we formally state and demonstrate their invariance properties, in particular the adjustability of the invariance in two conceptionally different ways. We characterize the definiteness of the kernels. We apply the kernels in different classification methods, which demonstrates various benefits of invariance.