Invariant kernel functions for pattern analysis and machine learning

Abstract

In many learning problems prior knowledge about pattern variations can be formalized and beneficially incorporated into the analysis system. The corresponding notion of invariance is commonly used in conceptionally different ways. We propose a more distinguishing treatment in particular in the active field of kernel methods for machine learning and pattern analysis. Additionally, the fundamental relation of invariant kernels and traditional invariant pattern analysis by means of invariant representations will be clarified. After addressing these conceptional questions, we focus on practical aspects and present two generic approaches for constructing invariant kernels. The first approach is based on a technique called invariant integration. The second approach builds on invariant distances. In principle, our approaches support general transformations in particular covering discrete and non-group or even an infinite number of pattern-transformations. Additionally, both enable a smooth interpolation between invariant and non-invariant pattern analysis, i.e. they are a covering general framework. The wide applicability and various possible benefits of invariant kernels are demonstrated in different kernel methods. © Springer Science+Business Media, LLC 2007.