Learning Equivariant Functions with Matrix Valued Kernels - Theory and Applications
At Freiburg, Ur Informatik · 2006
This paper presents a new class of matrix valued kernels, which are ideally suited to learn vector valued equivariant functions. Matrix valued kernels are a natural generalization of the common notion of a kernel. We set the theoretical foundations of so called equivariant matrix valued kernels. We work out several properties of equivariant kernels, we give an interpretation of their behavior and show relations to scalar kernels. Further we translate the notion of (ir)reducibility of group representations into the framework of matrix valued kernels. Finally we give two exemplary applications. We design a non-linear rotation and translation equivariant filter for 2D-images and propose an invariant object detector based on the generalized Hough transform. 1