Abstract

We tackle the problem of optimizing over all possible positive defifinite radial kernels on Riemannian manifolds for classifification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive defifi- nite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield signifificant performance drop-off. Here, we show that positive defifinite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall’s shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefifits of our kernel learning algorithm on object, face, action and shape recognition