Optimizing Over Radial Kernels on Compact Manifolds
This addresses the need for better kernel selection in computer vision applications on manifolds, though it appears incremental as it builds on existing SVM and kernel methods.
The authors tackled the problem of limited positive definite radial kernels on Riemannian manifolds for classification by developing a kernel learning algorithm that automatically optimizes kernel parameters within an SVM framework, demonstrating benefits on object, face, action, and shape recognition tasks.
We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite 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 significant performance drop-off. Here, we show that positive definite 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 benefits of our kernel learning algorithm on object, face, action and shape recognition.