Conditionally positive definite kernels for SVM based image recognition

Kernel based methods such as Support Vector Machine (SVM) have provided successful tools for solving many recognition problems. One of the reason of this success is the use of kernels. Positive defi niteness has to be checked for kernels to be suitable for most of these methods. For instance for SVM, the use of a positive defi nitekernel insures that the optimized problem is convex and thus the obtained solution is unique. Alternative class of kernels called conditionally positive defi nitehave been studied for a long time from the theoretical point of view and have drawn attention from the community only in the last decade. We propose a new kernel, named log kernel, which seems particularly interesting for images. Moreover, we prove that this new kernel is a conditionally positive defi nitekernel as well as the power kernel. Finally, we show from experimentations that using conditionally positive defi nite kernels allows us to outperform classical positive defi nitekernels.