Cross product kernels for fuzzy set similarity

We present a new kernel on fuzzy sets: the Cross Product kernel on fuzzy sets. This kernel implements a similarity measure between fuzzy sets with a geometrical interpretation in Reproducing Kernel Hilbert Spaces. We prove that this kernel is a convolution kernel that generalizes the widely know kernel on sets towards the space of fuzzy sets. Moreover, we show that the Cross Product kernel on fuzzy sets performs an embedding of probability measures into a Reproduction Kernel Hilbert space. Finally, we validated the kernel performance through experiments on supervised classification on noisy datasets.