Robust Estimation in Reproducing Kernel Hilbert

Our work shows that estimating the mean in a feature space induced by certain1 kinds of kernels is the same as doing a robust mean estimation using an M-estimator2 in the original problem space. In particular, we show that calculating the average on3 a feature space induced by a Gaussian kernel is equivalent to perform robust mean4 estimation with the Welsch M-estimator. Besides, a new framework is proposed5 that was used to build four new robust kernels: Tukey’s, Andrews’, Huber’s and6 Cauchy’s robust kernels. The new robust kernels, combined with kernel matrix7 factorization clustering algorithm, were compared to state-of-the-art algorithms in8 clustering tasks. The result shows that some of the new robust kernels perform in a9 par with state-of-the-art algorithms