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Robust kernels for robust location estimation
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DOI：10.1016/j.neucom.2020.10.090.png)
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Abstract
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This paper shows that least-square estimation (mean calculation) in a reproducing kernel Hilbert space (RKHS) F corresponds to different M-estimators in the original space depending on the kernel function associated with F. In particular, we present a proof of the correspondence of mean estimation in an RKHS for the Gaussian kernel with robust estimation in the original space performed with the Welsch Mestimator. This result is generalized to other types of M-estimators. This generalization facilitates the definition of new robust kernels associated to Huber, Tukey, Cauchy and Andrews M-estimators. The new kernels are empirically evaluated in different clustering tasks where state-of-the-art robust clustering methods are compared to kernel-based clustering using robust kernels. The results show that some robust kernels perform on a par with the best state-of-the-art robust clustering methods. (C) 2020 Elsevier B.V. All rights reserved.
Keywords:
Robust statistics
M-estimators
Kernel methods
Kernel clustering
Kernel matrix factorization
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