Robust kernels for robust location estimation

Joseph A. Gallego, Fabio A. González & Olfa Nasraoui
Neurocomputing, Volume 429, Pages 174–186 (2021)
DOI: https://doi.org/10.1016/j.neucom.2020.10.090
Publisher: Elsevier / ScienceDirect

Abstract:
This paper shows that least-square estimation (mean calculation) in a reproducing kernel Hilbert space (RKHS) corresponds to different M-estimators in the original space depending on the kernel function associated with . 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 M-estimator. 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.

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📌 BibTeX citation

@article{gallego2021robustKernels,
  title   = {Robust kernels for robust location estimation},
  author  = {Gallego, Joseph A. and Gonz\'alez, Fabio A. and Nasraoui, Olfa},
  journal = {Neurocomputing},
  volume  = {429},
  pages   = {174--186},
  year    = {2021},
  doi     = {10.1016/j.neucom.2020.10.090},
  url     = {https://www.sciencedirect.com/science/article/pii/S0925231220317033}
}