Robust kernels for robust location estimation November 2020Neurocomputing 429(1) Follow journal DOI: 10.1016/j.neucom.2020.10.090 Project: Robust Clustering Algorithms
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 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.
Cite as
@article{GALLEGO2021174,
title = {Robust kernels for robust location estimation},
journal = {Neurocomputing},
volume = {429},
pages = {174-186},
year = {2021},
issn = {0925-2312},
doi = {https://doi.org/10.1016/j.neucom.2020.10.090},
url = {https://www.sciencedirect.com/science/article/pii/S0925231220317033},
author = {Joseph A. Gallego and Fabio A. González and Olfa Nasraoui},
keywords = {Robust statistics, M-estimators, Kernel methods, Kernel clustering, Kernel matrix factorization},
abstract = {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 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.}
}