AUTHOR=Rudi Alessandro , De Vito Ernesto , Verri Alessandro , Odone Francesca TITLE=Regularized Kernel Algorithms for Support Estimation JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=3 YEAR=2017 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00023 DOI=10.3389/fams.2017.00023 ISSN=2297-4687 ABSTRACT=

In the framework of non-parametric support estimation, we study the statistical properties of a set estimator defined by means of Kernel Principal Component Analysis. Under a suitable assumption on the kernel, we prove that the algorithm is strongly consistent with respect to the Hausdorff distance. We also extend the above analysis to a larger class of set estimators defined in terms of a low-pass filter function. We finally provide numerical simulations on synthetic data to highlight the role of the hyper parameters, which affect the algorithm.