Frontiers in Applied Mathematics and Statistics (Nov 2017)
Regularized Kernel Algorithms for Support Estimation
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.
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