Robust Principal Component Analysis in Hilbert spaces

Autor:	Giulini, Ilaria
Rok vydání:	2016
Předmět:	Mathematics - Statistics Theory 62G35 62G05 62H25
Druh dokumentu:	Working Paper
Popis:	We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the covariance operator and in replacing it with a smooth cut-off of the eigenvalues. We study the problem from a statistical point of view, so that we assume that we do not have direct access to the covariance operator but we have to estimate it from an i.i.d. sample. We provide some results on the quality of the approximation of our spectral cut-off in terms of the quality of the approximation of the eigenvalues of the covariance operator. Comment: arXiv admin note: substantial text overlap with arXiv:1511.06263
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1606.00187 Zobrazit plný text záznamu View this record from Arxiv