Section: New Results

Kernel Principal Component Analysis and spectral clustering

Ilaria Giulini and Olivier Catoni continued their study of dimension free bounds for the estimation of the Gram matrix and more generally for the estimation of the expectation of a random symmetric matrix from an i.i.d. sample. This study, using PAC-Bayes bounds, both leads to new robust estimators with applications to Principal Component Analysis in high of even infinite dimension, and new bounds for the usual empirical Gram matrix estimate. Getting dimension free bounds is important to get new results on Kernel PCA. Applications were also studied to density estimation and to spectral clustering.