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Robust PCA and pairs of projections in a Hilbert space. (English) Zbl 1384.62185
The author studies dimension reduction by a robust version of the principal component analysis. A robust estimator of the covariance operator is used. In usual principal component analysis, the data is projected on the first few principal components, meaning that a component is either used to full extend or not at all. The author studies a projection where some components are used with a reduced weight, which is achieved by using a continuous transformation of the eigenvalues instead of a cut-off. To study the behavior of this procedure, new perturbation inequalities are needed: The author proves bounds for the norm of the difference of two transformed operators in terms of the operator norm of the difference.

MSC:
62H25 Factor analysis and principal components; correspondence analysis
62G35 Nonparametric robustness
62G05 Nonparametric estimation
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