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Activity Number: 55 - Complex Functional and Non-Euclidean Data Analysis
Type: Topic Contributed
Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #322103
Title: Nonlinear Two-Dimensional PCA
Author(s): Joni Virta* and Andreas Artemiou
Companies: University of Turku and Cardiff University
Keywords: Matrix data; Dimension reduction; Singular value decomposition; RKHS
Abstract:

We develop non-linear principal component analysis for matrix-valued data. Our approach is based on applying non-linear transformations separately to the left and right singular vectors of the observed matrices, guaranteeing that the estimated latent components enjoy the “left-right”-structure typically expected in matrix dimension reduction. We treat both population and sample-level estimation and also establish the convergence rates of the estimators. The results are illustrated with numerical examples.


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