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