A1 Refereed original research article in a scientific journal
Structure-preserving non-linear PCA for matrices
Authors: Virta, Joni; Artemiou, Andreas
Publisher: IEEE
Publication year: 2024
Journal: IEEE Transactions on Signal Processing
Journal name in source: IEEE Transactions on Signal Processing
Volume: 72
First page : 3658
Last page: 3668
ISSN: 1941-0476
eISSN: 1941-0476
DOI: https://doi.org/10.1109/TSP.2024.3437183
Web address : https://ieeexplore.ieee.org/document/10620336
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457457312
Abstract
We propose a new dimension reduction method for matrix-valued data called Matrix Non-linear PCA (MNPCA), which is a non-linear generalization of (2D)2PCA. MNPCA is based on optimizing over separate non-linear mappings on the left and right singular spaces of the observations, essentially amounting to the decoupling of the two sides of the matrices. We develop a comprehensive theoretical framework for MNPCA by viewing it as an eigenproblem in reproducing kernel Hilbert spaces. We study the resulting estimators on both population and sample levels, deriving their convergence rates and formulating a coordinate representation to allow the method to be used in practice. Simulations and a real data example demonstrate MNPCA’s good performance over its competitors.
We propose a new dimension reduction method for matrix-valued data called Matrix Non-linear PCA (MNPCA), which is a non-linear generalization of (2D)2PCA. MNPCA is based on optimizing over separate non-linear mappings on the left and right singular spaces of the observations, essentially amounting to the decoupling of the two sides of the matrices. We develop a comprehensive theoretical framework for MNPCA by viewing it as an eigenproblem in reproducing kernel Hilbert spaces. We study the resulting estimators on both population and sample levels, deriving their convergence rates and formulating a coordinate representation to allow the method to be used in practice. Simulations and a real data example demonstrate MNPCA’s good performance over its competitors.
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