Structure-preserving non-linear PCA for matrices

2023/10/10 by Joni Virta, Virta, Joni, Andreas Artemiou +1 · 1 citation
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Mathematics #Face and Expression Recognition #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2310.06485

openalex publication_date 2023/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose MNPCA, a novel non-linear generalization of (2D)²PCA, a classical linear method for the simultaneous dimension reduction of both rows and columns of a set of matrix-valued data. 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.

Cited by

• Structure-Preserving Nonlinear Sufficient Dimension Reduction for Tensors

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