Structure-preserving non-linear PCA for matrices




Virta, Joni; Artemiou, Andreas

PublisherIEEE

2024

IEEE Transactions on Signal Processing

IEEE Transactions on Signal Processing

72

3658

3668

1941-0476

1941-0476

DOIhttps://doi.org/10.1109/TSP.2024.3437183(external)

https://ieeexplore.ieee.org/document/10620336(external)

https://research.utu.fi/converis/portal/detail/Publication/457457312(external)



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.

Last updated on 2025-27-01 at 20:00