A New Tucker Model for Three-Way Functional Data: FTucker-3
- 1Department of Statistics, University of Salamanca, 37008 Salamanca, Spain
- 2State University of Milagro (UNEMI), Dr. Rómulo Minchala Murillo University Campus, km 1.5 Milagro–Virgen de Fátima Road, Milagro 091050, Guayas, Ecuador
- 3Center for Statistical Studies and Research (CEIE), Escuela Superior Politécnica del Litoral (ESPOL), Gustavo Galindo Campus, km 30.5 Via Perimetral, Guayaquil P.O. Box 09-01-5863, Guayas, Ecuador
Abstract
This paper introduces FTucker-3, a basis-preserving Tucker framework for three-way functional data in which each tensor cell is a function. Functional observations are represented in a common finite basis, organized as a fourth-order coefficient tensor, and reduced only along the three structural modes while preserving the selected functional coefficient mode. A preliminary theoretical characterization establishes an exact functional–coefficient error decomposition, identifiability of the structural loading subspaces under full-row-rank core unfoldings, and perturbation control for the conditional SVD updates. Numerical evaluation combined a five-scenario Monte Carlo study with 1500 fitted models, a controlled periodic experiment, a real NASA POWER application, a Tucker-4 benchmark, and a scalability analysis. In the controlled experiment, FTucker-3 explained 96.71% of coefficient variability and 97.14% of functional variability. For NASA POWER, leakage-free cross-validation selected ranks (4, 5, 1), yielding 94.67% coefficient-domain and 69.45% functional explained variability across 240 daily trajectories. Under functional and structural misspecification, dominant loading-subspace similarities remained above 0.999 at 5 dB. Tucker-4 compression reduced storage but also reduced functional reconstruction accuracy, whereas the full-rank fourth-mode case was numerically equivalent to FTucker-3. These results support FTucker-3 as an interpretable framework for three-way arrays of functions.
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BibTeX
@article{cascanteyarleque2026tucker,
title = {{A New Tucker Model for Three-Way Functional Data: FTucker-3}},
author = {Roberto Cascante-Yarlequé and Purificación Galindo-Villardón and Fabricio Guevara-Viejó and Purificación Vicente-Galindo},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193589},
url = {https://www.mdpi.com/2227-7390/14/19/3589},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A New Tucker Model for Three-Way Functional Data: FTucker-3
AU - Roberto Cascante-Yarlequé
AU - Purificación Galindo-Villardón
AU - Fabricio Guevara-Viejó
AU - Purificación Vicente-Galindo
PY - 2026
DA - 2026/10/02
JO - Mathematics
DO - 10.3390/math14193589
UR - https://www.mdpi.com/2227-7390/14/19/3589
AB - This paper introduces FTucker-3, a basis-preserving Tucker framework for three-way functional data in which each tensor cell is a function. Functional observations are represented in a common finite basis, organized as a fourth-order coefficient tensor, and reduced only along the three structural modes while preserving the selected functional coefficient mode. A preliminary theoretical characterization establishes an exact functional–coefficient error decomposition, identifiability of the structural loading subspaces under full-row-rank core unfoldings, and perturbation control for the conditional SVD updates. Numerical evaluation combined a five-scenario Monte Carlo study with 1500 fitted models, a controlled periodic experiment, a real NASA POWER application, a Tucker-4 benchmark, and a scalability analysis. In the controlled experiment, FTucker-3 explained 96.71% of coefficient variability and 97.14% of functional variability. For NASA POWER, leakage-free cross-validation selected ranks (4, 5, 1), yielding 94.67% coefficient-domain and 69.45% functional explained variability across 240 daily trajectories. Under functional and structural misspecification, dominant loading-subspace similarities remained above 0.999 at 5 dB. Tucker-4 compression reduced storage but also reduced functional reconstruction accuracy, whereas the full-rank fourth-mode case was numerically equivalent to FTucker-3. These results support FTucker-3 as an interpretable framework for three-way arrays of functions.
SN - 2227-7390
ER -