{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Statistics, University of Salamanca, 37008 Salamanca, Spain",
    "State University of Milagro (UNEMI), Dr. Rómulo Minchala Murillo University Campus, km 1.5 Milagro–Virgen de Fátima Road, Milagro 091050, Guayas, Ecuador",
    "Center 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"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Roberto Cascante-Yarlequé",
      "orcid": "0000-0001-7875-0125"
    },
    {
      "affs": [
        0,
        1,
        2
      ],
      "name": "Purificación Galindo-Villardón",
      "orcid": "0000-0001-6977-7545"
    },
    {
      "affs": [
        1
      ],
      "name": "Fabricio Guevara-Viejó",
      "orcid": "0000-0003-2615-9872"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Purificación Vicente-Galindo",
      "orcid": "0000-0002-5854-273X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ef42ntndncdse.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193589",
  "fulltext_url": null,
  "id": "ef42ntndncdse",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3589",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7215728283",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/ef42ntndncdse.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193589",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3589"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2605|Tensor decomposition and applications",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A New Tucker Model for Three-Way Functional Data: FTucker-3",
  "title_text": "A New Tucker Model for Three-Way Functional Data: FTucker-3",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/ef42ntndncdse",
  "venue": "Mathematics",
  "versions": []
}