Learning Ordinal–Hierarchical Constraints for Deep Learning Classifiers
Riccardo Rosati 
Luca Romeo 
Víctor Manuel Vargas-Yun 
Pedro Antonio Gutiérrez 
César Hervás-Martínez IEEE Transactions on Neural Networks and Learning Systems
COMPUTER SCIENCE, THEORY & METHODS
Abstract
Real-world classification problems may disclose different hierarchical levels where the categories are displayed in an ordinal structure. However, no specific deep learning (DL) models simultaneously learn hierarchical and ordinal constraints while improving generalization performance. To fill this gap, we propose the introduction of two novel ordinal–hierarchical DL methodologies, namely, the hierarchical cumulative link model (HCLM) and hierarchical–ordinal binary decomposition (HOBD), which are able to model the ordinal structure within different hierarchical levels of the labels. In particular, we decompose the hierarchical–ordinal problem into local and global graph paths that may encode an ordinal constraint for each hierarchical level. Thus, we frame this problem as simultaneously minimizing global and local losses. Furthermore, the ordinal constraints are set by two approaches ordinal binary decomposition (OBD) and cumulative link model (CLM) within each global and local function. The effectiveness of the proposed approach is measured on four real-use case datasets concerning industrial, biomedical, computer vision, and financial domains. The extracted results demonstrate a statistically significant improvement to state-of-the-art nominal, ordinal, and hierarchical approaches.
Keywords
BibTex Citation
@article{Rosati2025Learning,
author = {Rosati, Riccardo and Romeo, Luca and Vargas-Yun, V{\' i}ctor Manuel and Guti{\' e}rrez, Pedro Antonio and Frontoni, Emanuele and Herv{\' a}s-Mart{\' i}nez, C{\' e}sar},
journal = {IEEE Transactions on Neural Networks and Learning Systems},
doi = {10.1109/TNNLS.2024.3360641},
number = {3},
year = {2025},
pages = {4765--4778},
title = {Learning {Ordinal}--{Hierarchical} {Constraints} for {Deep} {Learning} {Classifiers}},
url = {https://ieeexplore.ieee.org/document/10432994},
howpublished = {https://ieeexplore.ieee.org/document/10432994},
volume = {36},
}
BibTex Unicode Citation
@article{Rosati2025Learning,
author = {Rosati, Riccardo and Romeo, Luca and Vargas-Yun, Víctor Manuel and Gutiérrez, Pedro Antonio and Frontoni, Emanuele and Hervás-Martínez, César},
journal = {IEEE Transactions on Neural Networks and Learning Systems},
doi = {10.1109/TNNLS.2024.3360641},
number = {3},
year = {2025},
pages = {4765--4778},
title = {Learning {Ordinal}--{Hierarchical} {Constraints} for {Deep} {Learning} {Classifiers}},
url = {https://ieeexplore.ieee.org/document/10432994},
howpublished = {https://ieeexplore.ieee.org/document/10432994},
volume = {36},
}
APA Citation
Rosati, R., Romeo, L., Vargas-Yun, V. M., Gutiérrez, P. A., Frontoni, E., & Hervás-Martínez, C. (2025). Learning Ordinal–Hierarchical Constraints for Deep Learning Classifiers. IEEE Transactions on Neural Networks and Learning Systems, 36(3), 4765–4778. https://doi.org/10.1109/TNNLS.2024.3360641
RIS Citation
TY - JOUR
AU - Rosati, Riccardo
AU - Romeo, Luca
AU - Vargas-Yun, Víctor Manuel
AU - Gutiérrez, Pedro Antonio
AU - Frontoni, Emanuele
AU - Hervás-Martínez, César
DA - 2025///
PY - 2025
DO - 10.1109/TNNLS.2024.3360641
ID - temp_id_969462537745
IS - 3
SP - 4765-4778
T2 - IEEE Transactions on Neural Networks and Learning Systems
TI - Learning Ordinal–Hierarchical Constraints for Deep Learning Classifier
s
UR - https://ieeexplore.ieee.org/document/10432994
VL - 36
ER -
CV Citation
R. Rosati (CA), L. Romeo, V.M. Vargas-Yun, P.A. Gutiérrez, E. Frontoni, C. Hervás-Martínez (3/6). "Learning Ordinal–Hierarchical Constraints for Deep Learning Classifiers". IEEE Transactions on Neural Networks and Learning Systems, Vol. 36(3), pp. 4765–4778, 2025. (Q1D1, IF: 8.9).