An Ordinal Classification (OC) problem corresponds to a special type of classification characterised by the presence of a natural order relationship among the classes. This type of problem, that can be found in a number of real-world applications, has motivated the design and development of many ordinal methodologies over the last years. However, it is important to highlight that the development of the OC field suffers from one main disadvantage: the lack of a comprehensive set of datasets on which novel approaches to the literature are benchmarked. In order to approach this objective, this manuscript from the University of Córdoba (UCO), which has previous experience on the OC field, provides the literature with a publicly available repository of tabular data for a robust validation of novel OC approaches, namely TOC-UCO (Tabular Ordinal Classification repository of the UCO). Specifically, this repository includes a set of tabular ordinal datasets that have been preprocessed under a common framework and that have a reasonable number of patterns and an appropriate class distribution. We also provide the sources and preprocessing steps of each dataset, along with details on how to benchmark a novel approach using the TOC-UCO repository. For this, indices for different randomised train-test partitions are provided to facilitate the reproducibility of the experiments. • Introduction of a novel ordinal classification repository: TOC-UCO . • Extension of the number of datasets with a high number of classes. • Analysis of the previous ordinal classification benchmarking repository. • In-depth comparison between TOC-UCO and the previous repository. • Presentation of a baseline experimentation on the new TOC-UCO archive.

Ordinal Classification (OC) addresses those classification tasks where the labels exhibit a natural order. Unlike nominal classification, which treats all classes as mutually exclusive and unordered, OC takes the ordinal relationship into account, producing more accurate and relevant results. This is particularly critical in applications where the magnitude of classification errors has significant consequences. Despite this, OC problems are often tackled using nominal methods, leading to suboptimal solutions. Although decision trees are among the most popular classification approaches, ordinal tree-based approaches have received less attention when compared to other classifiers. This work provides a comprehensive survey of ordinal splitting criteria, standardising the notations used in the literature to enhance clarity and consistency. Three ordinal splitting criteria, Ordinal Gini (OGini), Weighted Information Gain, and Ranking Impurity, are compared to the nominal counterparts of the first two (Gini and information gain), by incorporating them into a decision tree classifier. An extensive repository considering 45 publicly available OC datasets is presented, supporting the first experimental comparison of ordinal and nominal splitting criteria using well-known OC evaluation metrics. The results have been statistically analysed, highlighting that OGini stands out as the best ordinal splitting criterion to date, reducing the mean absolute error achieved by Gini by more than 3.02 % . To promote reproducibility, all source code developed, a detailed guide for reproducing the results, the 45 OC datasets, and the individual results for all the evaluated methodologies are provided.

Ordinal classification, where labels follow a natural order, has gained increasing attention, particularly in the deep learning community due to its relevance in tasks such as age estimation, medical grading, and quality assessment. Despite the growing number of deep ordinal classification methods, a comprehensive experimental analysis of their core ordinal components remains lacking. This work presents a systematic evaluation of deep ordinal classifiers by analysing the impact of three key modelling choices: the loss function, output layer, and labelling strategy. To analyse their effects, we adopt a unified architecture and evaluate one nominal and 19 ordinal configurations, resulting from combination of two loss functions, two output layers, and five labelling strategies. These configurations are assessed on 12 diverse ordinal image datasets using six performance metrics, including both ordinal and nominal measures. Results show that ordinal output layers consistently outperform softmax, and that soft labelling generally improves generalisation. While categorical cross-entropy achieves better average performance, especially on nominal metrics, no configuration performs best across all datasets. Statistical analyses indicate significant interactions between losses, outputs, labelling strategies, and datasets, highlighting the need to adapt methodological choices to specific tasks. These findings provide valuable guidance for designing robust deep ordinal classification models.

dlordinal is a new Python library that unifies many recent deep ordinal classification methodologies available in the literature. Developed using PyTorch as underlying framework, it implements the top performing state-of-the-art deep learning techniques for ordinal classification problems. Ordinal approaches are designed to leverage the ordering information present in the target variable. Specifically, it includes loss functions, various output layers, dropout techniques, soft labelling methodologies, and other classification strategies, all of which are appropriately designed to incorporate the ordinal information. Furthermore, as the performance metrics to assess novel proposals in ordinal classification depend on the distance between target and predicted classes in the ordinal scale, suitable ordinal evaluation metrics are also included. dlordinal is distributed under the BSD-3-Clause license and is available at https://github.com/ayrna/dlordinal.

Time-series classification (TSC) covers the supervised learning problem where input data is provided in the form of series of values observed through repeated measurements over time, and whose objective is to predict the category to which they belong. When the class values are ordinal, classifiers that take this into account can perform better than nominal classifiers. Time-series ordinal classification (TSOC) is the field bridging this gap, yet unexplored in the literature. There are a wide range of time-series problems showing an ordered label structure, and TSC techniques that ignore the order relationship discard useful information. Hence, this article presents the first benchmarking of TSOC methodologies, exploiting the ordering of the target labels to boost the performance of current TSC state of the art. Both convolutional- and deep-learning-based methodologies (among the best performing alternatives for nominal TSC) are adapted for TSOC. For the experiments, a selection of 29 ordinal problems has been made. In this way, this article contributes to the establishment of the state of the art in TSOC. The results obtained by ordinal versions are found to be significantly better than current nominal TSC techniques in terms of ordinal performance metrics, outlining the importance of considering the ordering of the labels when dealing with this kind of problems.