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, 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.

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.

In this paper we present a novel methodology, referenced as ORFEO (Ordinal classifier and Regressor Fusion for Estimating an Ordinal categorical target), to enhance the performance in ordinal classification problems for which the latent variable is observable. ORFEO is an artificial neural network model incorporating two outputs, one for ordinal classification, using the cumulative link model, and one for regression, using a linear model. Both outputs are simultaneously optimised considering a loss function that linearly combines both classification and regression losses. The main motivation behind developing the proposed approach is to enhance the performance of a standard ordinal classifier. This improvement is facilitated by considering the regression output, which allows the model to differentiate between patterns within the same category. The ORFEO model is applied to two problems in the field of marine and ocean engineering: short-term prediction of both significant wave height and flux of energy. Both problems are addressed considering four different coastal zones of the United States of America, using 13 datasets formed by buoys measurements and reanalysis data. A comprehensive comparison against 20 methodologies, including regression and nominal/ordinal classification approaches is performed, by using diverse nominal and ordinal performance metrics. Ranks achieved indicate that ORFEO outperforms all the compared methodologies in terms of all the performance measures, demonstrating the efficacy and robustness of the proposal. Finally, a statistical analysis is conducted, concluding that there are statistically significant differences across ordinal and nominal performance metrics in favour of the proposed ORFEO model.

In this study, we present EBANO (Ensemble BAsed on uNimodal Ordinal classifiers), which is a novel ensemble approach of ordinal classifiers that includes four soft labelling approaches along with an ordinal logistic regression model. These models are integrated within the ensemble using a new aggregation methodology that automatically weights each individual classifier using a randomised search algorithm. In addition, the proposed EBANO methodology is applied to tackle short-term prediction of Significant Wave Height (SWH). Thus, we employ EBANO using a diverse set of eight datasets derived from reanalysis data and buoy-recorded SWH measurements. To approach the problem from an ordinal classification perspective, the SWH values are discretised into five ordered classes by applying hierarchical clustering. EBANO is compared with each of the individual classifiers integrated in the proposed ensemble along with a different ensemble technique termed HESCA. Both the average results and the ranks obtained show the superiority of EBANO over the compared methodologies, being more pronounced in the metrics that account for the imbalance present in the datasets considered. Finally, a statistical analysis is performed, confirming the statistical significance of the observed differences in all comparisons. This analysis underscores the effectiveness of EBANO in addressing the problem of SWH prediction, showcasing its excellence.

Predictive Maintenance (PdM) methods aim to facilitate the scheduling of maintenance work before equipment failure. In this context, detecting early faults in automated teller machines (ATMs) has become increasingly important since these machines are susceptible to various types of unpredictable failures. ATMs track execution status by generating massive event-log data that collect system messages unrelated to the failure event. Predicting machine failure based on event logs poses additional challenges, mainly in extracting features that might represent sequences of events indicating impending failures. Accordingly, feature learning approaches are currently being used in PdM, where informative features are learned automatically from minimally processed sensor data. However, a gap remains to be seen on how these approaches can be exploited for deriving relevant features from event-log-based data. To fill this gap, we present a predictive model based on a convolutional kernel (MiniROCKET and HYDRA) to extract features from the original event-log data and a linear classifier to classify the sample based on the learned features. The proposed methodology is applied to a significant real-world collected dataset. Experimental results demonstrated how one of the proposed convolutional kernels (i.e. HYDRA) exhibited the best classification performance (accuracy of 0.759 and AUC of 0.693). In addition, statistical analysis revealed that the HYDRA and MiniROCKET models significantly overcome one of the established state-of-the-art approaches in time series classification (InceptionTime), and three non-temporal ML methods from the literature. The predictive model was integrated into a container-based decision support system to support operators in the timely maintenance of ATMs.

Activation functions lie at the core of every neural network model from shallow to deep convolutional neural networks. Their properties and characteristics shape the output range of each layer and, thus, their capabilities. Modern approaches rely mostly on a single function choice for the whole network, usually ReLU or other similar alternatives. In this work, we propose two new activation functions and analyze their properties and compare them with 17 different function proposals from recent literature on six distinct problems with different characteristics. The objective is to shed some light on their comparative performance. The results show that the proposed functions achieved better performance than the most commonly used ones.

Abstract Nowadays, decision support systems (DSSs) are widely used in several application domains, from industrial to healthcare and medicine fields. Concerning the industrial scenario, we propose a DSS oriented to the aesthetic quality control (AQC) task, which has quickly established itself as one of the most crucial challenges of Industry 4.0. Taking into account the increasing amount of data in this domain, the application of machine learning (ML) and deep learning (DL) techniques offers great opportunities to automatize the overall AQC process. State-of-the-art is mainly oriented to approach this problem with a nominal DL classification method which does not exploit the ordinal structure of the AQC task, thus not penalizing the error among distant AQC classes (which is a relevant aspect for the real use case). The paper introduces a DL ordinal methodology for the AQC classification. Differently from other deep ordinal methods, we combined the standard categorical cross-entropy with the cumulative link model and we imposed the ordinal constraint via the thresholds and slope parameters. Experimental results were performed for solving an AQC task on a novel image dataset originated from a specific company’s demand (i.e., aesthetic assessment of wooden stocks). We demonstrated how the proposed methodology is able to reduce misclassification errors (up to 0.937 quadratic weight kappa loss) among distant classes while overcoming other state-of-the-art deep ordinal models and reducing the bias factor related to the item geometry. The proposed DL approach was integrated as the main core of a DSS supported by Internet of Things (IoT) architecture that can support the human operator by reducing up to 90% the time needed for the qualitative analysis carried out manually in this specific domain.

Currently, the use of deep learning for solving ordinal classification problems, where categories follow a natural order, has not received much attention. In this paper, we propose an unimodal regularisation based on the beta distribution applied to the cross-entropy loss. This regularisation encourages the distribution of the labels to be a soft unimodal distribution, more appropriate for ordinal problems. Given that the beta distribution has two parameters that must be adjusted, a method to automatically determine them is proposed. The regularised loss function is used to train a deep neural network model with an ordinal scheme in the output layer. The results obtained are statistically analysed and show that the combination of these methods increases the performance in ordinal problems. Moreover, the proposed beta distribution performs better than other distributions proposed in previous works, achieving also a reduced computational cost.

3D image scans are an assessment tool for neurological damage in Parkinson’s disease (PD) patients. This diagnosis process can be automatized to help medical staff through Decision Support Systems (DSSs), and Convolutional Neural Networks (CNNs) are good candidates, because they are effective when applied to spatial data. This paper proposes a 3D CNN ordinal model for assessing the level or neurological damage in PD patients. Given that CNNs need large datasets to achieve acceptable performance, a data augmentation method is adapted to work with spatial data. We consider the Ordinal Graph-based Oversampling via Shortest Paths (OGO-SP) method, which applies a gamma probability distribution for inter-class data generation. A modification of OGO-SP is proposed, the OGO-SP-β algorithm, which applies the beta distribution for generating synthetic samples in the inter-class region, a better suited distribution when compared to gamma. The evaluation of the different methods is based on a novel 3D image dataset provided by the Hospital Universitario ‘Reina Sofía’ (Córdoba, Spain). We show how the ordinal methodology improves the performance with respect to the nominal one, and how OGO-SP-β yields better performance than OGO-SP.

The adjustment of the hyperparameters and network structure of Convolutional Neural Networks (CNNs) composes an important step towards building effective, but still efficient learning models. The selection of the best configuration is a problem-dependent task that involves to explore an enormous and complex search space. Due to this reason, the use of heuristic-based search fits perfectly within this task, seeking to obtain a near to optimal solution in a complex and large exploratory space. This paper presents SCRODeep, a self-adapting algorithm based on a statistically-driven Coral Reef Optimisation algorithm (SCRO), for the selection of the most adequate CNNs architecture in a particular domain. This metaheuristic has been designed to navigate through a search space where the architecture (defining the particular set of layers, including convolutional or pooling layers), and the hyperparameters of the network (i.e. activation functions, number of units or the kernel initializer, among others) are represented, but where the connections weights and bias are inferred using typical CNNs optimisation algorithms. In contrast to other approaches, where the use of a metaheuristic implies in turn to fix a series of hyperparameters (i.e. the mutation probability in a genetic algorithm), our approach follows a self-parametrisation perspective, thus removing the necessity of fixing these values. The method has been tested in the design of CNNs for image classification, showing that SCRODeep is able to find competitive solutions, while the complexity of the architectures found is constrained.