In many real-world dynamical systems, the effect of an input on an output is not immediate but occurs after a time-varying delay, influenced by both the input and the system's internal state. These delays are typically unobservable, making system modelling particularly challenging, as the temporal relationship between inputs and outputs is not directly accessible. While inferring such dynamic delays is crucial for accurate modelling, most existing approaches either assume fixed delays or disregard delay structure altogether. This often leads to misaligned input-output relationships, especially in nonlinear, state-dependent systems, ultimately degrading predictive performance. We propose DelayNetODE, a novel delay-aware neural architecture that infers dynamic, input-dependent delays in an unsupervised manner while modelling system behaviour in continuous time. The framework consists of three key components: (1) a graph-based encoder that estimates continuous-valued delays from local temporal features, (2) a soft attention mechanism that aligns past inputs based on inferred delays, and (3) a Neural Ordinary Differential Equation (Neural ODE) decoder that models the continuous-time evolution of the output conditioned on delay-adjusted inputs. We evaluate DeiayNetODE on both synthetic and real-world datasets with nonlinear, time-varying delays. Results show this approach consistently outperforms the state-of-the-art models in both prediction accuracy and delay estimation. By inferring delays in an unsupervised manner and aligning inputs accordingly, DelayNetODE provides a principled and explainable approach for capturing latent temporal dependencies and improving system modelling in complex dynamical settings.

Abstract Class imbalance is a substantial challenge in classifying many real-world cases. Synthetic over-sampling methods have been effective to improve the performance of classifiers for imbalance problems. However, most synthetic over-sampling methods generate synthetic instances within the convex hull formed by the existing minority instances as they only concentrate on the minority class and ignore the vast information provided by the majority class. They also often do not perform well for extremely imbalanced data, as fewer minority instances mean less information with which to generate synthetic instances. Moreover, existing methods that generate synthetic instances using the majority class distributional information cannot perform effectively when the majority class has a multi-modal distribution. We propose a new method to generate diverse and adaptable synthetic instances using Synthetic Over-sampling with Minority and Majority classes (SOMM). SOMM generates synthetic instances diversely within the minority data space. It updates the generated instances adaptively to the neighbourhood including both classes. Thus, SOMM performs well for imbalance problems. We examine the performance of SOMM for binary multiclass imbalance classification problems for different imbalance levels. The empirical results and nonparametric statistical testing show the superiority of SOMM compared to existing methods. We also discuss the strengths and limitations of SOMM through visualisations.

We often compare time-dependent data elastically such that some compression or dilation along the time dimension can be ignored, for example, spatial trajectories of vehicles moving at different speeds or accelerometer data for exercises completed at variable rhythms. Traditionally this is possible via an alignment-based elastic distance measure, such as dynamic time warping (DTW). We may also control the degree of allowable warping with warping constraints. However, these elastic distance measures are not easy to use in large-scale time series classification, as they need to be evaluated pairwise and often cannot be directly converted into feature sets that we may use with arbitrary classifiers or combine with other features. In this research, we focus on the study of path signatures, a transformation with time warping invariance property, and how we may augment a time series to make its signature space representation reflect common warping constraints. We demonstrate that the comparing signatures is analogous to comparing time series with elastic distances, and that augmented signature features can serve as warping invariant or insensitive features in time series classification. Finally, we construct multiple path signatures with constraining augmentations classifier (MultiPSCA), a general-purpose minimal tuning time series classifier using augmented signatures and show that it is able to beat existing best-performing elastic time series classification algorithms without per-dataset hyperparameter tuning.

Multivariate time series classification (MTSC) has attracted significant research attention due to its diverse real-world applications. Recently, exploiting transformers for MTSC has achieved state-of the-art performance. However, existing methods focus on generic features, providing a comprehensive understanding of data, but they ignore class-specific features crucial for learning the representative characteristics of each class. This leads to poor performance in the case of imbalanced datasets or datasets with similar overall patterns but differing in minor class-specific details. In this paper, we propose a novel Shapelet Transformer (ShapeFormer), which comprises class-specific and generic transformer modules to capture both of these features. In the class-specific module, we introduce the discovery method to extract the discriminative subsequences of each class (i.e. shapelets) from the training set. We then propose a Shapelet Filter to learn the difference features between these shapelets and the input time series. We found that the difference feature for each shapelet contains important class-specific features, as it shows a significant distinction between its class and others. In the generic module, convolution filters are used to extract generic features that contain information to distinguish among all classes. For each module, we employ the transformer encoder to capture the correlation between their features. As a result, the combination of two transformer modules allows our model to exploit the power of both types of features, thereby enhancing the classification performance. Our experiments on 30 UEA MTSC datasets demonstrate that ShapeFormer has achieved the highest accuracy ranking compared to state-of-the-art methods. The code is available at https://github.com/xuanmay2701/shapeformer.

Bagging is a common approach in ensemble learning that generates a group of classifiers through bootstrapping for classification tasks. Despite its wide applications, generating redundant classifiers remains a central challenge in bagging. In recent years, many selective bagging models have been presented to deal with this challenge. These models mostly focused on the accuracy of classifiers and the diversity among them. Despite the importance of uncertainty in the performance of ensemble classifiers, this criterion has been neglected in selective bagging models. In this paper, we propose a two-stage selective bagging model. In the first stage, we formalize the selective bagging problem as a bi-objective optimization model considering both the uncertainty and accuracy of classifiers. We propose an adaptive evolutionary Two-Arch2 algorithm, named Diverse-Two-Arch2, to solve the bi-objective model. The output of this stage is a subset of classifiers that are diverse, certain about correct predictions, and uncertain about incorrect predictions. While most selective bagging models focus on the selection of a fixed subset of classifiers for all test samples (static approach), our proposed model has a dynamic approach to the selection process. So, in the second stage of the model, we select only certain classifiers to make an ensemble prediction for each test sample. Experimental results on twenty data sets and comparing with two ensemble models, and five state-of-the-art dynamic selective bagging models show the outperformance of the proposed model. We also compare the performance of the proposed Diverse-Two-Arch2 to alternative evolutionary computation methods.

Considering the coronavirus disease 2019 (COVID-19) pandemic, the government and health sectors are incapable of making fast and reliable decisions, particularly given the various effects of decisions on different contexts or countries across multiple sectors. Therefore, leaders often seek decision support approaches to assist them in such scenarios. The most common decision support approach used in this regard is multiattribute decision-making (MADM). MADM can assist in enforcing the most ideal decision in the best way possible when fed with the appropriate evaluation criteria and aspects. MADM also has been of great aid to practitioners during the COVID-19 pandemic. Moreover, MADM shows resilience in mitigating consequences in health sectors and other fields. Therefore, this study aims to analyse the rise of MADM techniques in combating COVID-19 by presenting a systematic literature review of the state-of-the-art COVID-19 applications. Articles on related topics were searched in four major databases, namely, Web of Science, IEEE Xplore, ScienceDirect, and Scopus, from the beginning of the pandemic in 2019 to April 2021. Articles were selected on the basis of the inclusion and exclusion criteria for the identified systematic review protocol, and a total of 51 articles were obtained after screening and filtering. All these articles were formed into a coherent taxonomy to describe the corresponding current standpoints in the literature. This taxonomy was drawn on the basis of four major categories, namely, medical (n = 30), social (n = 4), economic (n = 13) and technological (n = 4). Deep analysis for each category was performed in terms of several aspects, including issues and challenges encountered, contributions, data set, evaluation criteria, MADM techniques, evaluation and validation and bibliography analysis. This study emphasised the current standpoint and opportunities for MADM in the midst of the COVID-19 pandemic and promoted additional efforts towards understanding and providing new potential future directions to fulfil the needs of this study field.

This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In the sequel, we develop a new axiomatic framework of entropy measures for probabilistic hesitant fuzzy elements (PHFEs) by considering two facets of uncertainty associated with PHFEs which are known as fuzziness and nonspecificity. Respect to each kind of uncertainty, a number of formulae are derived to permit flexible selection of PHFE entropy measures. Moreover, based on the proposed PHFE entropy measures, we introduce some entropy-based distance measures which are used in the portion of comparative analysis. Eventually, the proposed PHFE entropy measures and PHFE entropy-based distance measures are applied to decision making in the strategy initiatives where their reliability and effectiveness are verified.

This paper primarily addresses a dataset relating to cellular, chemical and physical conditions of patients gathered at the time they are operated upon to remove colorectal tumours. This data provides a unique insight into the biochemical and immunological status of patients at the point of tumour removal along with information about tumour classification and post-operative survival. The relationship between severity of tumour, based on TNM staging, and survival is still unclear for patients with TNM stage 2 and 3 tumours. We ask whether it is possible to predict survival rate more accurately using a selection of machine learning techniques applied to subsets of data to gain a deeper understanding of the relationships between a patient's biochemical markers and survival. We use a range of feature selection and single classification techniques to predict the 5 year survival rate of TNM stage 2 and 3 patients which initially produces less than ideal results. The performance of each model individually is then compared with subsets of the data where agreement is reached for multiple models. This novel method of selective ensembling demonstrates that significant improvements in model accuracy on an unseen test set can be achieved for patients where agreement between models is achieved. Finally we point at a possible method to identify whether a patients prognosis can be accurately predicted or not.

Many machine learning algorithms assume that all input samples are independently and identically distributed from some common distribution on either the input space X, in the case of unsupervised learning, or the input and output space X × Y in the case of supervised and semi-supervised learning. In the last number of years the relaxation of this assumption has been explored and the importance of incorporation of additional information within machine learning algorithms became more apparent. Traditionally such fusion of information was the domain of semi-supervised learning. More recently the inclusion of knowledge from separate hypothetical spaces has been proposed by Vapnik as part of the supervised setting. In this work we are interested in exploring Vapnik’s idea of ‘master-class’ learning and the associated learning using ‘privileged’ information, however within the unsupervised setting. Adoption of the advanced supervised learning paradigm for the unsupervised setting instigates investigation into the difference between privileged and technical data. By means of our proposed aRi-MAX method stability of the K-Means algorithm is improved and identification of the best clustering solution is achieved on an artificial dataset. Subsequently an information theoretic dot product based algorithm called P-Dot is proposed. This method has the ability to utilize a wide variety of clustering techniques, individually or in combination, while fusing privileged and technical data for improved clustering. Application of the P-Dot method to the task of digit recognition confirms our findings in a real-world scenario.