Vladimir Makarenkov

Renato Cordeiro de Amorim, Vladimir Makarenkov

The Minkowski weighted k-means (mwk-means) algorithm extends classical k-means by incorporating feature weights and a Minkowski distance. Despite its empirical success, its theoretical properties remain insufficiently understood. We show that the mwk-means objective can be expressed as a power-mean aggregation of within-cluster dispersions, with the order determined by the Minkowski exponent p. This formulation reveals how p controls the transition between selective and uniform use of features. Using this representation, we derive bounds for the objective function and characterise the structure of the feature weights, showing that they depend only on relative dispersion and follow a power-law relationship with dispersion ratios. This leads to explicit guarantees on the suppression of high-dispersion features. Finally, we establish convergence of the algorithm and provide a unified theoretical interpretation of its behaviour.

Ousmane Assani Amate, Mohammadreza Bakhtyari, Émilie Roy et al.

Dimensionality reduction is a critical preprocessing step for clustering high-dimensional data, yet comprehensive evaluation of its impact across diverse methods and data types remains limited. In this study, we systematically assess the influence of five dimensionality reduction techniques - Principal Component Analysis (PCA), Kernel Principal Component Analysis (Kernel PCA), Variational Autoencoder (VAE), Isometric Mapping (Isomap), and Multidimensional Scaling (MDS) - on the performance of four popular clustering algorithms - k-means, Agglomerative Hierarchical Clustering (AHC), Gaussian Mixture Models (GMM), and Ordering Points to Identify the Clustering Structure (OPTICS). We evaluate clustering quality using the Adjusted Rand Index (ARI), comparing results without and with dimensionality reduction at different reduction levels recommended in the literature (i.e., k-1, where k is the number of clusters, and 25% and 50% of the original number of dimensions). Our findings underscore the importance of a careful selection of the dimensionality reduction technique and the dimensionality reduction level that should be tailored to intrinsic data geometry and clustering algorithms under consideration.

Moloud Abdar, Soorena Salari, Sina Qahremani et al.

The COVID-19 (Coronavirus disease 2019) pandemic has become a major global threat to human health and well-being. Thus, the development of computer-aided detection (CAD) systems that are capable to accurately distinguish COVID-19 from other diseases using chest computed tomography (CT) and X-ray data is of immediate priority. Such automatic systems are usually based on traditional machine learning or deep learning methods. Differently from most of existing studies, which used either CT scan or X-ray images in COVID-19-case classification, we present a simple but efficient deep learning feature fusion model, called UncertaintyFuseNet, which is able to classify accurately large datasets of both of these types of images. We argue that the uncertainty of the model's predictions should be taken into account in the learning process, even though most of existing studies have overlooked it. We quantify the prediction uncertainty in our feature fusion model using effective Ensemble MC Dropout (EMCD) technique. A comprehensive simulation study has been conducted to compare the results of our new model to the existing approaches, evaluating the performance of competing models in terms of Precision, Recall, F-Measure, Accuracy and ROC curves. The obtained results prove the efficiency of our model which provided the prediction accuracy of 99.08\% and 96.35\% for the considered CT scan and X-ray datasets, respectively. Moreover, our UncertaintyFuseNet model was generally robust to noise and performed well with previously unseen data. The source code of our implementation is freely available at: https://github.com/moloud1987/UncertaintyFuseNet-for-COVID-19-Classification.

Renato Cordeiro de Amorim, Vladimir Makarenkov

Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a crucial role in assessing clustering quality when external ground truth labels are unavailable. However, these measures can be affected by the feature relevance issue, potentially leading to unreliable evaluations in high-dimensional or noisy data sets. We introduce a theoretically grounded Feature Importance Rescaling (FIR) method that enhances the quality of clustering validation by adjusting feature contributions based on their dispersion. It attenuates noise features, clarifies clustering compactness and separation, and thereby aligns clustering validation more closely with the ground truth. Through extensive experiments on synthetic data sets under different configurations, we demonstrate that FIR consistently improves the correlation between the values of cluster validity indices and the ground truth, particularly in settings with noisy or irrelevant features. The results show that FIR increases the robustness of clustering evaluation, reduces variability in performance across different data sets, and remains effective even when clusters exhibit significant overlap. These findings highlight the potential of FIR as a valuable enhancement of clustering validation, making it a practical tool for unsupervised learning tasks where labelled data is unavailable.

Renato Cordeiro de Amorim, Vladimir Makarenkov

The data preprocessing stage is crucial in clustering. Features may describe entities using different scales. To rectify this, one usually applies feature normalisation aiming at rescaling features so that none of them overpowers the others in the objective function of the selected clustering algorithm. In this paper, we argue that the rescaling procedure should not treat all features identically. Instead, it should favour the features that are more meaningful for clustering. With this in mind, we introduce a feature rescaling method that takes into account the within-cluster degree of relevance of each feature. Our comprehensive simulation study, carried out on real and synthetic data, with and without noise features, clearly demonstrates that clustering methods that use the proposed data normalization strategy clearly outperform those that use traditional data normalization.

Moloud Abdar, Farhad Pourpanah, Sadiq Hussain et al.

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

Jeremy Charlier, Vladimir Makarenkov

Bootstrap aggregation, known as bagging, is one of the most popular ensemble methods used in machine learning (ML). An ensemble method is a ML method that combines multiple hypotheses to form a single hypothesis used for prediction. A bagging algorithm combines multiple classifiers modeled on different sub-samples of the same data set to build one large classifier. Banks, and their retail banking activities, are nowadays using the power of ML algorithms, including decision trees and random forests, to optimize their processes. However, banks have to comply with regulators and governance and, hence, delivering effective ML solutions is a challenging task. It starts with the bank's validation and governance department, followed by the deployment of the solution in a production environment up to the external validation of the national financial regulator. Each proposed ML model has to be validated and clear rules for every algorithm-based decision must be justified. In this context, we propose XtracTree, an algorithm capable of efficiently converting an ML bagging classifier, such as a random forest, into simple "if-then" rules satisfying the requirements of model validation. We use a public loan data set from Kaggle to illustrate the usefulness of our approach. Our experiments demonstrate that using XtracTree, one can convert an ML model into a rule-based algorithm, leading to easier model validation by national financial regulators and the bank's validation department. The proposed approach allowed our banking institution to reduce up to 50% the time of delivery of our AI solutions to the end-user.

Bogdan Mazoure, Thang Doan, Tianyu Li et al.

We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based methods allows us to derive strong theoretical guarantees on the expected return of the reconstructed policy. Such guarantees are typically lacking in black-box models, but are very desirable in tasks requiring stability. We conduct several experiments on classic RL domains. The results confirm that the policies can be robustly embedded in a low-dimensional space while the embedded policy incurs almost no decrease in return.

Renato Cordeiro de Amorim, Vladimir Makarenkov, Boris Mirkin

In this paper we make two novel contributions to hierarchical clustering. First, we introduce an anomalous pattern initialisation method for hierarchical clustering algorithms, called A-Ward, capable of substantially reducing the time they take to converge. This method generates an initial partition with a sufficiently large number of clusters. This allows the cluster merging process to start from this partition rather than from a trivial partition composed solely of singletons. Our second contribution is an extension of the Ward and Ward p algorithms to the situation where the feature weight exponent can differ from the exponent of the Minkowski distance. This new method, called A-Ward p\b{eta} , is able to generate a much wider variety of clustering solutions. We also demonstrate that its parameters can be estimated reasonably well by using a cluster validity index. We perform numerous experiments using data sets with two types of noise, insertion of noise features and blurring within-cluster values of some features. These experiments allow us to conclude: (i) our anomalous pattern initialisation method does indeed reduce the time a hierarchical clustering algorithm takes to complete, without negatively impacting its cluster recovery ability; (ii) A-Ward p\b{eta} provides better cluster recovery than both Ward and Ward p.