In the evolving landscape of targeted marketing, integrating deep learning (DL) and explainable AI (XAI) offers a promising avenue for enhanced customer segmentation. This paper introduces a groundbreaking approach, DeepLimeSeg, which synergizes DL methodologies with Lime-based Explainability to segment customers effectively. The approach employs a comprehensive mathematical model to harness demographic data, behavioral patterns, and purchase histories, categorizing customers into distinct clusters aligned with their preferences and needs. A pivotal component of this research is the mathematical underpinning of the DeepLimeSeg approach. The Lime-based Explainability module ensures that the segmentation results are accurate and interpretable. The mathematical rigor facilitates businesses tailoring their marketing strategies with precision, optimizing sales outcomes. To validate the efficacy of DeepLimeSeg, we employed two real-world datasets: Mall-Customer Segmentation Data and an E-Commerce dataset. A comparative analysis between DeepLimeSeg and the traditional Recency, Frequency, and Monetary (RFM) analysis is presented. The RFM analysis, grounded in its mathematical modeling, segments customers based on purchase recency, frequency, and monetary value. Our preprocessing involved computing RFM scores for each customer, followed by K-means clustering to delineate customer segments. Empirical results underscored the superiority of DeepLimeSeg over other models in terms of MSE, MAE, and $R^2$ metrics. Specifically, the model registered an MSE of 0.9412, indicative of its robust predictive accuracy concerning the spending score. The MAE value stood at 0.9874, signifying minimal deviation from actual values. This paper accentuates the importance of mathematical modeling in enhancing customer segmentation. The DeepLimeSeg approach, with its mathematical foundation and explainable AI integration, paves the way for businesses to make informed, data-driven marketing decisions.

Credit scoring models serve as pivotal instruments for lenders and financial institutions, facilitating the assessment of creditworthiness. Traditional models, while instrumental, grapple with challenges related to efficiency and subjectivity. The advent of machine learning heralds a transformative era, offering data-driven solutions that transcend these limitations. This research delves into a comprehensive analysis of various machine learning algorithms, emphasizing their mathematical underpinnings and their applicability in credit score classification. A comprehensive evaluation is conducted on a range of algorithms, including logistic regression, decision trees, support vector machines, and neural networks, using publicly available credit datasets. Within the research, a unified mathematical framework is introduced, which encompasses preprocessing techniques and critical algorithms such as Particle Swarm Optimization (PSO), the Light Gradient Boosting Model, and Extreme Gradient Boosting (XGB), among others. The focal point of the investigation is the LIME (Local Interpretable Model-agnostic Explanations) explainer. This study offers a comprehensive mathematical model using the LIME explainer, shedding light on its pivotal role in elucidating the intricacies of complex machine learning models. This study’s empirical findings offer compelling evidence of the efficacy of these methodologies in credit scoring, with notable accuracies of 88.84%, 78.30%, and 77.80% for the Australian, German, and South German datasets, respectively. In summation, this research not only amplifies the significance of machine learning in credit scoring but also accentuates the importance of mathematical modeling and the LIME explainer, providing a roadmap for practitioners to navigate the evolving landscape of credit assessment.

Background/Objectives: Accurate and efficient diagnosis of heart disease through electrocardiogram (ECG) analysis remains a critical challenge in clinical practice due to noise interference, morphological variability, and the complexity of overlapping cardiac signals. Methods: This study presents a comprehensive deep learning (DL) framework that integrates advanced ECG signal segmentation with transfer learning-based classification, aimed at improving diagnostic performance. The proposed ECG segmentation algorithm introduces a distinct and original approach compared to prior research by integrating adaptive preprocessing, histogram-based lead separation, and robust point-tracking techniques into a unified framework. While most earlier studies have addressed ECG image processing using basic filtering, fixed-region cropping, or template matching, our method uniquely focuses on automated and precise reconstruction of individual ECG leads from noisy and overlapping multi-lead images—a challenge often overlooked in previous work. This innovative segmentation strategy significantly enhances signal clarity and enables the extraction of richer and more localized features, boosting the performance of DL classifiers. The dataset utilized in this work of 12 lead-based standard ECG images consists of four primary classes. Results: Experiments conducted using various DL models—such as VGG16, VGG19, ResNet50, InceptionNetV2, and GoogleNet—reveal that segmentation notably enhances model performance in terms of recall, precision, and F1 score. The hybrid VGG19 + SVM model achieved 98.01% and 100% accuracy in multi-class classification, along with average accuracies of 99% and 97.95% in binary classification tasks using the original and reconstructed datasets, respectively. Conclusions: The results highlight the superiority of deep, feature-rich models in handling reconstructed ECG signals and confirm the value of segmentation as a critical preprocessing step. These findings underscore the importance of effective ECG segmentation in DL applications for automated heart disease diagnosis, offering a more reliable and accurate solution.

During the abrupt outbreak of the COVID-19 pandemic, the public health system of most of the world’s nations has been tested. However, it is the concern of governments and other responsible entities to provide the correct statistics and figures to take any practicable necessary steps such as allocation of the requisite quarantine operations, calculation of the needed number of places in hospitals, determination of the extent of personal security, and determining the degree of isolation of infectious people, among others. Where the statistical literature supposes that a model governs every real phenomenon, once we know the model, we can evaluate the dilemma. Therefore, in this article, we compare the COVID-19 pandemic dynamics of two neighboring Arabic countries, Egypt and Saudi Arabia, to provide a framework to arrange appropriate quarantine activities. A new generalized family of distributions is developed to provide the best description of COVID-19 daily cases and data on daily deaths in Egypt and Saudi Arabia. Some of the mathematical properties of the proposed family are studied.