Journal of Computational Mathematics and Data Science最新文献

{"title":"Exploring singularities in data with the graph Laplacian: An explicit approach","authors":"Martin Andersson,&nbsp;Benny Avelin","doi":"10.1016/j.jcmds.2025.100113","DOIUrl":"10.1016/j.jcmds.2025.100113","url":null,"abstract":"<div><div>We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifolds of datasets. Our theory provides theoretical guarantees and explicit bounds on the functional forms of the graph Laplacian when it acts on functions defined close to singularities of the underlying manifold. We use these explicit bounds to develop tests for singularities and propose methods that can be used to estimate geometric properties of singularities in the datasets.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"14 ","pages":"Article 100113"},"PeriodicalIF":0.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Penalizing Low-Rank Matrix Factorization: From theoretical connections to practical applications","authors":"Nicoletta Del Buono ,&nbsp;Flavia Esposito ,&nbsp;Laura Selicato","doi":"10.1016/j.jcmds.2025.100111","DOIUrl":"10.1016/j.jcmds.2025.100111","url":null,"abstract":"<div><div>Low-rank (LR) factorization techniques aim to represent data in a low-dimensional space by identifying fundamental sources. Standard LR approaches often require additional constraints to account for real-world complexity, resulting in penalized low-rank matrix factorizations. These techniques incorporate penalties or regularization terms to improve robustness and adaptability to practical constraints, bridging theoretical research with real-world applications.</div><div>This paper explores a nonnegative constrained low-rank decomposition technique, namely, Nonnegative Matrix Factorization (NMF), and its constrained variants as powerful tools for analyzing nonnegative data. We cover theoretical foundations and practical implementations, review algorithms for standard NMF, and address challenges in setting hyperparameters for penalized variants. We emphasize applications in omics data analysis with a model that incorporates biological constraints to extract meaningful insights, and highlight applications in environmental data analysis.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"14 ","pages":"Article 100111"},"PeriodicalIF":0.0,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Directional node strength entropy centrality: Ranking influential nodes in complex networks","authors":"Giridhar Maji","doi":"10.1016/j.jcmds.2025.100112","DOIUrl":"10.1016/j.jcmds.2025.100112","url":null,"abstract":"<div><div>Identifying influential spreaders within a network is an important research area. Existing centrality metrics have limitations of either performing well on certain networks, but being computationally demanding, or having lower resolution in ranking. Also, most of the earlier studies ignore the directional and weighted aspect of a(n) relationship/edge that we exploit in the present study. In the real world, the relationships and influences between entities are often not symmetric. For example, a charismatic individual may have a significant impact on a common citizen, while the reverse may not be true. We propose a new approach called <em>Directional Node Strength Entropy</em> (DNSE), a topology-based method to identify critical nodes in an undirected network that can maximize spreading influence. An important neighbor exerts more influence on a node than it exerts back to that neighbor if its own importance is less than the neighbor. Our premise is that the strengths of network edges (connections) are directional and this strength depends on the importance of the starting node. We assign potential weights to the edges and use the degree of a node as a proxy for its importance. Directional node entropy across the neighborhood is used to rank the nodes. We conducted an extensive evaluation on real-world networks from various domains. We compared the proposed DNSE method against similar topology-based methods using Kendall’s rank correlation, ranking uniqueness, ccdf, and spreading influence, utilizing the SIR model as the benchmark. Results show that the proposed DNSE demonstrates superior or at-par performance compared to the state-of-the-art.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"14 ","pages":"Article 100112"},"PeriodicalIF":0.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-driven ambiguous cognitive map for complex decision-making in supply chain management","authors":"Pritpal Singh","doi":"10.1016/j.jcmds.2025.100110","DOIUrl":"10.1016/j.jcmds.2025.100110","url":null,"abstract":"<div><div>Fuzzy cognitive maps (FCMs) have the potential to model complex systems, but they face challenges in uncertainty, complexity, and dynamic conditions. This study tackles three main issues: modeling and quantifying uncertainty in relationships and weights with imprecise inputs, managing the complexity as the number of activation levels and causal relationships increases, and determining appropriate weights and thresholds in uncertain contexts. By using ambiguous set theory, the research introduces the ambiguous cognitive map (ACM) to improve the traditional FCM and address these problems. This theory allows for the representation of states with four membership values: true, false, partially true, and partially false, which provides a more refined approach to managing uncertainty. Mathematical formulas are employed by ACM to calculate weights based on these membership values instead of randomly selecting. The introduction of rank allows for the identification of the most influential state by its highest rank in priority decisions. The application of ACM in decision-making scenarios related to the supply chain system demonstrates its efficiency in systematically prioritizing and resolving complex decisions. The ACM effectively identifies key variables and provides actionable rankings to support decision-making in the supply chain system. The results demonstrate that ACM offers a systematic approach to resolving complex decisions under uncertainty.</div><div><strong>Impact Statement</strong> ACMs replace the conventional random assignment of relationship weights with a mathematical formulation based on the four membership values, enhancing the accuracy and reliability of the modeled system. The study also introduces a rank-based decision-making process, where the most influential state is determined by the highest rank derived from the membership values. The proposed ACM framework not only addresses the limitations of traditional FCMs but also opens new avenues for artificial intelligence (AI)-driven analysis of complex, uncertain systems.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"14 ","pages":"Article 100110"},"PeriodicalIF":0.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modified least squares ratio estimator for autocorrelated data: Estimation and prediction","authors":"Satyanarayana Poojari,&nbsp;Sachin Acharya,&nbsp;Varun Kumar S.G.,&nbsp;Vinitha Serrao","doi":"10.1016/j.jcmds.2025.100109","DOIUrl":"10.1016/j.jcmds.2025.100109","url":null,"abstract":"<div><div>Autocorrelated errors in regression models make ordinary least squares (OLS) estimators inefficient, potentially leading to the misinterpretation of test procedures. Generalized least squares (GLS) estimation is a more efficient approach than OLS in the presence of autocorrelated errors. The GLS estimators based on Cochrane–Orcutt (COR) and Hildreth–Lu (HU) methods are the most commonly used to estimate unknown model parameters. This study investigates the impact of autocorrelation on parameter estimation and prediction in regression models and introduces a novel approach to address the challenge possessed by autocorrelated errors. In this paper, two modified GLS estimators based on the least square ratio method are proposed namely the Least Square Ratio-Cochrane–Orcutt Estimator (LSRE-COR) estimator and the Least Square Ratio-Hildreth–Lu (LSRE-HU) estimator. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimators with OLS, COR, HU, maximum likelihood estimator (MLE), and least square ratio estimator (LSRE) based on total mean square error (TMSE) and root mean square error (RMSE). The results show that the proposed LSRE-HU and LSRE-COR consistently outperform all other estimators across various levels of autocorrelation and numbers of regressors for moderately large samples. The effectiveness of these methods is illustrated through real-life applications.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"14 ","pages":"Article 100109"},"PeriodicalIF":0.0,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Impact of collocation point sampling techniques on PINN performance in groundwater flow predictions","authors":"Vittorio Bauduin ,&nbsp;Salvatore Cuomo ,&nbsp;Vincenzo Schiano Di Cola","doi":"10.1016/j.jcmds.2024.100107","DOIUrl":"10.1016/j.jcmds.2024.100107","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) represent a promising methodology for addressing partial differential equations in scientific computing. This study examines optimization strategies for PINNs in groundwater flow modeling, concentrating on two main aspects: the distribution of collocation points and training strategies. By examining both point spatial distribution and dynamic resampling approaches, we show how collocation points arrangements can improve solution accuracy, particularly for problems with localized features such as source/sink terms represented by Dirac delta functions.</div><div>We introduce and analyze the Chebyshev-exponential (ChebEx) distribution for collocation points, as well as non-adaptive resampling strategies used during training.</div><div>In an explainable AI (XAI) setting our findings show that a ChebEx distribution of points improves accuracy over uniform sampling, especially near source terms. We also demonstrate that periodic resampling of collocation points improves training stability. These findings contribute to a better understanding of PINNs optimization and help to broaden our understanding of how spatial point selection influences PINN training dynamics and solution quality, but more research is needed for heterogeneous media and complex boundary conditions.</div><div>While our implementation focuses on one-dimensional groundwater flow with homogeneous boundary conditions, the methodologies presented here could be applied to a variety of physical systems governed by partial differential equations (PDEs), including heat transfer, fluid dynamics, and electromagnetic fields.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"14 ","pages":"Article 100107"},"PeriodicalIF":0.0,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143105361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficiency of the multisection method","authors":"J.S.C. Prentice","doi":"10.1016/j.jcmds.2024.100106","DOIUrl":"10.1016/j.jcmds.2024.100106","url":null,"abstract":"<div><div>We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method, although this optimal algorithm is problem dependent. The number of sections required for optimality is determined by means of a Lambert <em>W</em> function.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"13 ","pages":"Article 100106"},"PeriodicalIF":0.0,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142577799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bayesian optimization of one-dimensional convolutional neural networks (1D CNN) for early diagnosis of Autistic Spectrum Disorder","authors":"Temidayo Oluwatosin Omotehinwa ,&nbsp;Morolake Oladayo Lawrence ,&nbsp;David Opeoluwa Oyewola ,&nbsp;Emmanuel Gbenga Dada","doi":"10.1016/j.jcmds.2024.100105","DOIUrl":"10.1016/j.jcmds.2024.100105","url":null,"abstract":"<div><div>Autistic Spectrum Disorder (ASD) is a challenging neurological development disorder, which involves poor social interaction, communication, and repetitive behaviours. If autism is identified early enough it can be treated with better outcomes but present diagnostic tests are dependent on subjective opinion, consume a lot of time, and are vague. This study is aimed at optimizing one-dimensional convolutional neural networks (1D CNN) to improve the precision and speed of early ASD diagnosis. Four ASD datasets representing different age groups — toddlers, children, adolescents, and adults were modelled using one-dimensional convolutional neural networks (1D CNN). These datasets are accessible to the public on the UCI Machine Learning Repository and Kaggle, they consist of behavioural features relevant to ASD diagnosis. Each dataset underwent feature selection, categorical encoding, and missing value handling. Then, baseline 1D CNN with predefined hyperparameters was modelled on each of the datasets. Subsequently, the baseline models were optimized using the Tree-structured Parzen Estimator (TPE). An interactive web-based ASD diagnostic tool was developed, where user inputs are processed through age-specific pre-trained optimized models to determine ASD probability. The optimized 1D CNN models significantly outperformed the baseline models across all age groups and achieved scores of 100% in accuracy, precision, recall, F1-score, MCC, and AUC ROC. This implies that the optimized models can reliably identify people in various age groups who have and do not have ASD. The development of an interactive web-based diagnostic tool extends the practical utility of the models, making them accessible for clinical and at-home use.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"13 ","pages":"Article 100105"},"PeriodicalIF":0.0,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Novel color space representation extracted by NMF to segment a color image","authors":"Ciro Castiello ,&nbsp;Nicoletta Del Buono ,&nbsp;Flavia Esposito","doi":"10.1016/j.jcmds.2024.100104","DOIUrl":"10.1016/j.jcmds.2024.100104","url":null,"abstract":"<div><div>This paper considers the task of separating pixels in color image into background and foreground classes. Using the machine learning technique known as Nonnegative Matrix Factorization, data pertaining to different color channels – selected by color spaces – are combined, and a novel space representation is extracted.</div><div>The novel representation of the image includes additional information, namely “metacolor”, which could be related to foreground and background and adopted to improve binary segmentation of the investigated image. In both qualitative and quantitative experiments, the use of novel color space representation produces some improvements in the binary segmentation results when it compared to those obtained applying common simpler thresholding algorithms directly to the original image.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"13 ","pages":"Article 100104"},"PeriodicalIF":0.0,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enhanced MRI brain tumor detection and classification via topological data analysis and low-rank tensor decomposition","authors":"Serena Grazia De Benedictis ,&nbsp;Grazia Gargano ,&nbsp;Gaetano Settembre","doi":"10.1016/j.jcmds.2024.100103","DOIUrl":"10.1016/j.jcmds.2024.100103","url":null,"abstract":"<div><div>The advent of artificial intelligence in medical imaging has paved the way for significant advancements in the diagnosis of brain tumors. This study presents a novel ensemble approach that uses magnetic resonance imaging (MRI) to identify and categorize common brain cancers, such as pituitary, meningioma, and glioma. The proposed workflow is composed of a two-fold approach: firstly, it employs non-trivial image enhancement techniques in data preprocessing, low-rank Tucker decomposition for dimensionality reduction, and machine learning (ML) classifiers to detect and predict the type of brain tumor. Secondly, persistent homology (PH), a topological data analysis (TDA) technique, is exploited to extract potential critical areas in MRI scans. When paired with the ML classifier output, this additional information can help domain experts to identify areas of interest that might contain tumor signatures, improving the interpretability of ML predictions. When compared to automated diagnoses, this transparency adds another level of confidence and is essential for clinical acceptance. The performance of the system was quantitatively evaluated on a well-known MRI dataset, with an overall classification accuracy of 97.28% using an extremely randomized trees model. The promising results show that the integration of TDA, ML, and low-rank approximation methods is a successful approach for brain tumor identification and categorization, providing a solid foundation for further study and clinical application.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"13 ","pages":"Article 100103"},"PeriodicalIF":0.0,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}