Journal of Computational Mathematics and Data Science最新文献

{"title":"On exact line search method for a polynomial matrix equation","authors":"Chacha Stephen Chacha","doi":"10.1016/j.jcmds.2025.100120","DOIUrl":"10.1016/j.jcmds.2025.100120","url":null,"abstract":"<div><div>In this work, we investigate the elementwise minimal non-negative (EMN) solution of the matrix polynomial equation using an exact line search (ELS) technique to enhance the convergence of the Newton method. Nonnegative solutions to matrix equations are essential in engineering, optimization, signal processing, and data mining, driving advancements and improving efficiency in these fields. While recent advancements in solving matrix equations with nonnegative constraints have emphasized iterative methods, optimization strategies, and theoretical developments, efficiently finding the EMN solution remains a significant challenge. The proposed method integrates the Newton method with an exact line search (ELS) strategy to accelerate convergence and improve solution accuracy. Numerical experiments demonstrate that this approach requires fewer iterations to reach the EMN solution compared to the standard Newton method. Moreover, the method shows improved stability, particularly when dealing with ill-conditioned input matrices and very small tolerance errors.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"15 ","pages":"Article 100120"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144189659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A neural network approach for solving the Monge–Ampère equation with transport boundary condition","authors":"Roel Hacking ,&nbsp;Lisa Kusch ,&nbsp;Koondanibha Mitra ,&nbsp;Martijn Anthonissen ,&nbsp;Wilbert IJzerman","doi":"10.1016/j.jcmds.2025.100119","DOIUrl":"10.1016/j.jcmds.2025.100119","url":null,"abstract":"<div><div>This paper introduces a novel neural network-based approach to solving the Monge–Ampère equation with the transport boundary condition, specifically targeted towards optical design applications. We leverage multilayer perceptron networks to learn approximate solutions by minimizing a loss function that encompasses the equation’s residual, boundary conditions, and convexity constraints. Our main results demonstrate the efficacy of this method, optimized using L-BFGS, through a series of test cases encompassing symmetric and asymmetric circle-to-circle, square-to-circle, and circle-to-flower reflector mapping problems. Comparative analysis with a conventional least-squares finite-difference solver reveals the competitive, and often superior, performance of our neural network approach on the test cases examined here. A comprehensive hyperparameter study further illuminates the impact of factors such as sampling density, network architecture, and optimization algorithm. While promising, further investigation is needed to verify the method’s robustness for more complicated problems and to ensure consistent convergence. Nonetheless, the simplicity and adaptability of this neural network-based approach position it as a compelling alternative to specialized partial differential equation solvers.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"15 ","pages":"Article 100119"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Machine learning-driven market value prediction for European football players","authors":"Abdullah Tamim ,&nbsp;Md. Wadud Jahan ,&nbsp;Md. Rashid Shahriar Chowdhury ,&nbsp;Ahammad Hossain ,&nbsp;Md. Mizanur Rahman ,&nbsp;A.H.M. Rahmatullah Imon","doi":"10.1016/j.jcmds.2025.100118","DOIUrl":"10.1016/j.jcmds.2025.100118","url":null,"abstract":"<div><div>Football is globally recognized as the most widely practiced and watched sport. Precise player value is crucial for clubs seeking to maximize their player acquisition strategy and overall success in football. Conventional player valuation methodologies are mainly dependent on expert judgments and subjective assessments, missing the objectivity and precision provided by data-driven approaches. This study seeks to close this disparity by utilizing machine learning techniques to predict the market valuations of football players. The analysis is conducted using an extensive dataset sourced from the FIFA 22 video game, which was obtained via sofifa.com. The collection includes more than 16,000 players. The Machine Learning (ML) techniques used in this study are Multiple Linear Regression (MLR), Ridge Regression (RR), Support Vector Regression (SVR), and Random Forest Regression (RFR). The machine learning algorithms undergo training using 80% of the samples and are subsequently tested using the remaining 20% of the samples. We evaluate each algorithm’s performance using metrics like Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared (R²) value. Numerical results show that the RFR model demonstrates superior performance by achieving the lowest MAE, MSE, RMSE, and the highest R² value across all samples. The RFR effectively captures non-linear interactions and reliably prevents overfitting. This research finding will enhance the existing knowledge in sports economics by demonstrating how ML can be used to anticipate the market prices of football players with better accuracy. This will provide football teams with valuable insights to make more strategic decisions.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"15 ","pages":"Article 100118"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improved descent hybrid gradient-based projection algorithm for nonlinear equations and signal recovery problems","authors":"M. Koorapetse,&nbsp;P. Kaelo,&nbsp;T. Diphofu,&nbsp;S. Lekoko,&nbsp;T. Yane,&nbsp;B. Modise,&nbsp;C.R. Sam","doi":"10.1016/j.jcmds.2025.100117","DOIUrl":"10.1016/j.jcmds.2025.100117","url":null,"abstract":"<div><div>Derivative-free projection methods for solving nonlinear monotone equations have recently gained favor with researchers. Based on a hybrid conjugate gradient algorithm and the projection techniques, in this work, we present a descent derivative-free projection method for finding solutions to large-scale nonlinear monotone equations. The proposed method satisfies the descent condition and, under some suitable assumptions, its global convergence is established. The presented method’s efficacy is demonstrated through numerical experiments. Results show that, compared to other methods with similar structure, the method performs better. The method is further applied to an application in signal recovery, and it is proving to be efficient.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"15 ","pages":"Article 100117"},"PeriodicalIF":0.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Universal approximation property of ODENet and ResNet with a single activation function","authors":"Masato Kimura ,&nbsp;Kazunori Matsui ,&nbsp;Yosuke Mizuno","doi":"10.1016/j.jcmds.2025.100116","DOIUrl":"10.1016/j.jcmds.2025.100116","url":null,"abstract":"<div><div>We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is considered a mathematical model of a ResNet-type deep learning system. We consider dynamical systems with vector fields given by a single composition of the activation function and an affine mapping, which is the most common choice of the ODENet or ResNet vector field in actual machine learning systems. We demonstrate that both ODENets and ResNets with the restricted vector field of a single composition of the activation function and an affine mapping can uniformly approximate ODENets within the broader class that utilize a general vector field.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"15 ","pages":"Article 100116"},"PeriodicalIF":0.0,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Crafting a Player Impact Metric through analysis of football match event data","authors":"Mohamed Elsharkawi,&nbsp;Raja Hashim Ali,&nbsp;Talha Ali Khan","doi":"10.1016/j.jcmds.2025.100115","DOIUrl":"10.1016/j.jcmds.2025.100115","url":null,"abstract":"<div><div>The evaluation of football players remains a challenging task due to the limitations of existing rating models as well as the diverse nature of in-game actions and their varying impact on outcome of the matches, which often emphasize offensive actions while overlooking key defensive and strategic contributions. While some player impact metrics exist for football, their effectiveness, complete in-depth analysis, and relationship with match outcomes (win, loss, draw) has not been studied well. In this study, we have developed a Player Impact Metric (PIM) that provides a more comprehensive and data-driven assessment of player performance by incorporating match event data, Expected Goals (xG), Expected Threat (xT), and defensive contributions. The PIM framework assigns weighted scores to player actions using ordinal logistic regression based on their influence on match outcomes. The model evaluates player contributions using event-level data, integrating both offensive and defensive actions. The dataset is sourced from WhoScored, with structured data processing in PostgreSQL and analytical modeling techniques applied to derive impact scores. The PIM was tested against WhoScored Ratings, revealing notable differences in player rankings, particularly for defensive players. Our findings show that PIM provides a more balanced assessment, capturing critical non-scoring contributions that traditional rating systems tend to undervalue. We have introduced PIM as an advanced evaluation metric for football analytics, offering a data-driven, context-aware, and holistic approach to player performance assessment in this study. We show that the PIM can serve as a valuable tool for coaches, analysts, and scouts, enabling more accurate talent identification and match analysis.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"15 ","pages":"Article 100115"},"PeriodicalIF":0.0,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"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}