Journal of Computational Mathematics and Data Science最新文献

英文中文

Modified least squares ratio estimator for autocorrelated data: Estimation and prediction

Journal of Computational Mathematics and Data Science

Pub Date : 2025-02-07 DOI: 10.1016/j.jcmds.2025.100109

Satyanarayana Poojari, Sachin Acharya, Varun Kumar S.G., Vinitha Serrao

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.

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引用次数: 0

Impact of collocation point sampling techniques on PINN performance in groundwater flow predictions

Journal of Computational Mathematics and Data Science

Pub Date : 2024-12-07 DOI: 10.1016/j.jcmds.2024.100107

Vittorio Bauduin , Salvatore Cuomo , Vincenzo Schiano Di Cola

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.

We introduce and analyze the Chebyshev-exponential (ChebEx) distribution for collocation points, as well as non-adaptive resampling strategies used during training.

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.

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.

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引用次数: 0

Efficiency of the multisection method 多分段法的效率

Journal of Computational Mathematics and Data Science

Pub Date : 2024-11-02 DOI: 10.1016/j.jcmds.2024.100106

J.S.C. Prentice

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 W function.

我们研究了单变量非线性方程的多分段法与著名的分段法相比的效率。我们的研究表明，有一种最省力的算法可以使用比分段法更多的分段，尽管这种最优算法与问题有关。最优化所需的截面数是通过兰伯特 W 函数确定的。

引用次数: 0

Bayesian optimization of one-dimensional convolutional neural networks (1D CNN) for early diagnosis of Autistic Spectrum Disorder 贝叶斯优化一维卷积神经网络 (1D CNN)，用于自闭症谱系障碍的早期诊断

Journal of Computational Mathematics and Data Science

Pub Date : 2024-10-19 DOI: 10.1016/j.jcmds.2024.100105

Temidayo Oluwatosin Omotehinwa , Morolake Oladayo Lawrence , David Opeoluwa Oyewola , Emmanuel Gbenga Dada

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.

自闭症（ASD）是一种具有挑战性的神经发育障碍，表现为社交、沟通和重复行为不良。如果能及早发现自闭症，治疗效果会更好，但目前的诊断测试依赖于主观意见，耗费大量时间，而且模糊不清。本研究旨在优化一维卷积神经网络（1D CNN），以提高早期 ASD 诊断的准确性和速度。我们使用一维卷积神经网络（1D CNN）对代表不同年龄组（幼儿、儿童、青少年和成人）的四个 ASD 数据集进行了建模。这些数据集可在 UCI 机器学习资料库和 Kaggle 上向公众开放，它们包含与 ASD 诊断相关的行为特征。每个数据集都经过了特征选择、分类编码和缺失值处理。然后，使用预定义的超参数在每个数据集上建立基线 1D CNN 模型。随后，使用树状结构帕尔森估计器（TPE）对基线模型进行了优化。我们开发了一种基于网络的交互式 ASD 诊断工具，通过预先训练的特定年龄优化模型来处理用户输入，从而确定 ASD 的概率。优化后的一维 CNN 模型在所有年龄组中的表现都明显优于基线模型，在准确率、精确度、召回率、F1 分数、MCC 和 AUC ROC 方面均达到了 100%。这意味着优化后的模型可以可靠地识别出不同年龄组中患有或未患有 ASD 的人群。基于网络的交互式诊断工具的开发扩展了模型的实用性，使其可以在临床和家庭中使用。

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引用次数: 0

Novel color space representation extracted by NMF to segment a color image 用 NMF 提取的新颖色彩空间表示法分割彩色图像

Journal of Computational Mathematics and Data Science

Pub Date : 2024-10-18 DOI: 10.1016/j.jcmds.2024.100104

Ciro Castiello , Nicoletta Del Buono , Flavia Esposito

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.

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.

本文探讨了将彩色图像中的像素分为背景和前景两类的任务。图像的新表示法包括额外的信息，即 "元颜色"（metacolor），这些信息可能与前景和背景相关，并可用于改进所研究图像的二元分割。在定性和定量实验中，与直接对原始图像应用普通的简单阈值算法相比，使用新颖的色彩空间表示法可在二值分割结果上产生一些改进。

引用次数: 0

Enhanced MRI brain tumor detection and classification via topological data analysis and low-rank tensor decomposition 通过拓扑数据分析和低阶张量分解增强磁共振成像脑肿瘤检测和分类能力

Journal of Computational Mathematics and Data Science

Pub Date : 2024-10-03 DOI: 10.1016/j.jcmds.2024.100103

Serena Grazia De Benedictis , Grazia Gargano , Gaetano Settembre

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.

医学成像领域人工智能的出现为脑肿瘤诊断的重大进展铺平了道路。本研究提出了一种新颖的组合方法，利用磁共振成像（MRI）来识别和分类垂体瘤、脑膜瘤和胶质瘤等常见脑癌。所提出的工作流程由两方面的方法组成：首先，它在数据预处理中采用了非琐碎的图像增强技术、用于降维的低秩塔克分解以及机器学习（ML）分类器来检测和预测脑肿瘤的类型。其次，利用拓扑数据分析（TDA）技术 "持久同源性"（PH）提取磁共振成像扫描中的潜在关键区域。当与 ML 分类器输出配对时，这些附加信息可以帮助领域专家识别可能包含肿瘤特征的感兴趣区域，从而提高 ML 预测的可解释性。与自动诊断相比，这种透明度增加了另一个层次的信心，对临床接受度至关重要。该系统的性能在一个著名的磁共振成像数据集上进行了定量评估，使用极随机树模型的总体分类准确率为 97.28%。这些令人鼓舞的结果表明，TDA、ML 和低阶近似方法的集成是脑肿瘤识别和分类的一种成功方法，为进一步研究和临床应用奠定了坚实的基础。

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引用次数: 0

Artifact removal from ECG signals using online recursive independent component analysis 利用在线递归独立成分分析去除心电信号中的伪影

Journal of Computational Mathematics and Data Science

Pub Date : 2024-09-27 DOI: 10.1016/j.jcmds.2024.100102

K. Gunasekaran , V.D. Ambeth Kumar , Mary Judith A.

The diagnosis of cardiac abnormalities and monitoring of heart health heavily rely on Electrocardiogram (ECG) signals. Unfortunately, these signals frequently encounter interference from diverse artifacts, impeding precise interpretation and analysis. To overcome this challenge, we suggest a novel method for real-time artifact removal from ECG signals through the utilization of Online Recursive Independent Component Analysis (ORICA). Our study outlines a systematic preprocessing pipeline, adaptively estimating the mixing matrix and demixing matrix of the ICA model while streaming data is processed. Additionally, we explore the selection of appropriate ICA components and the use of relevant feature extraction techniques to enhance the quality of extracted cardiac signals. This research presents a promising solution for removing artifacts from ECG signals in real-time, paving the way for improved cardiac diagnostics and monitoring systems. Comparative analyses demonstrate significant improvements in the accuracy of subsequent ECG analysis and interpretation following the application of our ORICA-based preprocessing.

诊断心脏异常和监测心脏健康在很大程度上依赖于心电图（ECG）信号。遗憾的是，这些信号经常会受到各种伪影的干扰，妨碍了精确的解读和分析。为了克服这一挑战，我们提出了一种新方法，利用在线递归独立成分分析（ORICA）实时去除心电信号中的伪影。我们的研究概述了一个系统化的预处理管道，在处理流数据的同时自适应地估计 ICA 模型的混合矩阵和去混合矩阵。此外，我们还探讨了如何选择合适的 ICA 分量，以及如何使用相关的特征提取技术来提高提取的心脏信号的质量。这项研究为实时去除心电信号中的伪影提供了一个前景广阔的解决方案，为改进心脏诊断和监测系统铺平了道路。对比分析表明，在应用基于 ORICA 的预处理后，后续心电图分析和解读的准确性有了显著提高。

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引用次数: 0

Leveraging feed-forward neural networks to enhance the hybrid block derivative methods for system of second-order ordinary differential equations 利用前馈神经网络增强二阶常微分方程系统的混合分块导数法

Journal of Computational Mathematics and Data Science

Pub Date : 2024-09-20 DOI: 10.1016/j.jcmds.2024.100101

Sabastine Emmanuel , Saratha Sathasivam , Muideen O. Ogunniran

This study introduces an innovative method combining discrete hybrid block techniques and artificial intelligence to enhance the solution of second-order Ordinary Differential Equations (ODEs). By integrating feed-forward neural networks (FFNN) into the hybrid block derivative method (HBDM), the modified approach shows improved accuracy and efficiency compared to traditional methods. Through comprehensive comparisons with exact and existing solutions, the study demonstrates the effectiveness of the proposed approach. The evaluation, utilizing root mean square error (RMSE), confirms its superior performance, robustness, and applicability in diverse scenarios. This research sets a new standard for solving complex ODE systems, offering promising avenues for future research and practical implementations.

本研究介绍了一种结合离散混合块技术和人工智能的创新方法，以提高二阶常微分方程（ODE）的求解能力。通过将前馈神经网络（FFNN）集成到混合分块导数法（HBDM）中，与传统方法相比，改进后的方法显示出更高的精度和效率。通过与精确解法和现有解法的综合比较，该研究证明了所提方法的有效性。利用均方根误差 (RMSE) 进行的评估证实了该方法的卓越性能、稳健性和在各种情况下的适用性。这项研究为解决复杂的 ODE 系统设定了新的标准，为未来的研究和实际应用提供了广阔的前景。

引用次数: 0

On resolution coresets for constrained clustering 关于约束聚类的分辨率核心集

Journal of Computational Mathematics and Data Science

Pub Date : 2024-09-01 DOI: 10.1016/j.jcmds.2024.100100

Maximilian Fiedler, Peter Gritzmann, Fabian Klemm

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the computations and hence allow to extend algorithms to much larger problem sizes. The present paper deals with a weight-balanced clustering problem, and is specifically motivated by an application in materials science where a voxel-based image is to be processed into a diagram representation. Here, the class of desired coresets is naturally confined to those which can be viewed as lowering the resolution of the input data. While one might expect that such resolution coresets are inferior to unrestricted coreset we prove bounds for resolution coresets which improve known bounds in the relevant dimensions and also lead to significantly faster algorithms in practice.

事实证明，以核心集概念为形式的特定数据压缩技术对许多优化问题都非常有效。事实上，在严格控制近似误差的同时，核心集可以显著加快计算速度，从而将算法扩展到更大的问题规模。本文讨论的是权重平衡聚类问题，其具体动机来自材料科学中的一个应用，即把基于体素的图像处理成图表表示。在这里，所需的核心集类别自然仅限于那些可被视为降低输入数据分辨率的核心集。虽然人们可能会认为这种分辨率核心集不如无限制核心集，但我们证明了分辨率核心集的边界，这改进了相关维度中的已知边界，并在实践中大大加快了算法的速度。

引用次数: 0

Fast empirical scenarios 快速经验方案

Journal of Computational Mathematics and Data Science

Pub Date : 2024-09-01 DOI: 10.1016/j.jcmds.2024.100099

Michael Multerer , Paul Schneider , Rohan Sen

We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a scenario-based representation of covariance matrices. The second proposal selects important data points from states of the world that have already realized, and are consistent with higher-order sample moment information. Both algorithms are efficient to compute and lend themselves to consistent scenario-based modeling and multi-dimensional numerical integration that can be used for interpretable decision-making under uncertainty. Extensive numerical benchmarking studies and an application in portfolio optimization favor the proposed algorithms.

我们试图从大型面板数据中提取少量与样本矩一致的代表性情景。在两种新颖的算法中，第一种算法能识别以前未观察到的情景，并提供基于情景的协方差矩阵表示。第二种建议是从已经实现的世界状态中选择重要数据点，并与高阶样本矩信息保持一致。这两种算法的计算效率都很高，并适合于基于情景的一致建模和多维数值积分，可用于不确定情况下的可解释决策。广泛的数值基准研究和在投资组合优化中的应用都有利于所提出的算法。

引用次数: 0

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