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Determination of the optimal number of independent components based on similarity measurement testing

Expert Systems with Applications 2025年 284卷

作者： Lu, Zeyi Yang, Mingshu E, Jianwei Liu, Chengji School of Mathematical Sciences & Center for Applied Mathematics of Guangxi Guangxi Minzu University Nanning530006 China School of Computer Science and Technology Xidian University Xi'an710071 China

Independent component analysis (ICA) has become a prominent statistical and computational method for signals separation and features extraction. ICA model can extract a great quantity of independent components (ICs) from the observed signals, some of which maybe not the pure components due to the random factors. There exist few approaches on determining the optimal number of the ICs accurately. This study proposes a novel method to determine the optimal number of ICs by running ICA separately on the sub-blocks of the observed signals, and determining the number of pure components which are remarkably similar between the blocks. Initially, a two stage sampling method is employed to the observed signals for obtaining two sub-blocks, which are representative of the observed signals. Secondly, a novel similarity measurement is proposed to identify the ICs that correspond to the pure signals between the two sub-blocks. Furthermore, we identify remarkably similar components utilizing the approach inspired by the principle of hypothesis testing, in which the Bonferroni correction is applied to mitigate the risk of Type-I errors. The experimental results on the manmade and real-word signals, including voice signals, electroencephalogram signals and hyperspectral data, verify the effectiveness and superiority of the proposed method in both small sample and sufficient sample scenarios. © 2025 Elsevier Ltd

关键词： Signal sampling

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STRUCTURE-AWARE ANALYSES AND ALGORITHMS FOR INTERPOLATIVE DECOMPOSITIONS

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SIAM Journal on Scientific Computing 2025年第3期47卷 A1527-A1554页

作者： Armstrong, Robin Buzali, Alex Damle, Anil Center for Applied Mathematics Cornell University IthacaNY14850 United States School of Engineering and Applied Sciences Harvard University AllstonMA02134 United States Department of Computer Science Cornell University IthacaNY14853 United States

Low-rank approximation is a task of critical importance in modern science, engineering, and statistics. Many low-rank approximation algorithms, such as the randomized singular value decomposition (RSVD), project their input matrix into a subspace approximating the span of its leading singular vectors. Other algorithms compress their input into a small subset of representative rows or columns, leading to a so-called interpolative decomposition. This paper investigates how the accuracy of interpolative decompositions is affected by the structural properties of the input matrix being operated on, including how these properties affect the performance comparison between interpolative decompositions and RSVD. We give particular focus to a randomized Golub-Klema-Stewart (RGKS) algorithm, an interpolative decomposition algorithm which combines RSVD with the Golub-Klema-Stewart pivoting strategy. Through numerical experiments, we find that matrix structures including singular subspace geometry and singular spectrum decay play a significant role in determining the performance comparison between these different algorithms. We also prove inequalities which bound the error of a general interpolative decomposition in terms of these matrix structures. Finally, we develop forms of these bounds specialized to RGKS while considering how randomization affects the approximation error of this algorithm. Copyright © by SIAM.

关键词： Matrix factorization

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Synergizing vision transformer with ensemble of deep learning model for accurate kidney stone detection using CT imaging

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Alexandria Engineering Journal 2025年 127卷 357-373页

作者： Arwa Alzughaibi Adwan A. Alanazi Mohammed Alshahrani Ines Hilali Jaghdam Abaker A. Hassaballa Applied college Taibah University Madinah Saudi Arabia Department of Computer Science and Information College of Computer Science and Engineering University of Hail Hail Saudi Arabia Department of Computer Sciences Applied College Najran University Najran 66462 Saudi Arabia Department of Computer Science and Information Technology Applied College Princess Nourah bint Abdulrahman University P.O. Box 84428 Riyadh 11671 Saudi Arabia Center for Scientific Research and Entrepreneurship Northern Border University Arar 73213 Saudi Arabia Department of Mathematics Faculty of Science Northern Border University Arar 73213 Saudi Arabia

The disease of Kidney stones is a risky disease for individuals all over the world. Many people with kidney stones in the early phase do not detect it as an illness, and it harms the organ gradually. Precise analysis of kidney illness is vital, as it is a major health concern that needs accurate detection for appropriate and effective treatment. CT scans are one of the most extensively accessible imaging models, and they are employed for effective diagnosis. Deep learning (DL) techniques are gradually identified as beneficial tools for analyzing illness in the medical field. However, present techniques employing deep networks often meet low accuracy and overfitting challenges, demanding further alteration for optimum performance. This study presents a Leveraging Flying Foxes Optimization with an Ensemble of Deep Learning for Accurate Kidney Stone Detection (LFFOEDL-AKSD) technique in CT scans. The presented LFFOEDL-AKSD technique mainly focuses on detecting kidney stones using CI imaging. At first, the presented LFFOEDL-AKSD technique applies the pre-processing phase, which involves image resizing for uniform CT scan dimensions and data augmentation through transformations like rotation and flipping to reduce overfitting, sobel filtering (SF) sharpens edges, and the data is separated into training, validation, and testing sets for model development. The presented LFFOEDL-AKSD technique employs the swin transformer (ST) model for the feature extraction method. Furthermore, the majority voting ensemble of three DL approaches, such as the graph convolutional network (GCN), temporal convolutional network (TCN), and three-dimensional convolutional autoencoder (3D-CAE) approaches, are employed to increase the precision and reliability of the kidney stone recognition. Finally, the presented LFFOEDL-AKSD technique implements the flying foxes optimization (FFO) approach for the hyperparameter tuning involved in the ensemble learning models. An extensive experiment is conduct

关键词： Flying foxes optimization Ensemble deep learning Kidney stone detection CI imaging Swin transformer

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Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem

arXiv

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arXiv 2025年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Computational Applied Mathematics & Operations Research Rice University United States Department of Mathematics The University of Arizona United States

We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing computational costs by integrating a surrogate model into a multilevel Monte Carlo method. The resulting surrogate-enhanced multilevel Monte Carlo methods reduce the cost of simulation by factors as large as 104 compared to standard Monte Carlo simulations involving direct numerical solutions of the associated Grad-Shafranov partial differential equation. Accuracy assessments also show that surrogate-based sampling closely aligns with the results of direct computation, confirming its effectiveness in capturing the behavior of plasma boundary and geometric *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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Improved Bounds on the Size of Permutation codes under Kendall τ-metric

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IEEE Transactions on Information Theory 2025年

作者： Parvaresh, Farzad Sobhani, Reza Abdollahi, Alireza Bagherian, Javad Jafari, Fatemeh Khatami, Maryam University of Isfahan Faculty of Engineering Department of Electrical Engineering Isfahan Iran School of Mathematics Tehran19395-5746 Iran University of Isfahan Faculty of Mathematics and Statistics Department of Applied Mathematics and Computer Science Isfahan81746-73441 Iran University of Isfahan Faculty of Mathematics and Statistics Department of Pure Mathematics Isfahan81746-73441 Iran

In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation method has been proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size P(n, d) of permutation codes of length n, i.e., subsets of the set Sn of all permutations on {1, ..., n} with the minimum distance at least (Formula presented) under the Kendall τ-metric. By presenting an algorithm and two theorems, we improve the known lower and upper bounds for P(n, d). In particular, we show that P(n, d) = 4 for all n ≥ 6 and (Formula presented). Additionally, we prove that for any prime number n and integer (Formula presented). This result greatly improves the upper bound of P(n, 3) for all primes n ≥ 37. © 1963-2012 IEEE.

关键词： Flash memory

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Representation with Minimized Max-Error in Optimal Piecewise Linear Approximation of Time Series Data 25th

Representation with Minimized Max-Error in Optimal Piecewi...

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25th International Conference on Web Information Systems Engineering, WISE 2024

作者： Zhao, Huanyu Li, Tongliang Wen, Shiting Shu, Zhenyu Deng, Ke Yang, Jian Pang, Chaoyi School of Computer Science and Technology Donghua University Shanghai China Institute of Applied Mathematics Hebei Academy of Sciences Shijiazhuang China Hebei Authentication Technology Engineering Research Center Shijiazhuang China Institute of Biology Hebei Academy of Sciences Shijiazhuang China School of Computer and Data Engineering NingboTech University Ningbo China RMIT University Melbourne Australia Macquarie University Sydney Australia

ISBN: (纸本)9789819605781

In the past two decades, Piecewise Linear Approximation under maximum error (max-error) bound (PLA∞) has been intensively studied for effective qualified representation and analysis of time series data. It divides a time series into fragments and then represents each fragment with a straight line to approximate the data points of that time slot. In this paper, to elevate the representation quality in the optimal PLA∞ results, we present a linear-time algorithm FindMin to construct the unique line representative of minimized maximum error (min-max error) for each fragment. Through extended experimental tests, we demonstrate that the proposed algorithm is very efficient in execution and achieves better performances than the state-of-the-art solutions. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Time series analysis

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Applying Layer-Wise Relevance Propagation on U-Net Architectures 27th

Applying Layer-Wise Relevance Propagation on U-Net Architect...

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27th International Conference on Pattern Recognition, ICPR 2024

作者： Weinberger, Patrick Fröhler, Bernhard Heim, Anja Gall, Alexander Bodenhofer, Ulrich Senck, Sascha Research Group Computed Tomography University of Applied Sciences Upper Austria Wels Austria School of Informatics Communication and Media University of Applied Sciences Upper Austria Wels Austria Johannes Kepler University Linz Linz Austria Faculty of Computer Science and Mathematics University of Passau Passau Germany Division Development Center X-ray Technology Fraunhofer Institute for Integrated Circuits IIS Erlangen Germany

ISBN: (纸本)9783031781971

For safety critical applications, it is still a challenge to use AI and fulfill all regulatory requirements. Medicine/healthcare and transportation are two fields where regulatory requirements are of fundamental importance. A wrong decision can lead to serious hazards or even deaths. In these fields, semantic segmentation is often utilized to extract features. Especially U-Net architectures are used. This paper shows how to apply layer-wise relevance propagation (LRP) to a trained U-Net architecture. We achieve an efficient explanation of a segmentation by back-propagating the whole resulting image. To tackle the non-linear results of the LRP, we introduce a threshold mechanism in combination with a logarithmic transfer function to preprocess the data for visualization. We demonstrate our method on three use cases: the segmentation of a fiber-reinforced polymer in the field of non-destructive testing, the segmentation of pedestrians in an automotive application, and a lung segmentation example from the medical domain. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Semantic Segmentation

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Integration of aggregated data in causally interpretable meta-analysis by inverse weighting

arXiv

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arXiv 2025年

作者： Vo, Tat Thang Le, Tran Trong Khoi Afach, Sivem Vansteelandt, Stijn Research Group EPIDERME Faculty of Medicine University Paris Est Creteil France Department of Applied Mathematics Computer Science and Statistics Ghent University Belgium

Obtaining causally interpretable meta-analysis results is challenging when there are differences in the distribution of effect modifiers between eligible trials. To overcome this, recent work on transportability methods has considered standardizing results of individual studies over the case-mix of a target population, prior to pooling them as in a classical random-effect meta-analysis. One practical challenge, however, is that case-mix standardization often requires individual participant data (IPD) on outcome, treatments and case-mix characteristics to be fully accessible in every eligible study, along with IPD case-mix characteristics for a random sample from the target population. In this paper, we aim to develop novel strategies to integrate aggregated-level data from eligible trials with non-accessible IPD into a causal meta-analysis, by extending moment-based methods frequently used for population-adjusted indirect comparison in health technology assessment. Since valid inference for these moment-based methods by M-estimation theory requires additional aggregated data that are often unavailable in practice, computational methods to address this concern are also developed. We assess the finite-sample performance of the proposed approaches by simulated data, and then apply these on real-world clinical data to investigate the effectiveness of risankizumab versus ustekinumab among patients with moderate to severe psoriasis. © 2025, CC BY.

关键词： Inverse problems

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Ramsey’s Conjecture for the Model with Non-liquid Capital 15th

Ramsey’s Conjecture for the Model with Non-liquid Capita...

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15th International Conference on Optimization and Applications, OPTIMA 2024

作者： Parastaev, Grigorii S. Shananin, Alexander A. Lomonosov Moscow State University Moscow Russia Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences Moscow Russia Moscow Institute of Physics and Technology Moscow Oblast Dolgoprudny Russia Peoples’ Friendship University of Russia Moscow Russia Moscow Center of Fundamental and Applied Mathematics Moscow Russia

ISBN: (纸本)9783031791185

Ramsey’s conjecture on social stratification states that economic agents divide into two classes: the class of thrifty agents, who jointly accumulate and share all the economy wealth, and the class of impatient ones forced to live on the wage level only. The present paper outlines the validity of Ramsey’s conjecture on social stratification for the household population in case when capital is non-liquid. The households’ behavior is described by the Ramsey type model of the rational representative consumer. We derive the solution in the synthesis form for the corresponding optimal control problem and use it in the social dynamics model for the household population, where the discount rates, according to Duesenberry’s relative income hypothesis, are set as functions dependent on ratio between capital holdings of specific agent and total capital available of economy. The agents behave in myopic manner, suggesting that the interest rate and the wage rate do not change over time. The connection between the Gini index and the Lyapunov function is also established. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Wages

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Teaching An Old Dog New Tricks: Porting Legacy Code to Heterogeneous Compute Architectures With Automated Code Translation

arXiv

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arXiv 2025年

作者： Nytko, Nicolas Reisner, Andrew Moulton, J. David Olson, Luke N. West, Matthew Department of Computer Science University of Illinois at Urbana-Champaign United States Applied Computer Science Los Alamos National Laboratory New Zealand Applied Mathematics and Plasma Physics Los Alamos National Laboratory New Zealand Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign United States

Legacy codes are in ubiquitous use in scientific simulations;they are well-tested and there is significant time investment in their use. However, one challenge is the adoption of new, sometimes incompatible computing paradigms, such as GPU hardware. In this paper, we explore using automated code translation to enable execution of legacy multigrid solver code on GPUs without significant time investment and while avoiding intrusive changes to the codebase. We developed a thin, reusable translation layer that parses Fortran 2003 at compile time, interfacing with the existing library Loopy (Klöckner 2014) to transpile to C++/GPU code, which is then managed by a custom MPI runtime system that we created. With this low-effort approach, we are able to achieve a payoff of an approximately 2–3× speedup over a full CPU socket, and 6× in multi-node settings. © 2025, CC BY-SA.

关键词： Investments

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