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Training of Convolutional Neural Networks for Image Classification with Fully Decoupled Extended Kalman Filter 利用完全去耦扩展卡尔曼滤波器训练用于图像分类的卷积神经网络
IF 2.3 Q2 Mathematics Pub Date : 2024-06-06 DOI: 10.3390/a17060243
Armando Gaytan, Ofelia Begovich-Mendoza, Nancy Arana-Daniel
First-order algorithms have long dominated the training of deep neural networks, excelling in tasks like image classification and natural language processing. Now there is a compelling opportunity to explore alternatives that could outperform current state-of-the-art results. From the estimation theory, the Extended Kalman Filter (EKF) arose as a viable alternative and has shown advantages over backpropagation methods. Current computational advances offer the opportunity to review algorithms derived from the EKF, almost excluded from the training of convolutional neural networks. This article revisits an approach of the EKF with decoupling and it brings the Fully Decoupled Extended Kalman Filter (FDEKF) for training convolutional neural networks in image classification tasks. The FDEKF is a second-order algorithm with some advantages over the first-order algorithms, so it can lead to faster convergence and higher accuracy, due to a higher probability of finding the global optimum. In this research, experiments are conducted on well-known datasets that include Fashion, Sports, and Handwritten Digits images. The FDEKF shows faster convergence compared to other algorithms such as the popular Adam optimizer, the sKAdam algorithm, and the reduced extended Kalman filter. Finally, motivated by the finding of the highest accuracy of FDEKF with images of natural scenes, we show its effectiveness in another experiment focused on outdoor terrain recognition.
长期以来,一阶算法一直主导着深度神经网络的训练,在图像分类和自然语言处理等任务中表现出色。现在,探索能超越当前最先进结果的替代方法是一个引人注目的机会。从估算理论来看,扩展卡尔曼滤波器(EKF)是一种可行的替代方法,并已显示出优于反向传播方法的优势。当前的计算技术进步为我们提供了机会,重新审视源自 EKF 的算法,这些算法几乎被排除在卷积神经网络的训练之外。本文重新审视了一种解耦 EKF 方法,并提出了用于图像分类任务中卷积神经网络训练的全解耦扩展卡尔曼滤波器(FDEKF)。FDEKF 是一种二阶算法,与一阶算法相比具有一些优势,因此,由于找到全局最优的概率较高,它可以带来更快的收敛速度和更高的精度。本研究在知名数据集上进行了实验,这些数据集包括时尚、体育和手写数字图像。与其他算法(如流行的 Adam 优化器、sKAdam 算法和简化扩展卡尔曼滤波器)相比,FDEKF 的收敛速度更快。最后,由于发现 FDEKF 在自然场景图像中的准确率最高,我们在另一项侧重于室外地形识别的实验中展示了它的有效性。
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引用次数: 0
A Comparative Study of Machine Learning Methods and Text Features for Text Authorship Recognition in the Example of Azerbaijani Language Texts 以阿塞拜疆语文本为例,机器学习方法与文本特征在文本作者身份识别中的比较研究
IF 2.3 Q2 Mathematics Pub Date : 2024-06-05 DOI: 10.3390/a17060242
Rustam Azimov, Efthimios Providas
This paper presents various machine learning methods with different text features that are explored and evaluated to determine the authorship of the texts in the example of the Azerbaijani language. We consider techniques like artificial neural network, convolutional neural network, random forest, and support vector machine. These techniques are used with different text features like word length, sentence length, combined word length and sentence length, n-grams, and word frequencies. The models were trained and tested on the works of many famous Azerbaijani writers. The results of computer experiments obtained by utilizing a comparison of various techniques and text features were analyzed. The cases where the usage of text features allowed better results were determined.
本文以阿塞拜疆语为例,介绍了各种具有不同文本特征的机器学习方法,并对这些方法进行了探讨和评估,以确定文本的作者身份。我们考虑了人工神经网络、卷积神经网络、随机森林和支持向量机等技术。这些技术使用了不同的文本特征,如单词长度、句子长度、单词长度和句子长度的组合、n-grams 和词频。这些模型在许多阿塞拜疆著名作家的作品上进行了训练和测试。通过比较各种技术和文本特征,对计算机实验结果进行了分析。确定了在哪些情况下使用文本特征可以获得更好的结果。
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引用次数: 0
Fitness Landscape Analysis of Product Unit Neural Networks 产品单元神经网络的适配性分析
IF 2.3 Q2 Mathematics Pub Date : 2024-06-04 DOI: 10.3390/a17060241
Andries P. Engelbrecht, Robert Gouldie 
A fitness landscape analysis of the loss surfaces produced by product unit neural networks is performed in order to gain a better understanding of the impact of product units on the characteristics of the loss surfaces. The loss surface characteristics of product unit neural networks are then compared to the characteristics of loss surfaces produced by neural networks that make use of summation units. The failure of certain optimization algorithms in training product neural networks is explained through trends observed between loss surface characteristics and optimization algorithm performance. The paper shows that the loss surfaces of product unit neural networks have extremely large gradients with many deep ravines and valleys, which explains why gradient-based optimization algorithms fail at training these neural networks.
为了更好地理解产品单元对损失面特征的影响,我们对产品单元神经网络产生的损失面进行了适配性景观分析。然后,将产品单元神经网络的损失面特征与使用求和单元的神经网络产生的损失面特征进行比较。通过观察损失面特征与优化算法性能之间的趋势,解释了某些优化算法在训练产品神经网络时的失败。论文表明,产品单元神经网络的损失面具有极大的梯度,其中有许多深谷和沟壑,这就解释了为什么基于梯度的优化算法在训练这些神经网络时会失败。
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引用次数: 0
An Interface to Monitor Process Variability Using the Binomial ATTRIVAR SS Control Chart 使用二叉 ATTRIVAR SS 控制图监控过程变异性的界面
IF 2.3 Q2 Mathematics Pub Date : 2024-05-16 DOI: 10.3390/a17050216
João Pedro Costa Violante, Marcela A. G. Machado, Amanda dos Santos Mendes, Túlio S. Almeida
Control charts are tools of paramount importance in statistical process control. They are broadly applied in monitoring processes and improving quality, as they allow the detection of special causes of variation with a significant level of accuracy. Furthermore, there are several strategies able to be employed in different contexts, all of which offer their own advantages. Therefore, this study focuses on monitoring the variability in univariate processes through variance using the Binomial version of the ATTRIVAR Same Sample S2 (B-ATTRIVAR SS S2) control chart, given that it allows coupling attribute and variable inspections (ATTRIVAR means attribute + variable), i.e., taking advantage of the cost-effectiveness of the former and the wealth of information and greater performance of the latter. Its Binomial version was used for such a purpose, since inspections are made using two attributes, and the Same Sample was used due to being submitted to both the attribute and variable stages of inspection. A computational application was developed in the R language using the Shiny package so as to create an interface to facilitate its application and use in the quality control of the production processes. Its application enables users to input process parameters and generate the B-ATTRIVAR SS control chart for monitoring the process variability with variance. By comparing the data obtained from its application with a simpler code, its performance was validated, given that its results exhibited striking similarity.
控制图是统计过程控制中最重要的工具。它们被广泛应用于监控过程和提高质量,因为它们可以非常准确地检测出导致变异的特殊原因。此外,在不同的情况下还可以采用多种策略,它们都有各自的优势。因此,本研究的重点是利用 ATTRIVAR Same Sample S2(B-ATTRIVAR SS S2)控制图的二项式版本,通过变异监测单变量过程中的变异性,因为它可以将属性检查和变量检查(ATTRIVAR 指属性 + 变量)结合起来,即利用前者的成本效益和后者的丰富信息和更高的性能。由于使用两个属性进行检验,因此使用了其二项式版本;由于同时进行属性和变量阶段的检验,因此使用了相同样本。使用 Shiny 软件包以 R 语言开发了一个计算应用程序,以创建一个界面,方便在生产过程的质量控制中应用和使用。通过该应用程序,用户可以输入工艺参数并生成 B-ATTRIVAR SS 控制图,以监控工艺的变异性。通过比较从其应用中获得的数据和一个更简单的代码,其性能得到了验证,因为其结果表现出惊人的相似性。
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引用次数: 0
Boundary SPH for Robust Particle–Mesh Interaction in Three Dimensions 三维鲁棒性粒子-网格相互作用的边界 SPH
IF 2.3 Q2 Mathematics Pub Date : 2024-05-16 DOI: 10.3390/a17050218
Ryan Kim, Paul M. Torrens
This paper introduces an algorithm to tackle the boundary condition (BC) problem, which has long persisted in the numerical and computational treatment of smoothed particle hydrodynamics (SPH). Central to the BC problem is a need for an effective method to reconcile a numerical representation of particles with 2D or 3D geometry. We describe and evaluate an algorithmic solution—boundary SPH (BSPH)—drawn from a novel twist on the mesh-based boundary method, allowing SPH particles to interact (directly and implicitly) with either convex or concave 3D meshes. The method draws inspiration from existing works in graphics, particularly discrete signed distance fields, to determine whether particles are intersecting or submerged with mesh triangles. We evaluate the efficacy of BSPH through application to several simulation environments of varying mesh complexity, showing practical real-time implementation in Unity3D and its high-level shader language (HLSL), which we test in the parallelization of particle operations. To examine robustness, we portray slip and no-slip conditions in simulation, and we separately evaluate convex and concave meshes. To demonstrate empirical utility, we show pressure gradients as measured in simulated still water tank implementations of hydrodynamics. Our results identify that BSPH, despite producing irregular pressure values among particles close to the boundary manifolds of the meshes, successfully prevents particles from intersecting or submerging into the boundary manifold. Average FPS calculations for each simulation scenario show that the mesh boundary method can still be used effectively with simple simulation scenarios. We additionally point the reader to future works that could investigate the effect of simulation parameters and scene complexity on simulation performance, resolve abnormal pressure values along the mesh boundary, and test the method’s robustness on a wider variety of simulation environments.
本文介绍了一种解决边界条件(BC)问题的算法,该问题长期存在于平滑粒子流体力学(SPH)的数值计算处理中。BC 问题的核心是需要一种有效的方法来协调粒子的数值表示与二维或三维几何。我们描述并评估了一种算法解决方案--边界 SPH (BSPH)--它源自基于网格的边界方法的一种新转折,允许 SPH 粒子与凸或凹三维网格进行(直接或隐式)交互。该方法借鉴了图形学领域的现有研究成果,特别是离散符号距离场,以确定粒子是否与网格三角形相交或被网格三角形淹没。我们通过将 BSPH 应用于不同网格复杂度的多个仿真环境来评估其功效,展示了在 Unity3D 及其高级着色器语言(HLSL)中的实际实时实现,并在粒子操作的并行化中对其进行了测试。为了检验鲁棒性,我们描绘了模拟中的滑移和无滑移条件,并分别评估了凸面和凹面网格。为了证明经验效用,我们展示了在模拟静止水箱流体力学实施中测量到的压力梯度。我们的结果表明,尽管 BSPH 在靠近网格边界流形的颗粒间产生了不规则的压力值,但它成功地防止了颗粒与边界流形相交或浸入边界流形。对每种模拟场景的平均 FPS 计算表明,网格边界法仍然可以有效地用于简单的模拟场景。此外,我们还为读者指出了未来的工作方向,即研究仿真参数和场景复杂度对仿真性能的影响,解决网格边界上的异常压力值,以及在更广泛的仿真环境中测试该方法的鲁棒性。
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引用次数: 0
Fault Location Method Based on Dynamic Operation and Maintenance Map and Common Alarm Points Analysis 基于动态运行维护图和常见报警点分析的故障定位方法
IF 2.3 Q2 Mathematics Pub Date : 2024-05-16 DOI: 10.3390/a17050217
Sheng Wu, Jihong Guan
Under a distributed information system, the scale of various operational components such as applications, operating systems, databases, servers, and networks is immense, with intricate access relationships. The silo effect of each professional is prominent, and the linkage mechanism is insufficient, making it difficult to locate the infrastructure components that cause exceptions under a particular application. Current research only plays a role in local scenarios, and its accuracy and generalization are still very limited. This paper proposes a novel fault location method based on dynamic operation maps and alarm common point analysis. During the fault period, various alarm entities are associated with dynamic operation maps, and alarm common points are obtained based on graph search addressing methods, covering deployment relationship common points, connection common points (physical and logical), and access flow common points. This method, compared with knowledge graph approaches, eliminates the complex process of knowledge graph construction, making it more concise and efficient. Furthermore, in contrast to indicator correlation analysis methods, this approach supplements with configuration correlation information, resulting in more precise positioning. Through practical validation, its fault hit rate exceeds 82%, which is significantly better than the existing main methods.
在分布式信息系统下,应用程序、操作系统、数据库、服务器、网络等各种运行组件规模庞大,访问关系错综复杂。各专业 "孤岛 "效应突出,联动机制不足,很难定位导致特定应用出现异常的基础设施组件。目前的研究只能在局部场景发挥作用,其准确性和普适性还非常有限。本文提出了一种基于动态运行图和报警公共点分析的新型故障定位方法。在故障期间,将各种告警实体与动态运行图关联起来,基于图搜索寻址方法获得告警公共点,涵盖部署关系公共点、连接公共点(物理和逻辑)和访问流公共点。与知识图谱方法相比,该方法省去了复杂的知识图谱构建过程,更加简洁高效。此外,与指标相关性分析方法相比,该方法补充了配置相关性信息,定位更加精确。通过实际验证,其故障命中率超过 82%,明显优于现有的主要方法。
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引用次数: 0
Improving 2–5 Qubit Quantum Phase Estimation Circuits Using Machine Learning 利用机器学习改进 2-5 Qubit 量子相位估计电路
IF 2.3 Q2 Mathematics Pub Date : 2024-05-15 DOI: 10.3390/a17050214
Charles Woodrum, Torrey Wagner, David Weeks
Quantum computing has the potential to solve problems that are currently intractable to classical computers with algorithms like Quantum Phase Estimation (QPE); however, noise significantly hinders the performance of today’s quantum computers. Machine learning has the potential to improve the performance of QPE algorithms, especially in the presence of noise. In this work, QPE circuits were simulated with varying levels of depolarizing noise to generate datasets of QPE output. In each case, the phase being estimated was generated with a phase gate, and each circuit modeled was defined by a randomly selected phase. The model accuracy, prediction speed, overfitting level and variation in accuracy with noise level was determined for 5 machine learning algorithms. These attributes were compared to the traditional method of post-processing and a 6x–36 improvement in model performance was noted, depending on the dataset. No algorithm was a clear winner when considering these 4 criteria, as the lowest-error model (neural network) was also the slowest predictor; the algorithm with the lowest overfitting and fastest prediction time (linear regression) had the highest error level and a high degree of variation of error with noise. The XGBoost ensemble algorithm was judged to be the best tradeoff between these criteria due to its error level, prediction time and low variation of error with noise. For the first time, a machine learning model was validated using a 2-qubit datapoint obtained from an IBMQ quantum computer. The best 2-qubit model predicted within 2% of the actual phase, while the traditional method possessed a 25% error.
量子计算有可能利用量子相位估计(QPE)等算法解决经典计算机目前难以解决的问题;然而,噪声极大地阻碍了当今量子计算机的性能。机器学习有可能提高 QPE 算法的性能,尤其是在存在噪声的情况下。在这项工作中,我们用不同程度的去极化噪声模拟了 QPE 电路,以生成 QPE 输出数据集。在每种情况下,估算的相位都由相位门产生,每个建模电路都由随机选择的相位定义。确定了 5 种机器学习算法的模型准确度、预测速度、过拟合程度以及准确度随噪声水平的变化。将这些属性与传统的后处理方法进行比较,发现模型性能提高了 6 倍至 36 倍,具体取决于数据集。考虑到这 4 项标准,没有一种算法能明显胜出,因为误差最小的模型(神经网络)同时也是预测速度最慢的;过拟合最小、预测时间最快的算法(线性回归)误差水平最高,误差随噪声的变化程度也很大。XGBoost 集合算法的误差水平、预测时间和误差随噪声的变化较小,因此被认为是这些标准之间的最佳平衡。首次使用从 IBMQ 量子计算机获得的 2 量子比特数据点对机器学习模型进行了验证。最佳的 2 量子位模型预测的实际相位误差在 2% 以内,而传统方法的误差为 25%。
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引用次数: 0
EPSOM-Hyb: A General Purpose Estimator of Log-Marginal Likelihoods with Applications in Probabilistic Graphical Models EPSOM-Hyb:应用于概率图形模型的对数边际似然通用估计器
IF 2.3 Q2 Mathematics Pub Date : 2024-05-15 DOI: 10.3390/a17050213
Eric Chuu, Yabo Niu, A. Bhattacharya, Debdeep Pati
We consider the estimation of the marginal likelihood in Bayesian statistics, with primary emphasis on Gaussian graphical models, where the intractability of the marginal likelihood in high dimensions is a frequently researched problem. We propose a general algorithm that can be widely applied to a variety of problem settings and excels particularly when dealing with near log-concave posteriors. Our method builds upon a previously posited algorithm that uses MCMC samples to partition the parameter space and forms piecewise constant approximations over these partition sets as a means of estimating the normalizing constant. In this paper, we refine the aforementioned local approximations by taking advantage of the shape of the target distribution and leveraging an expectation propagation algorithm to approximate Gaussian integrals over rectangular polytopes. Our numerical experiments show the versatility and accuracy of the proposed estimator, even as the parameter space increases in dimension and becomes more complicated.
我们考虑的是贝叶斯统计中的边际似然估计,主要侧重于高斯图形模型,其中高维度边际似然的难解性是一个经常被研究的问题。我们提出了一种通用算法,该算法可广泛应用于各种问题设置,尤其在处理近对数凹后验时表现出色。我们的方法建立在之前提出的算法基础之上,该算法使用 MCMC 样本分割参数空间,并在这些分割集上形成片断常数近似值,以此来估计归一化常数。在本文中,我们利用目标分布的形状和期望传播算法来近似矩形多边形上的高斯积分,从而改进了上述局部近似方法。我们的数值实验表明,即使参数空间的维度增加、变得更加复杂,我们所提出的估计方法仍具有多功能性和准确性。
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引用次数: 0
A General Statistical Physics Framework for Assignment Problems 作业问题的一般统计物理学框架
IF 2.3 Q2 Mathematics Pub Date : 2024-05-14 DOI: 10.3390/a17050212
P. Koehl, H. Orland
Linear assignment problems hold a pivotal role in combinatorial optimization, offering a broad spectrum of applications within the field of data sciences. They consist of assigning “agents” to “tasks” in a way that leads to a minimum total cost associated with the assignment. The assignment is balanced when the number of agents equals the number of tasks, with a one-to-one correspondence between agents and tasks, and it is and unbalanced otherwise. Additional options and constraints may be imposed, such as allowing agents to perform multiple tasks or allowing tasks to be performed by multiple agents. In this paper, we propose a novel framework that can solve all these assignment problems employing methodologies derived from the field of statistical physics. We describe this formalism in detail and validate all its assertions. A major part of this framework is the definition of a concave effective free energy function that encapsulates the constraints of the assignment problem within a finite temperature context. We demonstrate that this free energy monotonically decreases as a function of a parameter β representing the inverse of temperature. As β increases, the free energy converges to the optimal assignment cost. Furthermore, we demonstrate that when β values are sufficiently large, the exact solution to the assignment problem can be derived by rounding off the elements of the computed assignment matrix to the nearest integer. We describe a computer implementation of our framework and illustrate its application to multi-task assignment problems for which the Hungarian algorithm is not applicable.
线性赋值问题在组合优化中占有举足轻重的地位,在数据科学领域有着广泛的应用。线性赋值问题包括将 "代理 "分配给 "任务",从而使与赋值相关的总成本最小。当代理的数量等于任务的数量时,代理和任务之间是一一对应的,这种分配是平衡的,否则就是不平衡的。还可以施加其他选项和限制,如允许代理执行多项任务或允许任务由多个代理执行。在本文中,我们提出了一个新颖的框架,它能利用统计物理学领域的方法解决所有这些分配问题。我们详细描述了这一形式主义,并验证了其所有论断。该框架的一个主要部分是定义了一个凹形有效自由能函数,它在有限温度背景下封装了赋值问题的约束条件。我们证明,该自由能作为代表温度倒数的参数 β 的函数单调递减。随着 β 的增加,自由能趋近于最优分配成本。此外,我们还证明,当 β 值足够大时,通过将计算出的赋值矩阵元素舍入到最接近的整数,就能得出赋值问题的精确解。我们介绍了我们框架的计算机实现,并说明了它在匈牙利算法不适用的多任务分配问题中的应用。
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引用次数: 0
Solving Least-Squares Problems via a Double-Optimal Algorithm and a Variant of the Karush–Kuhn–Tucker Equation for Over-Determined Systems 通过双优算法和过确定系统的卡鲁什-库恩-塔克方程变式解决最小二乘法问题
IF 2.3 Q2 Mathematics Pub Date : 2024-05-14 DOI: 10.3390/a17050211
Chein-Shan Liu, C. Kuo, Chih-Wen Chang
A double optimal solution (DOS) of a least-squares problem Ax=b,A∈Rq×n with q≠n is derived in an m+1-dimensional varying affine Krylov subspace (VAKS); two minimization techniques exactly determine the m+1 expansion coefficients of the solution x in the VAKS. The minimal-norm solution can be obtained automatically regardless of whether the linear system is consistent or inconsistent. A new double optimal algorithm (DOA) is created; it is sufficiently time saving by inverting an m×m positive definite matrix at each iteration step, where m≪min(n,q). The properties of the DOA are investigated and the estimation of residual error is provided. The residual norms are proven to be strictly decreasing in the iterations; hence, the DOA is absolutely convergent. Numerical tests reveal the efficiency of the DOA for solving least-squares problems. The DOA is applicable to least-squares problems regardless of whether qn. The Moore–Penrose inverse matrix is also addressed by adopting the DOA; the accuracy and efficiency of the proposed method are proven. The m+1-dimensional VAKS is different from the traditional m-dimensional affine Krylov subspace used in the conjugate gradient (CG)-type iterative algorithms CGNR (or CGLS) and CGRE (or Craig method) for solving least-squares problems with q>n. We propose a variant of the Karush–Kuhn–Tucker equation, and then we apply the partial pivoting Gaussian elimination method to solve the variant, which is better than the original Karush–Kuhn–Tucker equation, the CGNR and the CGNE for solving over-determined linear systems. Our main contribution is developing a double-optimization-based iterative algorithm in a varying affine Krylov subspace for effectively and accurately solving least-squares problems, even for a dense and ill-conditioned matrix A with q≪n or q≫n.
在 m+1 维变化仿射克雷洛夫子空间(VAKS)中推导出了最小二乘问题 Ax=b,A∈Rq×n 且 q≠n 的双最优解(DOS);两种最小化技术精确确定了解 x 在 VAKS 中的 m+1 个扩展系数。无论线性系统是一致还是不一致,都能自动获得最小规范解。我们创建了一种新的双最优算法(DOA);它通过在每个迭代步骤中反转 m×m 正定矩阵(其中 m≪min(n,q))来充分节省时间。对 DOA 的特性进行了研究,并提供了残差误差的估计。证明残差规范在迭代中严格递减,因此 DOA 是绝对收敛的。数值测试表明了 DOA 在解决最小二乘问题时的效率。采用 DOA 方法还解决了 Moore-Penrose 逆矩阵问题,证明了所提方法的准确性和高效性。m+1 维 VAKS 不同于共轭梯度(CG)型迭代算法 CGNR(或 CGLS)和 CGRE(或 Craig 方法)中用于求解 q>n 最小二乘问题的传统 m 维仿射 Krylov 子空间。我们提出了 Karush-Kuhn-Tucker 方程的一个变体,然后应用部分枢轴高斯消元法求解该变体,在求解超定线性系统方面,该变体优于原始的 Karush-Kuhn-Tucker 方程、CGNR 和 CGNE。我们的主要贡献是在变化的仿射克雷洛夫子空间中开发了一种基于双重优化的迭代算法,即使对于q≪n或q≫n的密集且条件不佳的矩阵A,也能有效、准确地求解最小二乘问题。
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引用次数: 0
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Algorithms
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