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Matrix methods in data mining and pattern recognition /

丛书名： Fundamentals of algorithms

2019年

作者： Elde?n Lars

ISBN: (数字)9781611975864

ISBN: (纸本)9781611975857

This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. Matrix methods in Data Mining and Pattern Recognition, Second Edition is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.

关键词： Data mining. Pattern recognition systems algebras, linear

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几类结构化Sylvester线性方程（组）的数值方法研究

几类结构化Sylvester线性方程（组）的数值方法研究

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作者：杨吉成都理工大学

学位级别：硕士

结构Sylvester线性方程(组)在控制、系统理论等领域中有重要的应用.结构Sylvester方程(组)的求解是数值线性代数领域研究的一个重要问题之一.本文主要研究了几类结构Sylvester线性方程(组)数值方法.首先,分别给出了求解线性矩阵方程AXB+... 详细信息

结构Sylvester线性方程(组)在控制、系统理论等领域中有重要的应用.结构Sylvester方程(组)的求解是数值线性代数领域研究的一个重要问题之一.本文主要研究了几类结构Sylvester线性方程(组)数值方法.首先,分别给出了求解线性矩阵方程AXB+CXD=F和方程组（AXB+CYD,GXH+MYN）=（F,E）的Hermitian解的梯度迭代算法.并且证明了该算法收敛于Hermitian解.分别给出了两个充分条件,以保证所提算法的解收敛于任何初始矩阵的Hermitian解.其次,针对广义耦合Sylvester共轭线性矩阵方程组（？）的Hermitian自反解的求解,提出了一种有限迭代算法.证明了本文算法的收敛性.在这个矩阵方程组是相容的假设条件下,对于任意的初始Hermitian自反矩阵解,证明了该迭代算法在有限迭代步内能够收敛到没有舍入误差的精确解.进一步利用该方法得到了广义耦合Sylvester共轭矩阵方程组的具有最小Frobenius范数的Hermitian自反解.最后,给出了几个数值实例,说明了所研究的算法的有效性.

关键词：广义耦合Sylvester共轭矩阵方程组迭代算法 Hermitian自反解最小Frobenius范数

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Intellectualization of Computation Based on Neural Networks for Mathematical Modeling

Intellectualization of Computation Based on Neural Networks ...

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2019 IEEE International conference on Advanced Trends in Information theory, ATIT 2019

作者： Khimich, Alexander Sydoruk, Volodymyr Yershov, Pavlo VM Glushkov Institute of Cybernetics of NAS of Ukraine Department of Numerical Methods and Computer Modeling Kyiv Ukraine

ISBN: (纸本)9781728161440

The problem of automation of efficient algorithm choice for solving linear algebra problems with a priori undefined structure of sparse matrices is considered. An approach of matrix classification and selection of an effective algorithm based on a visual portrait of a sparse matrix using a neural networks is proposed. Datasets for training of convolutional neural network «Sparse Matrix Vision» were prepared. Computational experiments, conducted in a scope of a current research showed that the algorithm chosen by neural network is effective for a specific problem. © 2019 IEEE.

关键词： Matrix algebra

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Performing linear convergence for distributed constrained optimisation over time-varying directed unbalanced networks

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IET CONTROL theory AND applications 2019年第17期13卷 2800-2810页

作者： Lu, Qingguo Li, Huaqing Wang, Zheng Han, Qi Ge, Wei Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligen Chongqing 400715 Peoples R China Chongqing Univ Sci & Technol Coll Elect & Informat Engn Chongqing 401331 Peoples R China Nanjing Univ Coll Chem & Chem Engn Nanjing 210046 Jiangsu Peoples R China

The problem of distributed constrained optimisation over a network of agents, where the goal is to cooperatively minimise the sum of all local convex objective functions is studied. Each agent in the network possesses only its private local convex objective function and is constrained to a coupling equality constraint and its local inequality constraint. Moreover, the authors particularly focus on the scenario where each agent is only allowed to interact with their in-neighbours over a series of time-varying directed unbalanced networks. To collectively address the optimisation problem, a novel distributed primal-dual push-DIGing (integrated push-sum strategy with distributed inexact gradient tracking method) algorithm (termed as DPD-PD) in which agents employ uncoordinated step-sizes is proposed. Unlike other methods, DPD-PD allows not only the mixing matrices are column-stochastic, but also the step-sizes are uncoordinated. An important feature of DPD-PD is handling distributed constrained optimisation problems in the case of time-varying directed unbalanced networks. When objective functions are strongly convex and smooth, the authors demonstrate that DPD-PD converges linearly to the optimal solution given that the uncoordinated step-sizes are smaller than an upper bound. Explicit convergence rate is also conducted. Preliminary results on some numerical experiments validate the theoretical findings.

关键词： stochastic processes matrix algebra convergence of numerical methods convex programming optimisation convergence gradient methods minimisation iterative methods integrated push-sum strategy distributed inexact gradient tracking method uncoordinated step-sizes constrained optimisation problems time-varying unbalanced networks DPD-PD converges performing linear convergence distributed constrained optimisation local convex objective functions private local convex objective function coupling equality constraint local inequality constraint optimisation problem primal-dual push-DIGing

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Approximations of Schatten Norms via Taylor Expansions 1

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14th International Computer Science Symposium in Russia (CSR)

作者： Braverman, Vladimir Johns Hopkins Univ Baltimore MD 21218 USA

ISBN: (数字)9783030199555

ISBN: (纸本)9783030199555;9783030199548

In many applications of data science and machine learning data is represented by large matrices. Fast and accurate analysis of such matrices is a challenging task that is of paramount importance for the aforementioned applications. Randomized numerical linear algebra (RNLA) is an popular area of research that often provides such fast and accurate algorithmic methods for massive matrix computations. Many critical problems in RNLA boil down to approximating spectral functions and one of the most fundamental examples of such spectral functions is Schatten p norm. The p-th Schatten norm for matrix A is an element of R-n1xn2 is defined as the l(p) norm of a vector comprised of singular values of matrix A, i.e., parallel to A parallel to(p) = ((i=1)Sigma(min(n1,n2)) vertical bar sigma i(A)vertical bar(p))(1/p), where sigma(i) (A) is the i-th singular value of A. In this paper we consider symmetric, positive semidefinite (SPSD) matrix A and present an algorithm for computing the p-Schatten norm AMP. Our methods are simple and easy to implement and can be extended to general matrices. Our algorithms improve, for a range of parameters, recent results of Musco, Netrapalli, Sidford, Ubaru and Woodruff (ITCS 2018), e.g., for p > 2 and sufficiently small values of epsilon.

关键词： Randomized numerical linear algebra Schatten norms Algorithms

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Solution of boundary value problems for a system of polyharmonic equations of a special type with applications 12

Solution of boundary value problems for a system of polyharm...

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12th International conference on Mesh methods for Boundary - Value Problems and applications

作者： Mikishanina, E. A. Chuvash State Univ 15 Moskovskiy Ave Cheboksary 428015 Russia

The method of numerical solution of the system of polyharmonic equations of two types is proposed: 1) the right part is a given polyharmonic function;2) the right part is also the desired polyharmonic function. The method is based on Green's integral identity and the boundary element method. The system of polyharmonic equations with boundary conditions is reduced to a system of integral identities, and then after the discretization to a system of linear algebraic equations. numerical examples of solving boundary value problems on the plane are considered, including the problem of shell and plate theory.

关键词： Boundary value problems

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State bounding for positive singular discrete-time systems with time-varying delay and bounded disturbances

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IET CONTROL theory AND applications 2019年第16期13卷 2571-2582页

作者： Nguyen Huu Sau Mai Viet Thuan Hanoi Univ Ind Fac Fundamental Sci 298 Caudien Hanoi Vietnam Ton Duc Thang Univ Dept Management Sci & Technol Dev Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Math & Stat Ho Chi Minh City Vietnam Duy Tan Univ Inst Res & Dev Danang 550000 Vietnam

This study deals with the problem of state bounding for positive singular discrete-time systems with time-varying delay and bounded disturbances. First, the authors derive some new conditions for the existence of componentwise bounds of the state vector of the systems without disturbances. Then, in the case of systems with bounded disturbances, they obtain a sufficient condition for the existence of componentwise ultimate bounds. Since the conditions are given in terms of the spectral radius of the system matrices, they can check them easily and compute directly the smallest componentwise ultimate bound. In addition, the problem of state bounding for positive time-varying singular systems is also investigated in this study. Finally, numerical examples are provided to illustrate the effectiveness and advantages of their results.

关键词： matrix algebra linear systems delays continuous time systems time-varying systems Lyapunov methods discrete time systems bounded disturbances componentwise ultimate bounds system matrices directly the smallest componentwise ultimate state bounding positive time-varying singular systems discrete-time systems time-varying delay componentwise bounds state vector

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Stabilisation of coupled delayed regime-switching diffusion with continuous-state-dependent switching via intermittent control

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IET CONTROL theory AND applications 2019年第12期13卷 1823-1833页

作者： Xu, Yao Chu, Chenyin Li, Wenxue Harbin Inst Technol Weihai Dept Math Weihai 264209 Peoples R China

Motivated by Markovian regime-switching diffusion (MRSD), time-varying delays and non-linear coupling forms, this study is concerned with stabilisation of coupled regime-switching diffusion with time-varying delays (CRSDTD) under periodically intermittent control. Compared with most papers investigating MRSD, a striking feature of regime-switching diffusion is that in the two-component process (x(t),\alpha (t))x(t),alpha(t)), switching process alpha (t)alpha(t) depends on the diffusion x(t)x(t), which can be regarded as the x-dependent process briefly. It is worth mentioning that time-varying delays and non-linear coupling forms are taken into consideration when modelling, which makes their work more realistic. Moreover, a periodically intermittent controller is adopted to guarantee that CRSDTD can achieve the pth moment exponential stability and some sufficient conditions are derived by using the Lyapunov method and Kirchhoff's matrix tree theorem. Furthermore, to illustrate the applicability of their theoretical results, an application to regime-switching coupled oscillators with time-varying delays (RSCOTD) is presented and a stability criterion is given. Conclusively, numerical simulations on RSCOTD are presented to illustrate the effectiveness of the theoretical results.

关键词： asymptotic stability delays matrix algebra Lyapunov methods stochastic systems stability time-varying systems Markov processes coupled delayed regime-switching diffusion continuous-state-dependent switching MRSD time-varying delays nonlinear coupling forms coupled regime-switching diffusion periodically intermittent control process (t) dependent process briefly periodically intermittent controller regime-switching coupled oscillators

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Design of Delayed Output Feedback of linear Time-Varying Systems With applications to Spacecraft Magnetic Attitude Control 31

Design of Delayed Output Feedback of Linear Time-Varying Sys...

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31st Chinese Control And Decision conference (CCDC)

作者： Xu, Chuanchuan Thou, Bin Hou, Mingzhe Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China

ISBN: (纸本)9781728101057

This paper studies the low-pass filter (LPF) design in the delayed output feedback control of linear time-varying systems. In the case of linear time-invariant systems, the safe implementation of the distributed delay (integral terms) needs to introduce an LPF in the control loop and the LPF can be designed by using the pole assignment method. However, the parameters of LPF in linear time-varying systems are time-varying and the existing design methods are not applicable. This paper provides a new method to design the LPF for time-varying systems. The designed LPFs are such that, if the closed-loop system without LPF is uniformly asymptotically stable, then the closed-loop system with LPF is also uniformly asymptotically stable, while the later is robust with respect to approximated numerical implementation. Finally, simulations are carried out on a magnetic attitude control system and the results verify the effectiveness of the methods proposed in this paper.

关键词： Low-pass Filter Delayed Output Feedback Time-delay Systems Spacecraft Attitude Control Magnetic Attitude Control

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The Maximum Localization Error Bound of Distributed Array for Focused Energy Delivery in Precision Electronic Warfare

The Maximum Localization Error Bound of Distributed Array fo...

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International conference on Computer and Communications (ICCC)

作者： Zhongping Yang Shuning Yang Jianyun Zhang Qingsong Zhou College of Electronic Engineering National University of Defense Technology Hefei China

ISBN: (数字)9781728186351

ISBN: (纸本)9781728186368

Focused energy delivery is the core technology for bringing energy to a specific area by the ultra-sparse array. This paper mainly focuses on one of its typical applications: precision electronic warfare (PREW), and analyzes the influence of localization errors caused by each nodes on focused energy delivery. According to the model proposed, we obtain the analytical expressions of the objective function appropriately and introduce the localization errors. Under the reasonable assumption based on the theory of algebra and geometry, the maximum localization error bound is concluded that it should be less than 1/8 of the carrier wavelength. Finally, numerical results demonstrate the correctness of the maximum localization error bound derived, and indicate the impact of different errors on the model.

关键词： Location awareness Geometry Electronic warfare numerical simulation linear programming Robustness numerical models

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