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Reduce Training Error of Extreme Learning Machine by Selecting Appropriate Hidden Layer Output Matrix

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Journal of Systems Science and Systems Engineering 2021年第5期30卷 552-571页

作者： Yang Lv Bang Li Jinghu Yu Yiming Ding School of Science Wuhan University of TechnologyWuhan 430070China Center for Mathematical Sciences Wuhan University of TechnologyWuhan 430070China

Extreme learning machine(ELM)is a feedforward neural network with a single layer of hidden nodes,where the weight and the bias connecting input to hidden nodes are randomly *** output weight between hidden nodes and outputs are learned by a linear *** is interesting to ask whether the training error of ELM is significantly affected by the hidden layer output matrix H,because a positive answer will enable us obtain smaller training error from better *** single hidden layer feedforward neural network(SLFN)with one input neuron,there is significant difference between the training errors of different *** find there is a reliable strong negative rank correlation between the training errors and some singular values of the moore-penrose generalized inverse of *** on the rank correlation,a selection algorithm is proposed to choose robust appropriate H to achieve smaller training error among numerous *** experiments are carried out to validate the selection algorithm,including tests on real data *** results show that it achieves better performance in validity,speed and robustness.

关键词： ELM SLFNs training error moore-penrose generalized inverse selection algorithm

THE METRIC generalized inverse AND ITS SINGLE-VALUE SELECTION IN THE PRICING OF CONTINGENT CLAIMS IN AN INCOMPLETE FINANCIAL MARKET

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Acta Mathematica Scientia 2022年第4期42卷 1681-1689页

作者： Zi WANG Xiaoling WANG Yuwen WANG School of Mathematics Sciences Harbin Normal UniversityHarbin150025China Institute of Finance Heilongjiang University of Finance and EconomicsHarbin150025China International School Krirk UniversityBangkok 10220Thailand School of Mathematics Science Harbin Normal UniversityHarbin150025China

This article continues to study the research suggestions in depth made by *** and *** in the journal"***."in *** with the pricing of non-reachable"contingent claims"in an incomplete financial market,when constructing a specific bounded linear operator A:l_(1)^(n)→l_(2) from a non-reflexive Banach space l_(1)^(n) to a Hilbert space l_(2),the problem of non-reachable"contingent claims"pricing is reduced to researching the(single-valued)selection of the(set-valued)metric generalized inverse A■ of the operator *** this paper,by using the Banach space structure theory and the generalized inverse method of operators,we obtain a bounded linear single-valued selection A^(σ)=A+of A■.

关键词： Incomplete financial market bounded linear operator metric generalized inverse single-value selection moore-penrose generalized inverse

Position Control of Flexible Joint Carts Using Adaptive generalized Dynamics Inversion

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Computers, Materials & Continua 2022年第3期70卷 4691-4705页

作者： Ibrahim M.Mehedi Mohd Heidir Mohd Shah Soon Xin Ng Abdulah Jeza Aljohani Mohammed El-Hajjar Muhammad Moinuddin Department of Electrical and Computer Engineering(ECE) King Abdulaziz UniversityJeddah21589Saudi Arabia Center of Excellence in Intelligent Engineering Systems(CEIES) King Abdulaziz UniversityJeddah21589Saudi Arabia Next Generation Wireless Research Group University of SouthamptonUK

This paper presents the design and implementation of Adaptive generalized Dynamic Inversion(AGDI)to track the position of a Linear Flexible Joint Cart(LFJC)system along with vibration suppression of the flexible *** proposed AGDI control law will be comprised of two control *** baseline(continuous)control law is based on principle of conventional GDI approach and is established by prescribing the constraint dynamics of controlled state variables that reflect the control *** control law is realized by inverting the prescribed dynamics using dynamically scaledmoore-penrose generalized *** boost the robust attributes against system nonlinearities,parametric uncertainties and external perturbations,a discontinuous control law will be augmented which is based on the concept of sliding mode *** discontinuous control law,the sliding mode gain is made adaptive in order to achieve improved tracking performance and chattering *** closed-loop stability of resultant control law is established by introducing a positive define Lyapunov candidate function such that semi-global asymptotic attitude tracking of LFJC system is *** computer simulations followed by experimental investigation will be performed on Quanser’s LFJC system to authenticate the feasibility of proposed control approach for its application to real world problems.

关键词： Adaptive control generalized dynamic inversion moore-penrose generalized inverse sliding mode control lyapunov stability semi-global asymptotic stability

A Geometric View on Inner Transformation between the Variables of a Linear Regression Model

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Applied Mathematics 2021年第10期12卷 931-938页

作者： Zhaoyang Li Bostjan Antoncic Shanghai University of International Business and Economics Shanghai China School of Economics and Business University of Ljubljana Ljubljana Slovenia

In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and moore-penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.

关键词： Matrix Singular Value Decomposition moore-penrose generalized inverse Matrix Inner Transformation Regression Analysis

四元数矩阵方程AXB=C的三对角Hermite极小范数最小二乘解

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高等学校计算数学学报 2010年第4期32卷 353-368页

作者：袁仕芳廖安平段雪峰五邑大学数学与计算科学学院湖南大学数学与计量经济学院桂林电子科技大学数学与计算科学学院

1引言本文用R;表示全体m×n实矩阵的集合,Q;表示全体m×n四元数矩阵的集合,R;表示全体n阶三对角实矩阵的集合,Q;表示全体n阶三对角四元数矩阵的集合,I;表示n阶单位矩阵的集合,A;和A;分别表示A的转置和moore-penrose广义逆,0表示零矩阵,|... 详细信息

1引言本文用R;表示全体m×n实矩阵的集合,Q;表示全体m×n四元数矩阵的集合,R;表示全体n阶三对角实矩阵的集合,Q;表示全体n阶三对角四元数矩阵的集合,I;表示n阶单位矩阵的集合,A;和A;分别表示A的转置和moore-penrose广义逆,0表示零矩阵,||x||2表示向量x的2范数,S;=（e;,e;,…,e;）,其中e;为单位矩阵I;的第i列.对

关键词： tridiagonal Hermitian quaternion matrix tridiagonal bi-Hermitian quaternion matrix least norm solution least squares solution moore-penrose generalized inverse Kronecker product.

两类矩阵方程的极小范数最小二乘三对角Hermite解

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高等学校计算数学学报 2020年第2期42卷 106-119页

作者：冯艳昭张澜内蒙古工业大学理学院

1引言矩阵方程广泛应用于诸多领域,例如:控制理论[1],系统稳定性分析[2]等.对矩阵方程的研究虽然已取得一系列重要成果[3-9],但仍然是数值代数领域中热门的课题之一.此外,由于三对角矩阵在诸多学科领域中的广泛应用,使得三对角矩阵倍受... 详细信息

1引言矩阵方程广泛应用于诸多领域,例如:控制理论[1],系统稳定性分析[2]等.对矩阵方程的研究虽然已取得一系列重要成果[3-9],但仍然是数值代数领域中热门的课题之一.此外,由于三对角矩阵在诸多学科领域中的广泛应用,使得三对角矩阵倍受人们的关注.文献[10]利用moore-penrose广义逆及Kronecker积,给出四元数矩阵方程AXB=C的三对角Hermite极小范数最小二乘解和三对角双Hermite极小范数最小二乘解;文献[11]利用矩阵的实表示结构,给出四元数矩阵方程AXB=C的三对角Hermite极小范数最

关键词： Complex matrix equation moore-penrose generalized inverse Kronecker product Matrix straighten Tridiagonal Hermite solution