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Application of the error function in Analyzing the Learning Dynamics Near Singularities of the Multilayer Perceptrons

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Application of the Error Function in Analyzing the Learning ...

第三十一届中国控制会议

作者： GUO Weili WEI Haikun ZHAO Junsheng LI Weiling ZHANG Kanjian School of Automation Southeast University Nanjing 210096 P.R.China

＜正＞Analyzing the learning dynamics near singularities of the feedforward neural networks is a research hotspot in recent years,but the unintegrability of the log-sigmoid function make us hardly to detailed analyze the singular behaviors of the multilayer *** this paper,the error function is adopted to the activation function of the multilayer perceptrons because of its *** obtain the explicit expressions of two important expectations based on which we would easily obtain the averaged learning equations of the multilayer perceptrons and then could deeply analyzed the learning dynamics near singularities. The simulation results indicate that it is proper to use the error function to be the activation function of the multilayer perceptrons in analyzing the singular behaviors.

关键词： Singular multilayer perceptrons error function log-sigmoid

Accuracy Analysis of Gravity Model Based on Fictitious Compress Recovery Approach

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Geo-Spatial Information Science 2007年第3期10卷 157-162页

作者： SHEN Wenbin TAO Benzao Key Lab. of Geospace Environment and Geodesy of MEC 129 Luoyu Road Wuhan 430079 China School of Geodesy and Geomatics Wuhan University 129 Luoyu Road Wuhan 430079 China. 不详

The potential field determined based on the fictitious compress recovery approach is influenced by the errors contained in the boundary （the Earth＇s surface or the surface corresponding to the satellite altitude） values. Given the boundary value with definite accuracy, the accuracy of the field determined based on the fictitious compress recovery approach is estimated, and it is theoretically shown that the determined field has the same accuracy level as the given boundary value.

关键词： fictitious compress recovery error function error estimate accuracy of the potential field

Quadratic Radical function Better Than Fisher z Transformation

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Transactions of Tianjin University 2013年第5期19卷 381-384页

作者：杨正瓴段志峰王晶晶王腾宋延文张军 School of Electrical Engineering and Automation Tianjin University Tianjin Key Laboratory of Process Measurement and Control

A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z ***,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is *** with the Fisher z transformation,this piecewise function has only 38.206%of the total *** new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.

关键词： normal distribution cumulative distribution function error function confidence interval correlation coefficient combination of forecasts

error Model of Rotary Ring Laser Gyro Inertial Navigation System

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Journal of Beijing Institute of Technology 2010年第4期19卷 439-444页

作者：张伦东练军想吴美平郑志强 College of Mechatronics Engineering and Automation National University of Defense Technology

To improve the precision of inertial navigation system（INS） during long time operation,the rotation modulated technique（RMT） was employed to modulate the errorr of the inertial sensors into periodically varied signals,and,as a result,to suppress the divergence of INS *** principle of the RMT was introduced and the error propagating functions were derived from the rotary navigation *** of the measurement error for the rotation angle of the platform on the system precision were *** simulation and experimental results show that the precision of INS was ① dramatically improved with the use of the RMT,and ② hardly reduced when the measurement error for the rotation angle was in arc-second *** study results offer a theoretical basis for engineering design of rotary INS.

关键词： inertial navigation system(INS) rotation modulated technique(RMT) error function inertial sensor

A New Approach for Solving Fuzzy Linear Multi-Criterion Problems: An Approach Based on Minimization of the errors functions

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American Journal of Operations Research 2023年第1期13卷 1-17页

作者： Joél Lema Makubikua Amani Wema Yves Tinda Mangongo Joseph-Désiré Kyemba Bukweli Justin Dupar Busili Kampempe Département des Mathématiques et Informatique Université de Kinshasa Kinshasa The Democratic Republic of the Congo Conférence Congolaise de Recherche en Informatique et en Mathématiques Appliquées COCORIMA Kinshasa The Democratic Republic of the Congo

The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to construct the error function. In addition, we introduce the concept of deviation variable in the definition of the error function. The algorithm of the new approach is summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing a specific level . second, we solve separately each uni-criteria problem and we compute the error function for each criteria. Finally, we minimize the sum of error functions in order to obtain the desired compromise solution. A numerical example is done for a comparative study with some existing approaches to show the effectiveness of the new approach.

关键词： Deviation Variable Compromise Solution Membership function error function Decision-Making function

Maxwell-Boltzmann Distribution Mathematica Based Practitioner’s Approach

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American Journal of Computational Mathematics 2022年第1期12卷 79-86页

作者： Haiduke Sarafian The Pennsylvania State University University College York USA

Utilizing Mathematica this report shows how from a practitioner’s point of view useful quantities some known, and some unknown and fresh properties about the Maxwell-Boltzmann distribution are calculated. We shortcut circling the usage of antiquated incomplete tabulated error functions given in the textbooks and professional literature replacing them with efficient upgrades. And, utilizing the animation features of Mathematica displaying the temperature-dependence of the distribution function assists in visualizing the character of the distribution.

关键词： Maxwell-Boltzmann Distribution error function Computer Algebra System Mathematica

BP algorithm of Hessian matrix based on fuzzy optimization model and its application

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BP algorithm of Hessian matrix based on fuzzy optimization m...

2011年中国智能自动化学术会议

作者：郭瑜陈守煜 Pearl River Hydraulic Research Institute Ministry of Water Resources School of Civil Engineering and Architecture Dalian University of Technology

On the basis of fuzzy optimization model,the concept of equivalent error function is introduced to establish a new back propagation(BP) algorithm of Hessian matrix to promote the *** Newton’s iteration method is applied to promote the training efficiency and accelerate the *** method is used in the decision-making analysis for economic,water resources and environmental planning of the Dalian City.

关键词： fuzzy optimization model neural networks error function Hessian matrix BP algorithm

Blind Equalization Algorithm Based on Different error Equations with Exponential Variable Step Size

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Blind Equalization Algorithm Based on Different Error Equati...

第一届国际测量仪器与测试自动化学术会议

作者： Guo Yecai Han Yingge Rao Wei (Department of Electrical Engineering Anhui University of Science and Technology Huainan 232001 China)

＜正＞Based on the analysis of different error functions and the performance of variable step size in improving convergence rate, blind equalization algorithms based on difference error equations with exponential variable step size are proposed. The proposed algorithms are used to equalize for negative acoustic gradient in underwater acoustic channels under condition of exponential variable step size with the same parameters. The research results show that the error function must be odd symmetrical and does not change with the change of the equalizer output when the equalizer output moves to a higher values. This error function is suitable for blind equalization of underwater acoustic channels.

关键词： error function exponential variable step size negative acoustic gradient in underwater acoustic channels.

A Fast Algorithm for Ontology Similarity Measure and Ontology Mapping

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A Fast Algorithm for Ontology Similarity Measure and Ontolog...

2011 4th IEEE International Conference on Computer Science and Information Technology(ICCSIT 2011)

作者： Xiao Huang 1 2 1 College of Mathematics Physics and Information Engineering Zhejiang Normal University Zhejiang Jinhua 321004 P.R. China 2 College of Education Zhejiang Normal University Zhejiang Jinhua 321004 P.R. China Wei Gao 3 4 3 Department of Information Yunnan Normal University Kunming 650092 P.R. China 4 Department of Mathematics Soochow University Suzhou 215006 P.R. China Tianwei Xu 3 3 Department of Information Yunnan Normal University Kunming 650092 P.R. China Zhiyang Jia 5 5 Tourism and Literature College Yunnan University Lijiang 674100 P.R.China

Ontology similarity calculation and ontology mapping are important research topics in information retrieval. By analyzing the fast algorithm for learning large scale preference relations, we propose the fast algorithm for ontology similarity measure and ontology mapping. Via the ranking learning algorithm, the ontology graph is mapped into a line consists of real numbers. The similarity between two concepts then can be measured by comparing the difference between their corresponding real numbers. Experimental results show that the proposed algorithm has high accuracy and efficiency.

关键词： ontology similarity computation ranking error function conjugate gradient H -exact approximation