scholarly journals The Time Complexity Analysis for a Kind of Neural Network with Rational Spline Functions

2015 ◽  
Author(s):  
Daiyuan Zhang ◽  
Hongyan Bao
Keyword(s):  
Neural Network ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Spline Functions ◽  
Rational Spline

Complexity Analysis of Neural Network Based on Rational Spline Weight Functions

2014 ◽  
Vol 644-650 ◽  
pp. 1658-1661
Author(s):  
Dai Yuan Zhang ◽  
Hai Nan Yang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Theoretical Analysis ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Weight Functions ◽  
Rational Spline ◽  
The Neural Network ◽  
The Neural Networks

This paper aims to obtain the time complexity for a new kind of neural network using rational spline weight functions. In this paper, we introduce the architecture of the neural network, and analyze the time complexity in detail. Finally, some examples are also given to verify the theoretical analysis. The results show that the time complexity depends on the number of patterns, the input and out dimensions of the neural networks.

Environmental Quality Assessment Based on a New Kind of Neural Network Using Rational Spline Weight Functions

2015 ◽  
Vol 713-715 ◽  
pp. 1708-1711
Author(s):  
Dai Yuan Zhang ◽  
Shan Jiang Hou
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Quality Assessment ◽  
Environmental Quality ◽  
Weight Functions ◽  
Spline Functions ◽  
Environmental Quality Assessment ◽  
Rational Spline ◽  
The Neural Network ◽  
Very High

As we all known, artificial neural network can be used in the process of environmental quality assessment. To improve the accuracy and science of assessment, a method of environmental quality assessment is presented in this paper, which is based on spline weight function (SWF) neural networks. The weigh functions of the neural network are composed of rational spline functions with cubic numerator and linear denominator (3/1 rational SWF). The simulation results show that, compared with the conventional BP neural networks, this method can get very high precision and accuracy. This case demonstrates that SWF neural networks can offer a very prospective tool for environmental quality assessment.

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

Error Analysis of Neural Network with Rational Spline Weight Function

2014 ◽  
Vol 644-650 ◽  
pp. 2407-2410
Author(s):  
Dai Yuan Zhang ◽  
Jia Kai Wang
Keyword(s):  
Neural Network ◽  
Weight Function ◽  
Topological Structure ◽  
High Accuracy ◽  
Local Minima ◽  
Slow Convergence ◽  
Rational Spline ◽  
Fast Learning ◽  
Learning Speed ◽  
Training Neural Network

Training neural network by spline weight function (SWF) has overcomed many defects of traditional neural networks (such as local minima, slow convergence and so on). It becomes more important because of its simply topological structure, fast learning speed and high accuracy. To generalize the SWF algorithm, this paper introduces a kind of rational spline weight function neural network and analyzes the performance of approximation for this neural network.

Real-time engine model development based on time complexity analysis

2021 ◽  
pp. 146808742110397
Author(s):  
Haotian Chen ◽  
Kun Zhang ◽  
Kangyao Deng ◽  
Yi Cui
Keyword(s):  
Real Time ◽  
Time Complexity ◽  
Complexity Analysis ◽  
High Accuracy ◽  
The Real ◽  
Cycle Simulation ◽  
Crank Angle ◽  
Time Requirements ◽  
Improved Model ◽  
Simulation Time

Real-time simulation models play an important role in the development of engine control systems. The mean value model (MVM) meets real-time requirements but has limited accuracy. By contrast, a crank-angle resolved model, such as the filling -and-empty model, can be used to simulate engine performance with high accuracy but cannot meet real-time requirements. Time complexity analysis is used to develop a real-time crank-angle resolved model with high accuracy in this study. A method used in computer science, program static analysis, is used to theoretically determine the computational time for a multicylinder engine filling-and-empty (crank-angle resolved) model. Then, a prediction formula for the engine cycle simulation time is obtained and verified by a program run test. The influence of the time step, program structure, algorithm and hardware on the cycle simulation time are analyzed systematically. The multicylinder phase shift method and a fast calculation method for the turbocharger characteristics are used to improve the crank-angle resolved filling-and-empty model to meet real-time requirements. The improved model meets the real-time requirement, and the real-time factor is improved by 3.04 times. A performance simulation for a high-power medium-speed diesel engine shows that the improved model has a max error of 5.76% and a real-time factor of 3.93, which meets the requirement for a hardware-in-the-loop (HIL) simulation during control system development.

Final Remarks for the Research With Advanced Machine Learning Methods in Colon Cancer Analysis

2021 ◽  
pp. 151-154
Keyword(s):  
Colon Cancer ◽  
Time Complexity ◽  
High Performance ◽  
Complexity Analysis ◽  
Search Algorithm ◽  
Cancer Treatments ◽  
Cancer Dataset ◽  
Performance Accuracy ◽  
Research Questions

Generally, classification accuracy is very important to gene processing and selection and cancer classification. It is needed to achieve better cancer treatments and improve medical drug assignments. However, the time complexity analysis will enhance the application's significance. To answer the research questions in Chapter 1, several case studies have been implemented (see Chapters 4 and 5), each was essential to sustain the methodologies discussed in Chapter 3. The study used a colon-cancer dataset comprising 2000 genes. The best search algorithm, GA, showed high performance with a good efficient time complexity. However, both DTs and SVMs showed the best classification contribution with reference to performance accuracy and time efficiency. However, it is difficult to apply a completely fair comparative study because existing algorithms and methods were tested by different authors to reflect the effectiveness and powerful of their own methods.

Adaptive Skip Graph Framework for Peer-to-Peer Networks: Search Time Complexity Analysis

2018 ◽  
Author(s):  
Amit Goyal ◽  
Shalini Batra ◽  
Neeraj Kumar ◽  
Gagangeet Singh Aujla ◽  
Mohammad S. Obaidat
Keyword(s):  
Time Complexity ◽  
Complexity Analysis ◽  
Search Time ◽  
Peer To Peer ◽  
Peer Networks ◽  
Peer To Peer Networks

Error Analysis of Neural Network with Multiply Neurons Using Rational Spline Weight Functions

2015 ◽  
Vol 713-715 ◽  
pp. 1716-1720
Author(s):  
Dai Yuan Zhang ◽  
Lei Lei Wang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Error Analysis ◽  
Weight Functions ◽  
Generalization Ability ◽  
Rational Spline ◽  
Error Formula ◽  
Denominator Polynomial

In order to describe the generalization ability, this paper discusses the error analysis of neural network with multiply neurons using rational spline weight functions. We use the cubic numerator polynomial and linear denominator polynomial as the rational splines for weight functions. We derive the error formula for approximation, the results can be used to algorithms for training neural networks.

Neural Network Algorithm for Solving Large Scale Travelling Salesman Problems

2012 ◽  
Vol 542-543 ◽  
pp. 1398-1402
Author(s):  
Guo Zhong Cheng ◽  
Wei Feng ◽  
Fang Song Cui ◽  
Shi Lu Zhang
Keyword(s):  
Neural Network ◽  
Time Complexity ◽  
Large Scale ◽  
Travelling Salesman Problem ◽  
Effective Algorithm ◽  
Travelling Salesman ◽  
Satisfactory Solution ◽  
Network Algorithm ◽  
The Neural Network ◽  
Neural Network Algorithm

This study improves the neural network algorithm that was presented by J.J.Hopfield for solving TSP(travelling salesman problem) and gets an effective algorithm whose time complexity is O(n*n), so we can solve quickly TSP more than 500 cities in microcomputer. The paper considers the algorithm based on the replacement function of the V Value. The improved algorithm can greatly reduces the time and space complexities of Hopfield method. The TSP examples show that the proposed algorithm could efficiently find a satisfactory solution and has a fast convergence speed.

Sign in / Sign up

Export Citation Format

Share Document