scholarly journals A Resource-Allocating Network for Function Interpolation

1991 ◽  
Vol 3 (2) ◽  
pp. 213-225 ◽  
Author(s):  
John Platt
Keyword(s):  
Time Series ◽  
Learning Process ◽  
Gradient Descent ◽  
Chaotic Time Series ◽  
Local Region ◽  
Unusual Pattern ◽  
Network Parameters ◽  
Learning Patterns ◽  
Compact Representations

We have created a network that allocates a new computational unit whenever an unusual pattern is presented to the network. This network forms compact representations, yet learns easily and rapidly. The network can be used at any time in the learning process and the learning patterns do not have to be repeated. The units in this network respond to only a local region of the space of input values. The network learns by allocating new units and adjusting the parameters of existing units. If the network performs poorly on a presented pattern, then a new unit is allocated that corrects the response to the presented pattern. If the network performs well on a presented pattern, then the network parameters are updated using standard LMS gradient descent. We have obtained good results with our resource-allocating network (RAN). For predicting the Mackey-Glass chaotic time series, RAN learns much faster than do those using backpropagation networks and uses a comparable number of synapses.

Local Piecewise-Linearity Prediction Method of Chaotic Time Series

2013 ◽  
Vol 712-715 ◽  
pp. 2415-2418
Author(s):  
Juan Liu ◽  
Xue Wei Bai ◽  
Dao Cai Chi
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Prediction Method ◽  
Chaotic Time Series ◽  
Local Region ◽  
Liaoning Province ◽  
Largest Lyapunov Exponent ◽  
Region Method ◽  
Local Prediction ◽  
Piecewise Linearity

A Local Piecewise-Linearity Prediction method is presented, Based on the advantages and limitations of local prediction of chaotic time series. Taking time series of rainfall as example for prediction the rainfall of one city in Liaoning province, which includes the application of the largest Lyapunov exponent, Local-region method and Local Piecewise-Linearity method. The method proposed is proved practical in comparison with the observed data.

Local Adaptive Nonlinear Filter Prediction Model with a Parameter for Chaotic Time Series

2010 ◽  
Vol 44-47 ◽  
pp. 3180-3184
Author(s):  
Fen Fang ◽  
Hai Yan Wang ◽  
Zhou Mu Yang
Keyword(s):  
Time Series ◽  
Prediction Model ◽  
Gradient Descent ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Logistic Map ◽  
Predictive Performance ◽  
Nonlinear Filter ◽  
Chaotic Time Series ◽  
Proposed Model

In order to improve the predictive performance for chaotic time series， we propose a novel local adaptive nonlinear filter prediction model. We use a function with a parameter to build an adaptive nonlinear filter in this model, and we train this model with an adaptive algorithm, deduced by the minimum square-root-error criterion and the steepest gradient descent rule. We evaluate the proposed model using four well-known chaotic systems, namely Logistic map, Henon map, Lorenz system and Rosslor system. All the results show a remarkable increase in predictive performance, comparing with the local adaptive nonlinear filter prediction model.

The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Quality System ◽  
Quality Level ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Data Set ◽  
Electronic Manufacturing ◽  
Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

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