Neural Network Toolbox.pdf

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Neural Network Toolbox
For Use with MATLAB ®
Howard Demuth
Mark Beale
Comput ation
Visualiz ation
Program ming
User’s Guide
Version 4
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Neural Network Toolbox User’s Guide
 COPYRIGHT 1992 - 2003 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc .
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by
or for the federal government of the United States. By accepting delivery of the Program, the government
hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR
Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part
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TargetBox is a trademark of The MathWorks, Inc.
Other product or brand names are trademarks or registered trademarks of their respective holders.
Printing History: June 1992
First printing
April 1993
Second printing
January 1997
Third printing
July 1997
Fourth printing
January 1998
Fifth printing
Revised for Version 3 (Release 11)
September 2000
Sixth printing
Revised for Version 4 (Release 12)
June 2001
Seventh printing Minor revisions (Release 12.1)
July 2002
Online only
Minor revisions (Release 13)
January 2003 Online only
Minor revisions (Release 13+)
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Contents
Preface
Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
Basic Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
Mathematical Notation for Equations and Figures . . . . . . . xxi
Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Weight Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Layer Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Figure and Equation Examples . . . . . . . . . . . . . . . . . . . . . . . . xxii
Mathematics and Code Equivalents . . . . . . . . . . . . . . . . . . . xxiii
Neural Network Design Book . . . . . . . . . . . . . . . . . . . . . . . . . xxiv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv
Introduction
1
Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Basic Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Help and Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
What’s New in Version 4.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Control System Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
New Training Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Design of General Linear Networks . . . . . . . . . . . . . . . . . . . . . . 1-4
Improved Early Stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
iii
 
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Generalization and Speed Benchmarks . . . . . . . . . . . . . . . . . . . 1-4
Demonstration of a Sample Training Session . . . . . . . . . . . . . . 1-4
Neural Network Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Applications in this Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Aerospace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Automotive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Banking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Credit Card Activity Checking . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Defense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Entertainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Financial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Industrial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Medical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Oil and Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Speech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Telecommunications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Neuron Model and Network Architectures
2
Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
Simple Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Neuron with Vector Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Network Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
A Layer of Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
Multiple Layers of Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
iv
Contents
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Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
Simulation With Concurrent Inputs in a Static Network . . . . 2-13
Simulation With Sequential Inputs in a Dynamic Network . . 2-14
Simulation With Concurrent Inputs in a Dynamic Network . 2-16
Training Styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18
Incremental Training (of Adaptive and Other Networks) . . . . 2-18
Batch Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24
Figures and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25
Perceptrons
3
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
Important Perceptron Functions . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
Perceptron Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
Creating a Perceptron (newp) . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
Simulation (sim) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8
Initialization (init) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Learning Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12
Perceptron Learning Rule (learnp) . . . . . . . . . . . . . . . . . . . . 3-13
Training (train) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
Limitations and Cautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-21
Outliers and the Normalized Perceptron Rule . . . . . . . . . . . . . 3-21
v
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