Matlab

Neural Network Toolbox
For Use with MATLAB
®

Howard Demuth Mark Beale

Computation Visualization Programming

User’s Guide
Version 4

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Neural Network Toolbox User’s Guide © COPYRIGHT 1992 - 2000by 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 reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program andDocumentation 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 252.227-7014. The terms and conditions of The MathWorks, Inc. Software LicenseAgreement shall pertain to the government’s use and disclosure of the Program and Documentation, and shall supersede any conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to MathWorks. MATLAB, Simulink, Stateflow,Handle Graphics, and Real-Time Workshop are registered trademarks, and Target Language Compiler 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 April 1993 January 1997 July 1997 January 1998 September 2000

First printing Second printing Third printing Fourth printing Fifthprinting Revised for Version 3 (Release 11) Sixth printing Revised for Version 4 (Release 12)

Contents
Preface

Explaining Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Basic Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Mathematical Notation for Equations and Figures . . . . . . . xix Basic Concepts . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Weight Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Layer Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Figure and Equation Examples . . . . . . . . . . .. . . . . . . . . . . . . . . xx Mathematics and Code Equivalents . . . . . . . . . . . . . . . . . . . . xxi Neural Network Design Book . . . . . . . . . . . . . . . . . . . . . . . . . xxii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii Related Products List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv

Introduction

1Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Basic Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Help and Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Neural Network Applications . . . . . . . . . . . . . . . . . . . . . . . . . . Applications in this Toolbox . ....