Neural Network Toolbox 6 User S Guide
Neural Network Toolbox 6User’s GuideHoward DemuthMark BealeMartin HaganDownloaded from www.Manualslib.com manuals search engine
How to Contact The MathWorksWebNewsgroupwww.mathworks.com/contact TS.html Technical service@mathworks.cominfo@mathworks.comProduct enhancement suggestionsBug reportsDocumentation error reportsOrder status, license renewals, passcodesSales, pricing, and general information508-647-7000 (Phone)508-647-7001 (Fax)The MathWorks, Inc.3 Apple Hill DriveNatick, MA 01760-2098For contact information about worldwide offices, see the MathWorks Web site.Neural Network Toolbox User’s Guide COPYRIGHT 1992–2010 by The MathWorks, Inc.The software described in this document is furnished under a license agreement. The software may be usedor 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 and Documentation by,for, or through the federal government of the United States. By accepting delivery of the Program orDocumentation, the government hereby agrees that this software or documentation qualifies as commercialcomputer software or commercial computer software documentation as such terms are used or defined inFAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of thisAgreement and only those rights specified in this Agreement, shall pertain to and govern the use,modification, reproduction, release, performance, display, and disclosure of the Program and Documentationby the federal government (or other entity acquiring for or through the federal government) and shallsupersede any conflicting contractual terms or conditions. If this License fails to meet the government'sneeds or is inconsistent in any respect with federal procurement law, the government agrees to return theProgram and Documentation, unused, to The MathWorks, Inc.TrademarksMATLAB and Simulink are registered trademarks of The MathWorks, Inc. Seewww.mathworks.com/trademarks for a list of additional trademarks. Other product or brandnames may be trademarks or registered trademarks of their respective holders.PatentsThe MathWorks products are protected by one or more U.S. patents. Please seewww.mathworks.com/patents for more information.Downloaded from www.Manualslib.com manuals search engine
Revision HistoryJune 1992April 1993January 1997July 1997January 1998September 2000June 2001July 2002January 2003June 2004October 2004October 2004March 2005March 2006September 2006March 2007September 2007March 2008October 2008March 2009September 2009March 2010Downloaded from www.Manualslib.com manuals search engineFirst printingSecond printingThird printingFourth printingFifth printingSixth printingSeventh printingOnline onlyOnline onlyOnline onlyOnline onlyEighth printingOnline onlyOnline onlyNinth printingOnline onlyOnline onlyOnline onlyOnline onlyOnline onlyOnline onlyOnline onlyRevised for Version 3 (Release 11)Revised for Version 4 (Release 12)Minor revisions (Release 12.1)Minor revisions (Release 13)Minor revisions (Release 13SP1)Revised for Version 4.0.3 (Release 14)Revised for Version 4.0.4 (Release 14SP1)Revised for Version 4.0.4Revised for Version 4.0.5 (Release 14SP2)Revised for Version 5.0 (Release 2006a)Minor revisions (Release 2006b)Minor revisions (Release 2007a)Revised for Version 5.1 (Release 2007b)Revised for Version 6.0 (Release 2008a)Revised for Version 6.0.1 (Release 2008b)Revised for Version 6.0.2 (Release 2009a)Revised for Version 6.0.3 (Release 2009b)Revised for Version 6.0.4 (Release 2010a)
AcknowledgmentsThe authors would like to thank the following people:Joe Hicklin of The MathWorks for getting Howard into neural networkresearch years ago at the University of Idaho, for encouraging Howard andMark to write the toolbox, for providing crucial help in getting the first toolboxVersion 1.0 out the door, for continuing to help with the toolbox in many ways,and for being such a good friend.Roy Lurie of The MathWorks for his continued enthusiasm for the possibilitiesfor Neural Network Toolbox software.Mary Ann Freeman for general support and for her leadership of a great team ofpeople we enjoy working with.Rakesh Kumar for cheerfully providing technical and practical help,encouragement, ideas and always going the extra mile for us.Alan LaFleur for facilitating our documentation work.Tara Scott and Stephen Vanreusel for help with testing.Orlando De Jesús of Oklahoma State University for his excellent work indeveloping and programming the dynamic training algorithms described inChapter 6, “Dynamic Networks,” and in programming the neural networkcontrollers described in Chapter 7, “Control Systems.”Martin Hagan, Howard Demuth, and Mark Beale for permission to includevarious problems, demonstrations, and other material from Neural NetworkDesign, January, 1996.Downloaded from www.Manualslib.com manuals search engine
Neural Network Toolbox Design BookThe developers of the Neural Network Toolbox software have written atextbook, Neural Network Design (Hagan, Demuth, and Beale, ISBN0-9717321-0-8). The book presents the theory of neural networks, discussestheir design and application, and makes considerable use of the MATLAB environment and Neural Network Toolbox software. Demonstration programsfrom the book are used in various chapters of this user’s guide. (You can findall the book demonstration programs in the Neural Network Toolbox softwareby typing nnd.)This book can be obtained from John Stovall at (303) 492-3648, or by e-mail atJohn.Stovall@colorado.edu.The Neural Network Design textbook includes: An Instructor’s Manual for those who adopt the book for a class Transparency Masters for class useIf you are teaching a class and want an Instructor’s Manual (with solutions tothe book exercises), contact John Stovall at (303) 492-3648, or by e-mail atJohn.Stovall@colorado.edu.To look at sample chapters of the book and to obtain Transparency Masters, godirectly to the Neural Network Design page athttp://hagan.okstate.edu/nnd.htmlFrom this link, you can obtain sample book chapters in PDF format and youcan download the Transparency Masters by clicking Transparency Masters(3.6MB).You can get the Transparency Masters in PowerPoint or PDF format.Downloaded from www.Manualslib.com manuals search engine
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ContentsGetting Started1Product Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2Using the Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3Applications for Neural Network Toolbox Software . . . . 1-4Applications in This Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4Business Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4Fitting a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7Defining a Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7Using Command-Line Functions . . . . . . . . . . . . . . . . . . . . . . . . 1-7Using the Neural Network Fitting Tool GUI . . . . . . . . . . . . . . 1-13Recognizing Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Defining a Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Using Command-Line Functions . . . . . . . . . . . . . . . . . . . . . . .Using the Neural Network PatternRecognition Tool GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-241-241-25Clustering Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Defining a Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Using Command-Line Functions . . . . . . . . . . . . . . . . . . . . . . .Using the Neural Network Clustering Tool GUI . . . . . . . . . . .1-421-421-431-471-31Neuron Model and Network Architectures2Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simple Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Neuron with Vector Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-22-22-32-5iDownloaded from www.Manualslib.com manuals search engine
Network Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8A Layer of Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8Multiple Layers of Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10Input and Output Processing Functions . . . . . . . . . . . . . . . . . . 2-12Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation with Concurrent Inputs in a Static Network . . . .Simulation with Sequential Inputs in a Dynamic Network . .Simulation with Concurrent Inputs in a Dynamic Network . .2-142-142-152-17Training Styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Incremental Training (of Adaptive and Other Networks) . . . .Batch Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Training Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-202-202-222-25Perceptrons3Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2Important Perceptron Functions . . . . . . . . . . . . . . . . . . . . . . . . . 3-2Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3Perceptron Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5Creating a Perceptron (newp) . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6Simulation (sim) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7Initialization (init) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8Learning Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11Perceptron Learning Rule (learnp) . . . . . . . . . . . . . . . . . . . . 3-12Training (train) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15Limitations and Cautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-21iiContentsDownloaded from www.Manualslib.com manuals search engine
Outliers and the Normalized Perceptron Rule . . . . . . . . . . . . . 3-21Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Introduction to the GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Create a Perceptron Network (nntool) . . . . . . . . . . . . . . . . . . .Train the Perceptron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Export Perceptron Results to the Workspace . . . . . . . . . . . . . .Clear the Network/Data Window . . . . . . . . . . . . . . . . . . . . . . .Importing from the Command Line . . . . . . . . . . . . . . . . . . . . .Save a Variable to a File and Load It Later . . . . . . . . . . . . . . .3-233-233-233-273-293-303-303-31Linear Filters4Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4Creating a Linear Neuron (newlin) . . . . . . . . . . . . . . . . . . . . . . . 4-4Least Mean Square Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8Linear System Design (newlind) . . . . . . . . . . . . . . . . . . . . . . . . 4-9Linear Networks with Delays . . . . . . . . . . . . . . . . . . . . . . . . . 4-10Tapped Delay Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10Linear Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10LMS Algorithm (learnwh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13Linear Classification (train) . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15Limitations and Cautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18Overdetermined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18Underdetermined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18iiiDownloaded from www.Manualslib.com manuals search engine
Linearly Dependent Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18Too Large a Learning Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19Backpropagation5Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2Solving a Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4Improving Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6Under the Hood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8Feedforward Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10Simulation (sim) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-15Backpropagation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-15Faster Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Variable Learning Rate (traingda, traingdx) . . . . . . . . . . . . . .Resilient Backpropagation (trainrp) . . . . . . . . . . . . . . . . . . . . .Conjugate Gradient Algorithms . . . . . . . . . . . . . . . . . . . . . . . .Line Search Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Quasi-Newton Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Levenberg-Marquardt (trainlm) . . . . . . . . . . . . . . . . . . . . . . . .Reduced Memory Levenberg-Marquardt (trainlm) . . . . . . . . .5-195-195-215-225-265-295-305-32Speed and Memory Comparison . . . . . . . . . . . . . . . . . . . . . . . 5-34Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-50Improving Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . .Early Stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Index Data Division (divideind) . . . . . . . . . . . . . . . . . . . . . . . .Random Data Division (dividerand) . . . . . . . . . . . . . . . . . . . . .Block Data Division (divideblock) . . . . . . . . . . . . . . . . . . . . . . .ivContentsDownloaded from www.Manualslib.com manuals search engine5-525-535-545-545-54
Interleaved Data Division (divideint) . . . . . . . . . . . . . . . . . . . . 5-55Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-55Summary and Discussion of Early Stoppingand Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-58Preprocessing and Postprocessing . . . . . . . . . . . . . . . . . . . . .Min and Max (mapminmax) . . . . . . . . . . . . . . . . . . . . . . . . . . .Mean and Stand. Dev. (mapstd) . . . . . . . . . . . . . . . . . . . . . . . .Principal Component Analysis (processpca) . . . . . . . . . . . . . . .Processing Unknown Inputs (fixunknowns) . . . . . . . . . . . . . . .Representing Unknown or Don’t Care Targets . . . . . . . . . . . .Posttraining Analysis (postreg) . . . . . . . . . . . . . . . . . . . . . . . . .5-615-625-635-645-655-665-66Sample Training Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-68Limitations and Cautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-71Dynamic Networks6Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Examples of Dynamic Networks . . . . . . . . . . . . . . . . . . . . . . . . .Applications of Dynamic Networks . . . . . . . . . . . . . . . . . . . . . . .Dynamic Network Structures . . . . . . . . . . . . . . . . . . . . . . . . . . .Dynamic Network Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-26-26-76-86-9Focused Time-Delay Neural Network (newfftd) . . . . . . . . . 6-11Distributed Time-Delay Neural Network (newdtdnn) . . . . 6-15NARX Network (newnarx, newnarxsp, sp2narx) . . . . . . . . 6-18Layer-Recurrent Network (newlrn) . . . . . . . . . . . . . . . . . . . . 6-24vDownloaded from www.Manualslib.com manuals search engine
Control Systems7Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2NN Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Using the NN Predictive Controller Block . . . . . . . . . . . . . . . . .7-47-47-57-6NARMA-L2 (Feedback Linearization) Control . . . . . . . . . .Identification of the NARMA-L2 Model . . . . . . . . . . . . . . . . . .NARMA-L2 Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Using the NARMA-L2 Controller Block . . . . . . . . . . . . . . . . . .7-147-147-167-18Model Reference Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-23Using the Model Reference Controller Block . . . . . . . . . . . . . . 7-25Importing and Exporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-31Importing and Exporting Networks . . . . . . . . . . . . . . . . . . . . . 7-31Importing and Exporting Training Data . . . . . . . . . . . . . . . . . 7-35Radial Basis Networks8Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2Important Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . 8-2Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Exact Design (newrbe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .More Efficient Design (newrb) . . . . . . . . . . . . . . . . . . . . . . . . . .Demonstrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8-38-38-48-58-78-8Probabilistic Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . 8-9Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-9viContentsDownloaded from www.Manualslib.com manuals search engine
Design (newpnn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-10Generalized Regression Networks . . . . . . . . . . . . . . . . . . . . . 8-12Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12Design (newgrnn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-14Self-Organizing and LearningVector Quantization Nets9Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2Important Self-Organizing and LVQ Functions . . . . . . . . . . . . . 9-2Competitive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Creating a Competitive Neural Network (newc) . . . . . . . . . . . .Kohonen Learning Rule (learnk) . . . . . . . . . . . . . . . . . . . . . . . . .Bias Learning Rule (learncon) . . . . . . . . . . . . . . . . . . . . . . . . . . .Tr
from the book are used in various chapters of this user s guide. (You can find all the book demonstration programs in the Neural Network Toolbox software by typing nnd.) This book can be obtained from John Stovall at (303) 492-3648, or by e-mail at John.Stovall@colorado.edu. The Neural Network Design textbook includes:
Neural Network Based System Identification Toolbox User’s Guide 1-1 1 Tutorial The present toolbox: “Neural Network Based System Identification Toolbox”, contains a large number of functions for training and evaluation of multilayer perceptron type neural networks. The
Model-Based Calibration Toolbox 13, 21, 23, 24, 27 500 600 Control System Design and Analysis Control System Toolbox 200 200 System Identification Toolbox 200 200 Fuzzy Logic Toolbox 200 200 Robust Control Toolbox 4 200 200 Model Predictive Control Toolbox 4 200 23200 Aerospace Toolbox 200 200 Signal Processing and Communications
environment and Neural Network Toolbox software. Demonstration programs from the book are used in various chapters of this user’s guide. (You can find all the book demonstration programs in the Neural Network Toolbox software by typing nnd.) Obtain this book from John Stovall at (303) 492-3648, or by email at John.Stovall@colorado.edu.
from the book are used in various chapters of this user’s guide. (You can find all the book demonstration programs in the Neural Network Toolbox software by typing nnd.) This book can be obtained from John Stovall at (303) 492-3648, or by e-mail at John.Stovall@colorado.edu. The Neural Network Design textbook includes:
The toolbox is designed to work with both resting state scans and block designs. Installing the toolbox: 1. download conn.zip, unzip the file. 2. add ./conn/ directory to matlab path To start the toolbox: On the matlab prompt, type : conn (make sure your matlab path include the path to the connectivity toolbox)
and to review all NIH Toolbox measures as they relate to the needs of young children. NIH TOOLBOX APP Released in 2015, the NIH Toolbox iPad app takes advantage of portable technology and advanced software to provide users with a exible and easy-to-use NIH Toolbox test administration and data collection system. App
neural networks and substantial trials of experiments to design e ective neural network structures. Thus we believe that the design of neural network structure needs a uni ed guidance. This paper serves as a preliminary trial towards this goal. 1.1. Related Work There has been extensive work on the neural network structure design. Generic algorithm (Scha er et al.,1992;Lam et al.,2003) based .
Kindergarten and Grade 1 must lay a strong foundation for students to read on grade level at the end of Grade 3 and beyond. Students in Grade 1 should be reading independently in the Lexile range between 190L530L.
