TRAIN AND ANALYZE NEURAL NETWORKS TO FIT YOUR DATA
TRAIN AND ANALYZE NEURAL NETWORKS TO FIT YOUR DATATRAIN AND ANALYZE NEURAL NETWORKS TO FIT YOUR DATA
September 2005First editionIntended for use with Mathematica 5Software and manual written by: Jonas SjöbergProduct managers: Yezabel Dooley and Kristin KummerProject managers: Julienne Davison and Jennifer PetersonEditors: Rebecca Bigelow and Jan ProgenProofreader: Sam DanielSoftware quality assurance: Jay Hawkins, Cindie Strater, Angela Thelen, and Rachelle BergmannPackage design by: Larry Adelston, Megan Gillette, Richard Miske, and Kara WilsonSpecial thanks to the many alpha and beta testers and the people at Wolfram Research who gave me valuable input and feedback during thedevelopment of this package. In particular, I would like to thank Rachelle Bergmann and Julia Guelfi at Wolfram Research and Sam Daniel, atechnical staff member at Motorola’s Integrated Solutions Division, who gave thousands of suggestions on the software and the documentation.Published by Wolfram Research, Inc., 100 Trade Center Drive, Champaign, Illinois 61820-7237, USAphone: 1-217-398-0700; fax: 1-217-398-0747; email: info@wolfram.com; web: www.wolfram.comCopyright 1998–2004 Wolfram Research, Inc.All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,mechanical, photocopying, recording, or otherwise, without the prior written permission of Wolfram Research, Inc.Wolfram Research, Inc. is the holder of the copyright to the Neural Networks software and documentation (“Product”) described in this document,including without limitation such aspects of the Product as its code, structure, sequence, organization, “look and feel”, programming language, andcompilation of command names. Use of the Product, unless pursuant to the terms of a license granted by Wolfram Research, Inc. or as otherwiseauthorized by law, is an infringement of the copyright.Wolfram Research, Inc. makes no representations, express or implied, with respect to this Product, including without limitations, anyimplied warranties of merchantability, interoperability, or fitness for a particular purpose, all of which are expressly disclaimed. Usersshould be aware that included in the terms and conditions under which Wolfram Research, Inc. is willing to license the Product is aprovision that Wolfram Research, Inc. and its distribution licensees, distributors, and dealers shall in no event be liable for any indirect,incidental, or consequential damages, and that liability for direct damages shall be limited to the amount of the purchase price paid forthe Product.In addition to the foregoing, users should recognize that all complex software systems and their documentation contain errors andomissions. Wolfram Research, Inc. shall not be responsible under any circumstances for providing information on or corrections to errorsand omissions discovered at any time in this document or the package software it describes, whether or not they are aware of the errors oromissions. Wolfram Research, Inc. does not recommend the use of the software described in this document for applications in which errorsor omissions could threaten life, injury, or significant loss.Mathematica is a registered trademark of Wolfram Research, Inc. All other trademarks used herein are the property of their respective owners.Mathematica is not associated with Mathematica Policy Research, Inc. or MathTech, Inc.T4055 267204 0905.rcm
Table of Contents1 Introduction.11.1 Features of This Package.22 Neural Network Theory—A Short Tutorial.52.1 Introduction to Neural Networks.52.1.1 Function Approximation.72.1.2 Time Series and Dynamic Systems.82.1.3 Classification and Clustering.92.2 Data Preprocessing.102.3 Linear Models.122.4 The Perceptron.132.5 Feedforward and Radial Basis Function Networks.162.5.1 Feedforward Neural Networks.162.5.2 Radial Basis Function Networks.202.5.3 Training Feedforward and Radial Basis Function Networks.222.6 Dynamic Neural Networks.262.7 Hopfield Network.292.8 Unsupervised and Vector Quantization Networks.312.9 Further Reading.323 Getting Started and Basic Examples.353.1 Palettes and Loading the Package.353.1.1 Loading the Package and Data.353.1.2 Palettes.363.2 Package Conventions.373.2.1 Data Format.373.2.2 Function Names.403.2.3 Network Format.40
3.3 NetClassificationPlot.423.4 Basic Examples.453.4.1 Classification Problem Example.453.4.2 Function Approximation Example.494 The Perceptron.534.1 Perceptron Network Functions and Options.534.1.1 InitializePerceptron.534.1.2 PerceptronFit.544.1.3 NetInformation.564.1.4 NetPlot.574.2 Examples.594.2.1 Two Classes in Two Dimensions.594.2.2 Several Classes in Two Dimensions.664.2.3 Higher-Dimensional Classification.724.3 Further Reading.785 The Feedforward Neural Network.795.1 Feedforward Network Functions and Options.805.1.1 InitializeFeedForwardNet.805.1.2 NeuralFit.835.1.3 NetInformation.845.1.4 NetPlot.855.1.5 LinearizeNet and NeuronDelete.875.1.6 SetNeuralD, NeuralD, and NNModelInfo.885.2 Examples.905.2.1 Function Approximation in One Dimension.905.2.2 Function Approximation from One to Two Dimensions.995.2.3 Function Approximation in Two Dimensions. 1025.3 Classification with Feedforward Networks. 1085.4 Further Reading. 117
6 The Radial Basis Function Network. 1196.1 RBF Network Functions and Options. 1196.1.1 InitializeRBFNet. 1196.1.2 NeuralFit. 1216.1.3 NetInformation. 1226.1.4 NetPlot. 1226.1.5 LinearizeNet and NeuronDelete. 1226.1.6 SetNeuralD, NeuralD, and NNModelInfo. 1236.2 Examples. 1246.2.1 Function Approximation in One Dimension. 1246.2.2 Function Approximation from One to Two Dimensions. 1356.2.3 Function Approximation in Two Dimensions. 1356.3 Classification with RBF Networks. 1396.4 Further Reading. 1477 Training Feedforward and Radial Basis Function Networks. 1497.1 NeuralFit. 1497.2 Examples of Different Training Algorithms. 1527.3 Train with FindMinimum. 1597.4 Troubleshooting. 1617.5 Regularization and Stopped Search. 1617.5.1 Regularization. 1627.5.2 Stopped Search. 1627.5.3 Example. 1637.6 Separable Training. 1697.6.1 Small Example. 1697.6.2 Larger Example. 1747.7 Options Controlling Training Results Presentation. 1767.8 The Training Record. 1807.9 Writing Your Own Training Algorithms. 1837.10 Further Reading. 186
8 Dynamic Neural Networks. 1878.1 Dynamic Network Functions and Options. 1878.1.1 Initializing and Training Dynamic Neural Networks. 1878.1.2 NetInformation. 1908.1.3 Predicting and Simulating. 1918.1.4 Linearizing a Nonlinear Model. 1948.1.5 NetPlot—Evaluate Model and Training. 1958.1.6 MakeRegressor. 1978.2 Examples. 1978.2.1 Introductory Dynamic Example. 1978.2.2 Identifying the Dynamics of a DC Motor. 2068.2.3 Identifying the Dynamics of a Hydraulic Actuator. 2138.2.4 Bias-Variance Tradeoff—Avoiding Overfitting. 2208.2.5 Fix Some Parameters—More Advanced Model Structures. 2278.3 Further Reading. 2319 Hopfield Networks. 2339.1 Hopfield Network Functions and Options. 2339.1.1 HopfieldFit. 2339.1.2 NetInformation. 2359.1.3 HopfieldEnergy. 2359.1.4 NetPlot. 2359.2 Examples. 2379.2.1 Discrete-Time Two-Dimensional Example. 2379.2.2 Discrete-Time Classification of Letters. 2409.2.3 Continuous-Time Two-Dimensional Example. 2449.2.4 Continuous-Time Classification of Letters. 2479.3 Further Reading. 251
10 Unsupervised Networks. 25310.1 Unsupervised Network Functions and Options. 25310.1.1 InitializeUnsupervisedNet. 25310.1.2 UnsupervisedNetFit. 25610.1.3 NetInformation. 26410.1.4 UnsupervisedNetDistance, UnUsedNeurons, and NeuronDelete.
technical staff member at Motorola’s Integrated Solutions Division, who gave thousands of suggestions on the software and the documentation. . Neural Networks is a Mathematica package designed to train, visualize, and validate neural network models. A neural network model is a structure that can be adjusted to produce a mapping from a given .
A growing success of Artificial Neural Networks in the research field of Autonomous Driving, such as the ALVINN (Autonomous Land Vehicle in a Neural . From CMU, the ALVINN [6] (autonomous land vehicle in a neural . fluidity of neural networks permits 3.2.a portion of the neural network to be transplanted through Transfer Learning [12], and .
neural networks using genetic algorithms" has explained that multilayered feedforward neural networks posses a number of properties which make them particularly suited to complex pattern classification problem. Along with they also explained the concept of genetics and neural networks. (D. Arjona, 1996) in "Hybrid artificial neural
4 Graph Neural Networks for Node Classification 43 4.2.1 General Framework of Graph Neural Networks The essential idea of graph neural networks is to iteratively update the node repre-sentations by combining the representations of their neighbors and their own repre-sentations. In this section, we introduce a general framework of graph neural net-
Deep Neural Networks Convolutional Neural Networks (CNNs) Convolutional Neural Networks (CNN, ConvNet, DCN) CNN a multi‐layer neural network with – Local connectivity: Neurons in a layer are only connected to a small region of the layer before it – Share weight parameters across spatial positions:
34 NLP Programming Tutorial 8 - Recurrent Neural Nets Exercise Create an RNN for sequence labeling Training train-rnn and testing test-rnn Test: Same data as POS tagging Input: test/05-{train,test}-input.txt Reference: test/05-{train,test}-answer.txt Train a model with data/wiki-en-train.norm_pos and predict for data/wiki-en-test.norm Evaluate the POS performance, and compare with HMM:
Neuro-physiologists use neural networks to describe and explore medium-level brain function (e.g. memory, sensory system, motorics). Physicists use neural networks to model phenomena in statistical mechanics and for a lot of other tasks. Biologists use Neural Networks to interpret nucleotide sequences.
Video Super-Resolution With Convolutional Neural Networks Armin Kappeler, Seunghwan Yoo, Qiqin Dai, and Aggelos K. Katsaggelos, Fellow, IEEE Abstract—Convolutional neural networks (CNN) are a special type of deep neural networks (DNN). They have so far been suc-cessfully applied to image super-resolution (SR) as well as other image .
2013 AMC 8 Problems Problem 1 Amma wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way? Solution Problem 2 A sign at the fish market says, "50% off, today only: half-pound packages for just 3 per package." What is the regular price .
