Table of ContentsList of FiguresIntroductionBackgroundMethodology & Development of ProgramAdaptation FormulasTesting & Comparison of ResultsSinusoid Function TestingPiecewise-Linear FunctionPolynomial FunctionConclusion of ResultsAPPENDIXManual For RBN_adaptive.mManual For rbn_fixed_selfgen.mDerivation of Partial Derivatives (Adaptive RBF Network)Linear Weights Partial Derivative TermPositions of Centers Partial Derivative Term (hidden layer)Spreads of Centers Partial Derivative Term(hidden layer)Excel Spreadsheet Data for Sinusoidal, Polynomial,& Piecewise Linear FunctionsReferencesRADIAL BASIS NETWORK:AN IMPLEMENTATIONOFADAPTIVE CENTERSNivas DurairajFinal Project for ECE539Table of Contents (ctrl+click to follow contents)TABLE OF CONTENTS...............................................................................................................................2LIST OF FIGURES........................................................................................................................................3INTRODUCTION..........................................................................................................................................4BACKGROUND.............................................................................................................................................4METHODOLOGY & DEVELOPMENT OF PROGRAM........................................................................5Adaptation Formulas..............................................................................................................................6TESTING & COMPARISON OF RESULTS............................................................................................10SINUSOID FUNCTION TESTING....................................................................................................................12PIECEWISE-LINEAR FUNCTION...................................................................................................................14POLYNOMIAL FUNCTION............................................................................................................................16CONCLUSION OF RESULTS....................................................................................................................18APPENDIX...................................................................................................................................................19MANUAL FOR RBN_ADAPTIVE.M..............................................................................................................20MANUAL FOR RBN_FIXED_SELFGEN.M......................................................................................................25DERIVATION OF PARTIAL DERIVATIVES (ADAPTIVE RBF NETWORK)........................................................28Linear Weights Partial Derivative Term...............................................................................................28Positions of Centers Partial Derivative Term (hidden layer)...............................................................28Spreads of Centers Partial Derivative Term(hidden layer)..................................................................29EXCEL SPREADSHEET DATA FOR SINUSOIDAL, POLYNOMIAL,...................................................................30& PIECEWISE LINEAR FUNCTIONS.............................................................................................................30References......................................................................................................................................................322List of Figures (ctrl+click to follow contents)Figure 1: An RBF network with one output........................................................................4Figure 2: An RBF network with multiple outputs...............................................................5Figure 3: Training Set Plot from Trainset1.txt...................................................................10Figure 4: Output with 3 Radial Basis Function Inputs......................................................10Figure 5: Output with 2 Radial Basis Functions................................................................11Figure 6:RBF network output (Sinusoid Function) with 7 Radial Basis Functions..........12Figure 7: Sinosoid Function Cost Function Output...........................................................13Figure 8:Adaptive RBF Network with 10 Radial Basis Functions....................................14Figure 9: Adaptive RBF Network with 6 Radial Basis Functions.....................................14Figure 10: Piecewise-Linear Cost Function Output..........................................................15Figure 11:Adaptive center RBF network for Polynomical Function (6 Radial Basis Functions)..................................................................................................................16Figure 12: Polynomial Cost Function Output....................................................................163IntroductionWhat neural network model has the same benefits as a feedforward neural network? Of course, it is the Radial Basis Function Network. Similar to feedforward networks such as backpropagation and multilayer perceptron, the radial basis function network aids us in function approximation, classification, and modeling of dynamic systems. They have actually been used to produce results in stock market prediction and speech recognition. I chose to implement my Intro to Artificial Neural Networks project on RBFs (Radial Basis Functions) because they are still an active research area and there is a lot to be learned from them. These functions were first introduced in the solution of multivariate interpolation problems and now it is one of the main fields of research in numerical analysis. Since I was well acquainted with simple feedforward networks, I decided to implement an adaptive center RBF. In addition, I have some interest in Economics. The thought of producing an algorithm that could help predict the stock market was very appealing to me. BackgroundIn its most basic form, an RBF consists of three layers with entirely different roles. The input layer is made up of nodes that connect the network to its environment. The second layer is the hidden layer of neurons. At the input of each neuron, the distance between the neuron center and the input vector is calculated. By applying the radial basisfunction
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