# Principles of Artificial Neural Networks: 3rd Edition (Advanced Series in Circuits & Systems) (Advanced Series in Circuits and Systems)

## Daniel Graupe

Language: English

Pages: 500

ISBN: 9814522732

Format: PDF / Kindle (mobi) / ePub

Artificial neural networks are most suitable for solving problems that are complex, ill-defined, highly nonlinear, of many and different variables, and/or stochastic. Such problems are abundant in medicine, in finance, in security and beyond.

This volume covers the basic theory and architecture of the major artificial neural networks. Uniquely, it presents 18 complete case studies of applications of neural networks in various fields, ranging from cell-shape classification to micro-trading in finance and to constellation recognition all with their respective source codes. These case studies demonstrate to the readers in detail how such case studies are designed and executed and how their specific results are obtained.

The book is written for a one-semester graduate or senior-level undergraduate course on artificial neural networks.

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ws-book975x65 June 25, 2013 15:33 Principles of Artiﬁcial Neural Networks (3rd Edn) ws-book975x65 Back Propagation 77 The C-language Source Code for the aboves XOR problem is as follows: June 25, 2013 15:33 78 Principles of Artiﬁcial Neural Networks (3rd Edn) Principles of Artificial and Neural Networks ws-book975x65 June 25, 2013 15:33 Principles of Artiﬁcial Neural Networks (3rd Edn) ws-book975x65 Back Propagation 79 June 25, 2013 15:33 80 Principles of Artiﬁcial

Consider a time series {xi } of N samples: The Walsh Transform (WT) of {xi } is given by Xn where 1 N Xn = N −1 xi W al(n, i) (7.15) i=0 and the IWT (inverse Walsh transform) is: N −1 xi = Xn W al(n, i) (7.16) n=0 where i, n = 0, 1, . . . , N − 1 (7.17) Xn thus being the discrete Walsh transform and xi being its inverse, in parallelity to the discrete Fourier Transform of xi , which is given by: N −1 xn FNnk Xk = (7.18) n=0 and to the IFT (inverse Fourier transform), namely: 1

exact solution. When a problem deﬁes any analysis, this is, of course, not possible. Appendix 7.B below presents a case of applying the Hopﬁeld NN to the TSP problem (with computed results for up to 25 cities). 7.A. Hopﬁeld Network Case Study∗ : Character Recognition 7.A.1. Introduction The goal of this case study is to recognize three digits of ‘0’, ‘1’, ‘2’ and ‘4’. To this end, a one-layer Hopﬁeld network is created, it is trained with standard data sets (8*8); make the algorithm converge and

ylabel(‘Energy →’);xlabel(‘Iterations →’); subplot(2,2,2);plot(n10); title(‘Energy Convergence for 10 Cities’); ylabel(‘Energy →’);xlabel(‘Iterations →’); subplot(2,2,3);plot(n15); title(‘Energy Convergence for 15 Cities’); ylabel(‘Energy →’);xlabel(‘Iterations →’); subplot(2,2,4);plot(n20); title(‘Energy Convergence for 20 Cities’); ylabel(‘Energy →’);xlabel(‘Iterations →’); 7.C. Cell Shape Detection Using Neural Networks‡ 7.C.1. Introduction Intracellular microinjection is one of the most

Principles of Artiﬁcial Neural Networks (3rd Edn) ws-book975x65 Chapter 3 Basic Principles of ANNs and Their Early Structures 3.1. Basic Principles of ANN Design The basic principles of the artiﬁcial neural networks (ANNs) were ﬁrst formulated by McCulloch, and Pitts in 1943, in terms of ﬁve assumptions, as follows: (i) The activity of a neuron (ANN) is all-or-nothing. (ii) A certain ﬁxed number of synapses larger than 1 must be excited within a given interval of neural addition for a neuron