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Functional Networks with Applications

A Neural-Based Paradigm

  • Book
  • © 1999

Overview

Authors:
  1. Enrique Castillo

    1. Dpto.de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain

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  2. Angel Cobo

    1. Dpto.de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain

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  3. José Manuel Gutiérrez

    1. Dpto.de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain

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  4. Rosa Eva Pruneda

    1. Dpto.de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain

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Part of the book series: The Springer International Series in Engineering and Computer Science (SECS, volume 473)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
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  2. Neural Networks

    1. Front Matter

      Pages 1-3
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    2. Introduction to Neural Networks

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 5-46

  3. Functional Networks

    1. Front Matter

      Pages 47-50
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    2. Introduction to Functional Networks

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 51-69

    3. Functional Equations

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 71-96

    4. Some Functional Network Models

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 97-132

    5. Model Selection

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 133-146

  4. Applications

    1. Front Matter

      Pages 147-149
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    2. Applications to Time Series

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 151-193

    3. Applications to Differential Equations

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 195-220

    4. Applications to CAD

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 221-238

    5. Applications to Regression

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 239-258

  5. Computer Programs

    1. Front Matter

      Pages 259-261
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    2. Mathematica Programs

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 263-281

    3. A Java Applet

      • Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda
      Pages 283-289

  6. Back Matter

    Pages 291-309
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Keywords

About this book

Artificial neural networks have been recognized as a powerful tool to learn and reproduce systems in various fields of applications. Neural net­ works are inspired by the brain behavior and consist of one or several layers of neurons, or computing units, connected by links. Each artificial neuron receives an input value from the input layer or the neurons in the previ­ ous layer. Then it computes a scalar output from a linear combination of the received inputs using a given scalar function (the activation function), which is assumed the same for all neurons. One of the main properties of neural networks is their ability to learn from data. There are two types of learning: structural and parametric. Structural learning consists of learning the topology of the network, that is, the number of layers, the number of neurons in each layer, and what neurons are connected. This process is done by trial and error until a good fit to the data is obtained. Parametric learning consists of learning the weight values for a given topology of the network. Since the neural functions are given, this learning process is achieved by estimating the connection weights based on the given information. To this aim, an error function is minimized using several well known learning methods, such as the backpropagation algorithm. Unfortunately, for these methods: (a) The function resulting from the learning process has no physical or engineering interpretation. Thus, neural networks are seen as black boxes.

Authors and Affiliations

  • Dpto.de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain

    Enrique Castillo, Angel Cobo, José Manuel Gutiérrez, Rosa Eva Pruneda

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