Artificial Intelligence 2E – Michael – Negnevitsky (1)

First, it computes the net weighted input as before: n i¼1 xiwi

; where n is the number of inputs, and
is the threshold applied to the neuron. Next, this input value is passed through the activation function. However, unlike a percepron, neurons in the back-propagation network use a sigmoid activation function: Ysigmoid ¼ 1 þ e
X ð6:9Þ The derivative of this function is easy to compute. It also guarantees that the neuron output is bounded between 0 and 1.

What about the learning law used in the back-propagation networks? To derive the back-propagation learning law, let us consider the three-layer network shown in Figure 6.9. The indices i, j and k here refer to neurons in the input, hidden and output layers, respectively. Input signals, x1; x2; . . . ; xn, are propagated through the network from left to right, and error signals, e1; e2; . . . ; el, from right to left. The symbol wij denotes the weight for the connection between neuron i in the input layer and neuron j in the hidden layer, and the symbol wjk the weight between neuron j in the hidden layer and neuron k in the output layer.

Figure 6.9 Three-layer back-propagation neural network To propagate error signals, we start at the output layer and work backward to the hidden layer. The error signal at the output of neuron k at iteration p is defined by ekðpÞ ¼ yd;kðpÞ
ykðpÞ; ð6:10Þ where yd;kðpÞ is the desired output of neuron k at iteration p. Neuron k, which is located in the output layer, is supplied with a desired output of its own. Hence, we may use a straightforward procedure to update weight wjk. In fact, the rule for updating weights at the output layer is similar to the perceptron learning rule of Eq.

(6.7): wjkðp þ 1Þ ¼ wjkðpÞ þ wjkðpÞ; ð6:11Þ where wjkðpÞ is the weight correction. When we determined the weight correction for the perceptron, we used input signal xi. But in the multilayer network, the inputs of neurons in the output layer are different from the inputs of neurons in the input layer.

We work with leading authors to develop the strongest educational materials in computer science, bringing cutting-edge thinking and best learning practice to a global market. Under a range of well-known imprints, including Addison-Wesley, we craft high quality print and electronic publications which help readers to understand and apply their content, whether studying or at work. To find out more about the complete range of our publishing please visit us on the World Wide Web at: www.pearsoned.co.uk Artificial Intelligence A Guide to Intelligent Systems Second Edition Michael Negnevitsky Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the World.

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ISBN 0 321 20466 2 British Library Cataloguing-in-Publication Data A catalogue record for this book can be obtained from the British Library Library of Congress Cataloging-in-Publication Data Negnevitsky, Michael. Artificial intelligence: a guide to intelligent systems/Michael Negnevitsky. p. cm. Includes bibliographical references and index. ISBN 0-321-20466-2 (case: alk. paper) 1. Expert systems (Computer science) 2. Artificial intelligence. I. Title.

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