[...]... frequency of sound, and the ordinate, the intensity of the sound A pattern in this example is a graph of an acoustic spectrum To predict the performance of a particular stock in the stock market, the abscissa may represent various parameters of the stock (such as the price of the stock the day before, and so on), and the ordinate, values of these parameters A neural network is given correct pairs of (input... practice when the function to be differentiated has the power of 2; after differentiation, the original factor of (1/2) and the new factor of 2 from differentiation cancel out, and the coefficient of the derivative will become 1 The goal of the learning procedure is to minimize E We want to the reduce the error E by improving the current values of wij and w'ij In the following derivation of the backpropagation... for Sample 2, and the neural network is then able to map the correct t after, say, 8 iterations This is the end of the first epoch The end of the first epoch is not usually the end of the algorithm or outer loop After the training session for Sample 2, the neural network "forgets" part of what it learned for Sample 1 Therefore, the neural network has to be trained again for Sample 1 But, the second round... hidden layers There are neural network models in which such backward information passing occurs as feedback This category of models is called recurrent neural networks The meaning of the backward propagation of the backpropagation model should not be confused with these recurrent models To consider the difference of the two vectors y and t, we take the square of the error or "distance" of the two vectors... Applications of Chaos 242 Index 247 1 Introduction 1.1 An Overview of the Field of Artificial Intelligence What is artificial intelligence? The Industrial Revolution, which started in England around 1760, has replaced human muscle power with the machine Artificial intelligence (AI) aims at replacing human intelligence with the machine The work on artificial intelligence started in the. .. propagation of error corrections Compare y with t If y is equal or close enough to t, then go back to the beginning of the Outer loop Otherwise, backpropagate through the neural network and adjust the weights so that the next y is closer to t, then go back to the beginning of the Inner loop In the above, each Outer loop iteration is called an epoch An epoch is one cycle through the entire set of patterns... layers, then from the hidden to output layers, and get output vector y Step 3 Backward propagation for error corrections Compare y with t If y is equal or close enough to t, then go back to the beginning of the Outer loop Otherwise, backpropagate through the neural network and adjust the weights so that the next y is closer to t (see the next backpropagation process), then go back to the beginning of the. .. or evolutionary computing, fuzzy systems, rough set theory, and chaos - are the focus of this book 1.2 An Overview of the Areas Covered in this Book 3 1.2 An Overview of the Areas Covered in this Book In this book, five areas are covered: neural networks, genetic algorithms, fuzzy systems, rough sets, and chaos Very brief descriptions for the major concepts of these five areas are as follows: Neural. .. terminate the 2.3 Basic Idea of the Backpropagation Model 13 outer loop (i.e., the entire algorithm), the neural network must be able to produce the target vector for any input vector Suppose, for example, that we have two sample patterns to train the neural network We repeat the inner loop for Sample 1, and the neural network is then able to map the correct t after, say, 10 iterations We then repeat the. .. in these figures, we have inputs x1, x2, , xm coming into the neuron These inputs are the stimulation levels of a natural neuron Each input xi is multiplied by its 8 2 Neural Networks: Fundamentals and the Backpropagation Model (a) (b) Fig 2.1 (a)A neuron model that retains the image of a natural neuron (b) A further abstraction of Fig (a) corresponding weight wi, then the product xiwi is fed into the . to Software Engineering, Third Edition Toshinori Munakata Fundamentals of the New Artificial Intelligence Neural, Evolutionary, Fuzzy and More Second Edition Toshinori Munakata Computer and. titled Fundamentals of the New Artificial Intelligence: Beyond Traditional Paradigms.” I have changed the subtitle to better represent the contents of the book. The basic philosophy of the original. retains the image of a natural neuron. (b) A further abstraction of Fig. (a). corresponding weight w i , then the product x i w i is fed into the body of the neuron. The weights represent the