Neural Networks And Learning Machines Simon Haykin Pdf

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English Pages Year Fluid and authoritative, this well-organized book represents the first comprehensive treatment of neural networks and le. This book covers both classical and modern models in deep learning. The chapters of this book span three categories: The. The primary focus is on the theory and algorithms of. Problem 1. Hard limiter o y Figure 2: Problem 1. In other words, the network of Fig.

Problem 4. Each epoch corresponds to iterations. From the figure, we see that the network reaches a steady state after about 25 epochs. Each neuron uses a logistic function for its sigmoid nonlinearity. Note that we have used biases the negative of thresholds for the individual neurons. Figure 1: Problem 4.

The network has a single hidden layer. Ten different network configurations were trained to learn this mapping. Once each network was trained, the test dataset was applied to compare the performance and accuracy of each configuration. Table 1 summarizes the results obtained: Table 1 Number of hidden neurons 3 4 5 7 10 15 20 30 30 trained with , passes Average percentage error at the network output 4. Interestingly, in this second experiment the network peaked in accuracy with 10 hidden neurons, after which the accuracy of the network to produce the correct output started to decrease.

The experiment with 30 hidden neurons and , training passes was repeated, but this time the hyperbolic tangent function was used as the nonlinearity. The result obtained this time was an average percentage error of 3.

Problem 6. Misclassification of patterns can only arise if the patterns are nonseparable. If the patterns are nonseparable, it is possible for a pattern to lie inside the margin of separation and yet be on the correct side of the decision boundary. Hence, nonseparability does not necessarily mean misclassification. The example is a support vector. Result: Correct classification. The example lies inside the margin of separation but on the correct side of the decision boundary.

The example lies inside the margin of separation but on the wrong side of the decision boundary. Result: Incorrect classification. This definition applies to all sources of data, be they noisy or otherwise. It follows therefore that by the very nature of it, the support vector machine is robust to the presence of additive noise in the data used for training and testing, provided that all the data are drawn from the same population.

The inner-product i. Note that ui is not an eigenvector. Then, proceeding in a manner similar but much more cumbersome than that described for the two-dimensional XOR problem in Section 6. Problem 8. Equations 1 and 2 may be represented by the following vector-valued signal flow graph: w0 x o -y0 o o w0 w1 -y1 wj-1 o w The algorithm for adjusting the matrix of synaptic weights W n of the network is described by the recursive equation see Eq.

First, we note that the asymptotic stability theorem discussed in the text does not apply directly to the convergence analysis of stochastic approximation algorithms involving matrices; it is formulated to apply to vectors.

However, we may write the elements of the parameter synaptic weight matrix W n in 1 as a vector, that is, one column vector stacked up on top of another. We may then interpret the resulting nonlinear update equation in a corresponding way and so proceed to apply the asymptotic stability theorem directly. Here we use the fact that in light of the convergence of the maximum eigenfilter involving a single neuron, the first column of the matrix W n converges with probability 1 to the first eigenvector of R, and so on.

The network has 16 output neurons, and inputs arranged as a 64 x 64 grid of pixels. The training involved presentation of samples, which are produced by low-pass filtering a white Gaussian noise image and then multiplying wi6th a Gaussian window function. The low-pass filter was a Gaussian function with standard deviation of 2 pixels, and the window had a standard deviation of 8 pixels.

Figure 1, presented on the next page, shows the first 16 receptive field masks learned by the network Sanger, The results displayed in Fig. The second mask cannot be a low-pass filter, so it must be a band-pass filter with a mid-band frequency as small as possible since the input power decreases with increasing frequency. Continuing the analysis in the manner described above, the frequency response of successive masks approaches dc as closely as possible, subject of course to being orthogonal to previous masks.

The end result is a sequence of orthogonal masks that respond to progressively higher frequencies. The second term i. Problem 9. This particular self-organizing feature map pertains to a one-dimensional lattice fed with a two-dimensional input.

We see that counting from left to right neuron 14, say, is quite close to neuron It is therefore possible for a large enough input perturbation to make neuron 14 jump into the neighborhood of neuron 97, or vice versa.

If this change were to happen, the topological preserving property of the SOM algorithm would no longer hold For a more convincing demonstration, consider a higher-dimensional, namely, threedimensional input structure mapped onto a two-dimensional lattice of by neurons. The 2 network is trained with an input consisting of 8 Gaussian clouds with unit variance but different centers. The centers are located at the points 0,0,0, The clouds occupy the 8 corners of a cube as shown in Fig.

The resulting labeled feature map computed by the SOM algorithm is shown in Fig. Although each of the classes is grouped together in the map, the planar feature map fails to capture the complete topology of the input space. In particular, we observe that class 6 is adjacent to class 2 in the input space, but is not adjacent to it in the feature map. The conclusion to be drawn here is that although the SOM algorithm does perform clustering on the input space, it may not always completely preserve the topology of the input space.

Figure 1: Problem 9. Suppose that the neuron at the center of the lattice breaks down; this failure may have a dramatic effect on the evolution of the feature map. On the other hand, a small perturbation applied to the input space leaves the map learned by the lattice essentially unchanged. From Table 9. We are interested in rewriting 1 in a form that highlights the role of Voronoi cells. Hence, for all input patterns that lie in a particular Voronoi cell the same neighborhood function applies.

The stabilizing term is set equal to — y k w kj. The output yk of neuron k is set equal to a neighborhood function. The net result of these two modifications is to make the weight update for the SOM algorithm assume a form similar to that in competitive learning rather than Hebbian learning. The network is trained with a triangular input density. Two sets of results are displayed in this figure: 1.

The standard SOM Kohonen algorithm, shown as the solid line. In Fig. Although it appears that both algorithms fail to match the input density exactly, we see that the conscience algorithm comes closer to the exact result than the standard SOM algorithm. The experiment begins with random weights at zero time, and then the neurons start spreading out.

Two distinct phases in the learning process can be recognized from this figure: The neurons become ordered i. The neurons spread out to match the density of the input distribution, culminating in the steady-state condition attained after 25, iterations. Let wji denote the synaptic weight of hidden neuron j connected to source node i in the input layer. Let wkj denote the synaptic weight of output neuron k connected to hidden neuron j.

Dp q To perform supervised training of the multilayer perceptron, we use gradient descent on in weight space. From the definition of differential entropy, both h X and h Y attain their maximum value of 0. Moreover h X,Y is minimized when the joint probability of X and Y occupies the smallest possible region in the probability space. Problem Since the noise terms N1 and N2 are Gaussian and uncorrelated, it follows that they are statistically independent.

Both Y1 and Y2 are dependent on the same set of input signals, and so they are correlated with each other. Large noise variance. Low noise variance. Only one such combination yields a response with maximum variance.

A low-noise level favors diversity of response, in which case the two output neurons compute different linear combinations of inputs even though such a choice may result in a reduced output variance. However, they differ from each other in two important respects: 1. PCA performs decorrelation by minimizing second-order moments; higher-order moments are not involved in this computation.

On the other hand, ICA performs statistical independence by using higher-order moments. The output signal vector resulting from PCA has a diagonal covariance matrix. The first principal component defines a direction in the original signal space that captures the maximum possible variance; the second principal component defines another direction in the remaining orthogonal subspace that captures the next maximum possible variance, and so on. In particular, through a change of coordinates resulting from the use of ICA, the probability density function of multichannel data may be expressed as a product of marginal densities.

This change, in turn, permits density estimation with shorter observations. IV. Extra Credit for Attending Talks

English Pages Year Fluid and authoritative, this well-organized book represents the first comprehensive treatment of neural networks and le. This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of. The chapters of this book span three categories: The. Problem 1. Hard limiter o y Figure 2: Problem 1. Neural Network Simon Haykin Solution Manual

Preface x Introduction 1 1. What is a Neural Network? The Human Brain 6 3. Models of a Neuron 10 4. Feedback 18 6.

Neural Networks and Learning Machines (pdf) by Simon Haykin (ebook)

In mids, he shifted thrust of his research effort in direction of Neural Computation, which was re-emerging at that time and intrinsically resembled Adaptive Signal Processing. All along, he had a vision of revisiting fields of radar engineering and telecom technology from a brand new perspective. That vision became a reality in early years of this century with publication of two seminal journal papers:. Selected Areas in Communications, Feb. Signal Processing, Feb. Cognitive Radio and Cognitive Radar are two important parts of a much wider and integrative field: Cognitive Dynamic Systems, research into which has become his passion.

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For graduate-level neural network courses offered in the departments of Computer Engineering, Electrical Engineering, and Computer Science. Neural Networks and Learning Machines, Third Edition is renowned for its thoroughness and readability. This well-organized and completely up-to-date text remains the most comprehensive treatment of neural networks from an engineering perspective. This is ideal for professional engineers and research scientists. Matlab codes used for the computer experiments in the text are available for download at Refocused, revised and renamed to reflect the duality of neural networks and learning machines, this edition recognizes that the subject matter is richer when these topics are studied together. Ideas drawn from neural networks and machine learning are hybridized to perform improved learning tasks beyond the capability of either independently.

English Pages Year Fluid and authoritative, this well-organized book represents the first comprehensive treatment of neural networks and le. This book covers both classical and modern models in deep learning. Under these conditions, the error signal e n remains zero, and so from Eq. Problem 1. Also assume that The induced local eld of neuron 1 is We may thus construct the following table: The induced local eld of neuron is Accordingly, we may construct the following table: x 1 0 0 1 1 x 2 0 1 0 1 v 1 In other words, the network of Fig. Problem 4.

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