# ARTIFICIAL NEURAL NETWORK MATLAB CODE PDF

9. nn05_narnet - Prediction of chaotic time series with NAR neural network Published with MATLAB® . compare response with output coding (a,b,c,d). PDF | Neural networks are very appropriate at function fit problems. A neural network with enough features (called neurons) can fit any data. Matlab based artificial neural network algorithm for voltage stability Further various toolbox functions such as different types of feed forward neural network.

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For Use with MATLAB®. Howard Demuth Neural Network Toolbox User's Guide No part of this manual may be photocopied or repro- to the government's use and disclosure of the Program and Documentation, and shall supersede any. Deep learning is a type of machine learning in which a model learns to perform classification learning is usually implemented using a neural network architecture. The . Watch how-to video: Deep Learning in 11 Lines of MATLAB Code. Deep Learning is a very hot topic these days especially in computer You will be using the nprtool pattern recognition app from Deep Learning Toolbox. " MATLAB Matrix-Only Function" and save t the generated code.

Thus, the grids represent the new coordinate system of the transformation. In contrast to linear PCA left which does not describe the nonlinear characteristics of the data, NLPCA gives a nonlinear curved description of the data, shown on the right.

The two resulting components are plotted as a grid which illustrates the linear PCA transformation. Again, the two components are plotted as a grid, but the components are curved which illustrates the nonlinear transformation of NLPCA. Springer Berlin Heidelberg, Hochreiter and R. Springer-Verlag Berlin Heidelberg, University of Potsdam, Germany. What about the perceptrons in the second layer?

Each of those perceptrons is making a decision by weighing up the results from the first layer of decision-making. In this way a perceptron in the second layer can make a decision at a more complex and more abstract level than perceptrons in the first layer.

And even more complex decisions can be made by the perceptron in the third layer. In this way, a many-layer network of perceptrons can engage in sophisticated decision making. Incidentally, when I defined perceptrons I said that a perceptron has just a single output.

In the network above the perceptrons look like they have multiple outputs. In fact, they're still single output. The multiple output arrows are merely a useful way of indicating that the output from a perceptron is being used as the input to several other perceptrons.

It's less unwieldy than drawing a single output line which then splits. Let's simplify the way we describe perceptrons. Or to put it in more biological terms, the bias is a measure of how easy it is to get the perceptron to fire. Obviously, introducing the bias is only a small change in how we describe perceptrons, but we'll see later that it leads to further notational simplifications. Because of this, in the remainder of the book we won't use the threshold, we'll always use the bias.

I've described perceptrons as a method for weighing evidence to make decisions. And so our perceptron implements a NAND gate! The NAND example shows that we can use perceptrons to compute simple logical functions. In fact, we can use networks of perceptrons to compute any logical function at all. Here's the resulting network. Note that I've moved the perceptron corresponding to the bottom right NAND gate a little, just to make it easier to draw the arrows on the diagram: One notable aspect of this network of perceptrons is that the output from the leftmost perceptron is used twice as input to the bottommost perceptron.

When I defined the perceptron model I didn't say whether this kind of double-output-to-the-same-place was allowed.

Actually, it doesn't much matter. If we don't want to allow this kind of thing, then it's possible to simply merge the two lines, into a single connection with a weight of -4 instead of two connections with -2 weights.

If you don't find this obvious, you should stop and prove to yourself that this is equivalent. In fact, it's conventional to draw an extra layer of perceptrons - the input layer - to encode the inputs: This notation for input perceptrons, in which we have an output, but no inputs, is a shorthand.

It doesn't actually mean a perceptron with no inputs. To see this, suppose we did have a perceptron with no inputs. The adder example demonstrates how a network of perceptrons can be used to simulate a circuit containing many NAND gates. And because NAND gates are universal for computation, it follows that perceptrons are also universal for computation. The computational universality of perceptrons is simultaneously reassuring and disappointing.

It's reassuring because it tells us that networks of perceptrons can be as powerful as any other computing device.

But it's also disappointing, because it makes it seem as though perceptrons are merely a new type of NAND gate. That's hardly big news! However, the situation is better than this view suggests.

It turns out that we can devise learning algorithms which can automatically tune the weights and biases of a network of artificial neurons. This tuning happens in response to external stimuli, without direct intervention by a programmer.

These learning algorithms enable us to use artificial neurons in a way which is radically different to conventional logic gates. Instead of explicitly laying out a circuit of NAND and other gates, our neural networks can simply learn to solve problems, sometimes problems where it would be extremely difficult to directly design a conventional circuit. Sigmoid neurons Learning algorithms sound terrific.

But how can we devise such algorithms for a neural network? Suppose we have a network of perceptrons that we'd like to use to learn to solve some problem. For example, the inputs to the network might be the raw pixel data from a scanned, handwritten image of a digit. And we'd like the network to learn weights and biases so that the output from the network correctly classifies the digit.

To see how learning might work, suppose we make a small change in some weight or bias in the network. What we'd like is for this small change in weight to cause only a small corresponding change in the output from the network. As we'll see in a moment, this property will make learning possible. Schematically, here's what we want obviously this network is too simple to do handwriting recognition!

For example, suppose the network was mistakenly classifying an image as an "8" when it should be a "9". We could figure out how to make a small change in the weights and biases so the network gets a little closer to classifying the image as a "9". And then we'd repeat this, changing the weights and biases over and over to produce better and better output. The network would be learning.

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The problem is that this isn't what happens when our network contains perceptrons. That flip may then cause the behaviour of the rest of the network to completely change in some very complicated way.

So while your "9" might now be classified correctly, the behaviour of the network on all the other images is likely to have completely changed in some hard-to-control way. That makes it difficult to see how to gradually modify the weights and biases so that the network gets closer to the desired behaviour. Perhaps there's some clever way of getting around this problem.

But it's not immediately obvious how we can get a network of perceptrons to learn. We can overcome this problem by introducing a new type of artificial neuron called a sigmoid neuron. Sigmoid neurons are similar to perceptrons, but modified so that small changes in their weights and bias cause only a small change in their output. That's the crucial fact which will allow a network of sigmoid neurons to learn. Okay, let me describe the sigmoid neuron. It's useful to remember this terminology, since these terms are used by many people working with neural nets.

However, we'll stick with the sigmoid terminology. The algebraic form of the sigmoid function may seem opaque and forbidding if you're not already familiar with it. In fact, there are many similarities between perceptrons and sigmoid neurons, and the algebraic form of the sigmoid function turns out to be more of a technical detail than a true barrier to understanding.

How can we understand that? So, strictly speaking, we'd need to modify the step function at that one point. But you get the idea.. Don't panic if you're not comfortable with partial derivatives!

This linearity makes it easy to choose small changes in the weights and biases to achieve any desired small change in the output. So while sigmoid neurons have much of the same qualitative behaviour as perceptrons, they make it much easier to figure out how changing the weights and biases will change the output. How should we interpret the output from a sigmoid neuron?

This can be useful, for example, if we want to use the output value to represent the average intensity of the pixels in an image input to a neural network. But sometimes it can be a nuisance. Suppose we want the output from the network to indicate either "the input image is a 9" or "the input image is not a 9". I'll always explicitly state when we're using such a convention, so it shouldn't cause any confusion. Show that the behaviour of the network doesn't change.

Suppose also that the overall input to the network of perceptrons has been chosen. We won't need the actual input value, we just need the input to have been fixed. The architecture of neural networks In the next section I'll introduce a neural network that can do a pretty good job classifying handwritten digits.

In preparation for that, it helps to explain some terminology that lets us name different parts of a network. Suppose we have the network: As mentioned earlier, the leftmost layer in this network is called the input layer, and the neurons within the layer are called input neurons.

The rightmost or output layer contains the output neurons, or, as in this case, a single output neuron. The middle layer is called a hidden layer, since the neurons in this layer are neither inputs nor outputs.

The term "hidden" perhaps sounds a little mysterious - the first time I heard the term I thought it must have some deep philosophical or mathematical significance - but it really means nothing more than "not an input or an output". The network above has just a single hidden layer, but some networks have multiple hidden layers.

For example, the following four-layer network has two hidden layers: Somewhat confusingly, and for historical reasons, such multiple layer networks are sometimes called multilayer perceptrons or MLPs, despite being made up of sigmoid neurons, not perceptrons. I'm not going to use the MLP terminology in this book, since I think it's confusing, but wanted to warn you of its existence. The design of the input and output layers in a network is often straightforward.

## Nonlinear PCA

For example, suppose we're trying to determine whether a handwritten image depicts a "9" or not. A natural way to design the network is to encode the intensities of the image pixels into the input neurons.

While the design of the input and output layers of a neural network is often straightforward, there can be quite an art to the design of the hidden layers. In particular, it's not possible to sum up the design process for the hidden layers with a few simple rules of thumb.

Instead, neural networks researchers have developed many design heuristics for the hidden layers, which help people get the behaviour they want out of their nets.

For example, such heuristics can be used to help determine how to trade off the number of hidden layers against the time required to train the network. We'll meet several such design heuristics later in this book.

## Associated Data

Up to now, we've been discussing neural networks where the output from one layer is used as input to the next layer. Such networks are called feedforward neural networks. This means there are no loops in the network - information is always fed forward, never fed back. That'd be hard to make sense of, and so we don't allow such loops.

However, there are other models of artificial neural networks in which feedback loops are possible.

These models are called recurrent neural networks. The idea in these models is to have neurons which fire for some limited duration of time, before becoming quiescent. That firing can stimulate other neurons, which may fire a little while later, also for a limited duration. That causes still more neurons to fire, and so over time we get a cascade of neurons firing. Loops don't cause problems in such a model, since a neuron's output only affects its input at some later time, not instantaneously.

Recurrent neural nets have been less influential than feedforward networks, in part because the learning algorithms for recurrent nets are at least to date less powerful. But recurrent networks are still extremely interesting. They're much closer in spirit to how our brains work than feedforward networks. And it's possible that recurrent networks can solve important problems which can only be solved with great difficulty by feedforward networks.

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## neural network using matlab

You previously purchased this article through ReadCube. Institutional Login. Log in to Wiley Online Library. Purchase Instant Access. View Preview. Learn more Check out. Citing Literature Number of times cited according to CrossRef: Kao and W.This means there are no loops in the network - information is always fed forward, never fed back.

That makes it difficult to figure out how to change the weights and biases to get improved performance. You previously purchased this article through ReadCube.

## publications

Such autoassociative neural network is a multi-layer perceptron that performs an identity mapping, meaning that the output of the network is required to be identical to the input. However, in the middle of the network is a layer that works as a bottleneck in which a reduction of the dimension of the data is enforced. People who are good at thinking in high dimensions have a mental library containing many different techniques along these lines; our algebraic trick is just one example.

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Suppose we want the output from the network to indicate either "the input image is a 9" or "the input image is not a 9". Note that the Network initialization code assumes that the first layer of neurons is an input layer, and omits to set any biases for those neurons, since biases are only ever used in computing the outputs from later layers.

That's going to be computationally costly.

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