neural network for beginners (part 1 of 3) - codeproject

Part 2: Will be about multi layer neural networks, and the back propogation training method to solve a non-linear classification problem such as the logic of an XOR logic gate.. So how a

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Articles » General Programming » Algorithms & Recipes » Neural Networks

AI : Neural Network for beginners (Part 1 of 3)

By Sacha Barber, 16 May 2007

Introduction

This article is Part 1 of a series of 3 articles that I am going to post The proposed article content will be as follows:

1 Part 1: This one, will be an introduction into Perceptron networks (single layer neural networks)

2 Part 2: Will be about multi layer neural networks, and the back propogation training method to solve a

non-linear classification problem such as the logic of an XOR logic gate This is something that a Perceptron can't do This is explained further within this article

3 Part 3: Will be about how to use a genetic algorithm (GA) to train a multi layer neural network to solve some logic problem

Let's start with some biology

Nerve cells in the brain are called neurons There is an estimated 1010 to the power(1013) neurons in the human

brain Each neuron can make contact with several thousand other neurons Neurons are the unit which the brain uses

to process information

So what does a neuron look like

A neuron consists of a cell body, with various extensions from it Most of these are branches called dendrites There is one much longer process (possibly also branching) called the axon The dashed line shows the axon hillock, where

transmission of signals starts

The following diagram illustrates this

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Figure 1 Neuron

The boundary of the neuron is known as the cell membrane There is a voltage difference (the membrane potential) between the inside and outside of the membrane

If the input is large enough, an action potential is then generated The action potential (neuronal spike) then travels down the axon, away from the cell body

Figure 2 Neuron Spiking

Synapses

The connections between one neuron and another are called synapses Information always leaves a neuron via its axon (see Figure 1 above), and is then transmitted across a synapse to the receiving neuron

Neuron Firing

Neurons only fire when input is bigger than some threshold It should, however, be noted that firing doesn't get bigger as the stimulus increases, its an all or nothing arrangement

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Figure 3 Neuron Firing

Spikes (signals) are important, since other neurons receive them Neurons communicate with spikes The information sent is coded by spikes

The input to a Neuron

Synapses can be excitatory or inhibitory

Spikes (signals) arriving at an excitatory synapse tend to cause the receiving neuron to fire Spikes (signals) arriving at

an inhibitory synapse tend to inhibit the receiving neuron from firing

The cell body and synapses essentially compute (by a complicated chemical/electrical process) the difference between the incoming excitatory and inhibitory inputs (spatial and temporal summation)

When this difference is large enough (compared to the neuron's threshold) then the neuron will fire

Roughly speaking, the faster excitatory spikes arrive at its synapses the faster it will fire (similarly for inhibitory spikes)

So how about artificial neural networks

Suppose that we have a firing rate at each neuron Also suppose that a neuron connects with m other neurons and so receives m-many inputs "x1 … … xm", we could imagine this configuration looking something like:

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Figure 4 Artificial Neuron configuration

This configuration is actually called a Perceptron The perceptron (an invention of Rosenblatt [1962]), was one of the earliest neural network models A perceptron models a neuron by taking a weighted sum of inputs and sending the output 1, if the sum is greater than some adjustable threshold value (otherwise it sends 0 - this is the all or nothing spiking described in the biology, see neuron firing section above) also called an activation function

The inputs (x1,x2,x3 xm) and connection weights (w1,w2,w3 wm) in Figure 4 are typically real values, both postive (+) and negative (-) If the feature of some xi tends to cause the perceptron to fire, the weight wi will be positive; if the feature xi inhibits the perceptron, the weight wi will be negative

The perceptron itself, consists of weights, the summation processor, and an activation function, and an adjustable threshold processor (called bias here after)

For convenience the normal practice is to treat the bias, as just another input The following diagram illustrates the revised configuration

Figure 5 Artificial Neuron configuration, with bias as additinal input

The bias can be thought of as the propensity (a tendency towards a particular way of behaving) of the perceptron to fire irrespective of its inputs The perceptron configuration network shown in Figure 5 fires if the weighted sum > 0, or

if you're into math-type explanations

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Activation Function

The activation usually uses one of the following functions

Sigmoid Function

The stronger the input, the faster the neuron fires (the higher the firing rates) The sigmoid is also very useful in multi-layer networks, as the sigmoid curve allows for differentation (which is required in Back Propogation training of multi layer networks)

or if your into maths type explanations

Step Function

A basic on/off type function, if 0 > x then 0, else if x >= 0 then 1

or if your into math-type explanations

Learning

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A foreword on learning

Before we carry on to talk about perceptron learning lets consider a real world example :

How do you teach a child to recognize a chair? You show him examples, telling him, "This is a chair That is not a chair," until the child learns the concept of what a chair is In this stage, the child can look at the examples we have shown him and answer correctly when asked, "Is this object a chair?"

Furthermore, if we show to the child new objects that he hasn't seen before, we could expect him to recognize

correctly whether the new object is a chair or not, providing that we've given him enough positive and negative

examples

This is exactly the idea behind the perceptron

Learning in perceptrons

Is the process of modifying the weights and the bias A perceptron computes a binary function of its input Whatever a perceptron can compute it can learn to compute

"The perceptron is a program that learn concepts, i.e it can learn to respond with True (1) or False (0) for inputs we

present to it, by repeatedly "studying" examples presented to it.

The Perceptron is a single layer neural network whose weights and biases could be trained to produce a correct target vector when presented with the corresponding input vector The training technique used is called the

perceptron learning rule The perceptron generated great interest due to its ability to generalize from its training vectors and work with randomly distributed connections Perceptrons are especially suited for simple problems in pattern classification."

Professor Jianfeng feng, Centre for Scientific Computing, Warwick university, England

The Learning Rule

The perceptron is trained to respond to each input vector with a corresponding target output of either 0 or 1 The learning rule has been proven to converge on a solution in finite time if a solution exists

The learning rule can be summarized in the following two equations:

b = b + [ T - A ]

For all inputs i:

W(i) = W(i) + [ T - A ] * P(i)

Where W is the vector of weights, P is the input vector presented to the network, T is the correct result that the neuron should have shown, A is the actual output of the neuron, and b is the bias

Training

Vectors from a training set are presented to the network one after another

If the network's output is correct, no change is made

Otherwise, the weights and biases are updated using the perceptron learning rule (as shown above) When each epoch

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(an entire pass through all of the input training vectors is called an epoch) of the training set has occured without error, training is complete

At this time any input training vector may be presented to the network and it will respond with the correct output vector If a vector, P, not in the training set is presented to the network, the network will tend to exhibit generalization

by responding with an output similar to target vectors for input vectors close to the previously unseen input vector P

So what can we use do with neural networks

Well if we are going to stick to using a single layer neural network, the tasks that can be achieved are different from those that can be achieved by multi-layer neural networks As this article is mainly geared towards dealing with single layer networks, let's dicuss those further:

Single layer neural networks

Single-layer neural networks (perceptron networks) are networks in which the output unit is independent of the others

- each weight effects only one output Using perceptron networks it is possible to achieve linear seperability functions like the diagrams shown below (assuming we have a network with 2 inputs and 1 output)

It can be seen that this is equivalent to the AND / OR logic gates, shown below

Figure 6 Classification tasks

So that's a simple example of what we could do with one perceptron (single neuron essentially), but what if we were to chain several perceptrons together? We could build some quite complex functionality Basically we would be

constructing the equivalent of an electronic circuit

Perceptron networks do however, have limitations If the vectors are not linearly separable, learning will never reach a point where all vectors are classified properly The most famous example of the perceptron's inability to solve problems with linearly nonseparable vectors is the boolean XOR problem

Multi layer neural networks

With muti-layer neural networks we can solve non-linear seperable problems such as the XOR problem mentioned

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above, which is not acheivable using single layer (perceptron) networks The next part of this article series will show how to do this using muti-layer neural networks, using the back propogation training method

Well that's about it for this article I hope it's a nice introduction to neural networks I will try and publish the other two articles when I have some spare time (in between MSc disseration and other assignments) I want them to be pretty graphical so it may take me a while, but i'll get there soon, I promise

What Do You Think ?

Thats it, I would just like to ask, if you liked the article please vote for it

Points of Interest

I think AI is fairly interesting, that's why I am taking the time to publish these articles So I hope someone else finds it interesting, and that it might help further someones knowledge, as it has my own

History

v1.0 17/11/06

Bibliography

Artificial Intelligence 2nd edition, Elaine Rich / Kevin Knight McGraw Hill Inc

Artificial Intelligence, A Modern Approach, Stuart Russell / Peter Norvig Prentice Hall

License

This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves If in doubt please contact the author via the discussion board below

A list of licenses authors might use can be found here

About the Author

Sacha Barber

Software Developer (Senior)

United Kingdom Member

I currently hold the following qualifications (amongst others, I also studied Music Technology and Electronics, for my sins)

- MSc (Passed with distinctions), in Information Technology for E-Commerce

- BSc Hons (1st class) in Computer Science & Artificial Intelligence

Both of these at Sussex University UK

Award(s)

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I am lucky enough to have won a few awards for Zany Crazy code articles over the years

Microsoft C# MVP 2012

Codeproject MVP 2012

And numerous codeproject awards which you can see over at my blog

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