Lab (1)

Neural Network – Perceptron Architecture

Objective:       Learn to create Perceptron networks

Learn to apply the Perceptron Learning Rule

In order to complete the lab, you need to have access to a machine with Matlab Neural Network Toolbox installed.  You can complete this lab on your machine at home, or use sc to do it.  Also, to complete the lab you need to use the Matlab Neural Network Manual.

A Perceptron can be created using the newp function, usually, by running a command like:

net = newp(PR,S,TF,LF)

Use the Matlab help on newp to explain what does each parameter of the function mean?

PR  :

S :

TF:

LF:

To answer this question, you can either use the help command at the Matlab prompt; help newp, or use the online help for Neural network Toolbox.

The following command creates a Perceptron network with a single one-element input vector and one neuron.  The range for the single element is [0 2].

net = newp([0 2], 1);

To see what has been created so far, you can use this:

Inputweights = net.inputweights{1, 1}

inputweights =

delays: 0

initFcn: 'initzero'

learn: 1

learnFcn: 'learnp'

learnParam: []

size: [1 1]

userdata: [1x1 struct]

weightFcn: 'dotprod'

The default learning function is learnp.  The net input to the hardlim transfer function is dotprod.  Thus, the DOT product of the input vector and weight matrix will be computed then the bias will be added to compute the net input.

The default initialization function, initzero, is used to set the initial values of the weights to zero.

To check the bias, we can run:

biases = net.biases{1}

biases =

initFcn: 'initzero'

learn: 1

learnFcn: 'learnp'

learnParam: []

size: 1

userdata: [1x1 struct]

As one can immediately notice, the bias is 0.

Simulation (sim)

When a network is created, that does not necessary mean it is ready for use.  A network should be trained for the given cases, and then be used for other inputs.

Suppose we want to create a network with a single-neuron, a bias, and two inputs.  The limit for the inputs are [-2 and 2].  As we mentioned before, the weights and the bias are set to 0 by default.

net = newp([-2 2; -2 2], 1);

Let’s set the weights to –1 for w11 = -1, w12 = 1, and bias = 1.

net.IW{1,1} = [-1 1];

net.b{1} = [1];

Note: at anytime of the process, if you want to check the outcome, just ignore the ; at the end of the command.  Now, let’s create some inputs.  Each input matrix in our case should have two values, a pair.

p1 = [1; 1];

A test simulation of our network with this input is:

a1 = sim(net, p1)

What is the output?

Try p2 = [1 –1].

Find out how you can run the network for both p1 and p2 together.

Note: Just in case you want to reset the weights and bias back to the default of 0, you can use the init command.  For example in the network that we just created, we can type:

net=  init(net). to reset them back to 0 again.

Sometimes, one may want to assign the weights and biases randomly.  There is a function that does this:

net.inputweights{1,1}.initFcn = ‘rands’;

net.biases{1}.initFcn = ‘rands’;

net = init(net);

Let’s chek it out:

wts = net.IW{1,1}

What do you have for the weights and the bias?

Perceptron Learning Rules

We learned in class the following rules:

e = t – p                       The error is the difference between target and input

wnew = wold + e*p

bnew = bold + e

How do we implement this in Matlab?

Suppose in our previous example, we would have a target:

t = [ 0 ] for the input pair p = [2 2]

Let’s create the network again:

net = newp([-2 2; -2 2], 1);

net.b{1} = [0];

w = [1  -0.8];

net.IW{1, 1} = w;

p = [1 ; 2];

t = [1];

a = sim(net, p)

e = t – a;

So now that you have the error, what is the next step?  Can you use the learning rules given above to proceed?

The two steps are:

w  = w’;         (to temporarily transpose it)

w = w + e*p;

b = b + e;

w = w’;

Now try again to simulate the network.

a = sim(net, p)

e = t – a;

Did it converge?  If not we should repeat this.  There was a better way to do this.  Let’s go back and repeat the first few steps:

net = newp([-2 2; -2 2], 1);

net.b{1} = [0];

w = [1  -0.8];

net.IW{1, 1} = w;

p = [1 ; 2];

t = [1];

a = sim(net, p)

e = t – a;

Now, we can use the function learnp. Use help to find out what each parameter mean.

dw = learnp(w, p, [], [], [], [], e, [], [], [])

w = w + dw;

Now use this to simulate the network again.

Let’s try to further improve this process.  We can set the number of iteration (epochs). To set for one iteration:

net = newp([-2 2; -2 2], 1);

p = [2 ; 2];

t = [0];

net.trainParam.epochs = 1;

net = train(net, p, t);

What are the weights and the bias?  What is the error?

Did your network produce the right result with one epoch?

Lets’ try this for a set of input but keep the number of epochs the same.

p = [ [-2; 2] [1; -2]  [-2; 2]  [-1; 1]];

t = [ 0  1  0 1];

net = train(net, p, t);

Now what are the weights and the bias?

Suppose that this network has been trained, let see what it produces for a set of inputs:

a = sim(net, p);

Lab Assignment

Problem (1)

Now that you learned to set up a Perceptron network, design a network to separate apples and oranges using the criteria give in class and in brief below:  ,

thus the input parameter for an apple: will generate the target value of [1].  Similarly, the input parameter for and apple:  will generate the target value of [-1].

Once your network is trained, try the following inputs:and then

What to submit?

The list of all commands that you have used following by the outcome of Matlab run.  You can create a blank file and cut an paste your commands as you will progress.  Then print that file.

What comes next?

Perceptron Network with more neurons.