Implementing and ploting a perceptron in MATLAB

Question

I´m reviewing a code from Toronto perceptron MATLAB code

The code is

function [w] = perceptron(X,Y,w_init)

w = w_init;
for iteration = 1 : 100  %&l         


        

Answer 1

You should first understand what is the meaning of each of the inputs:

• X is the input matrix of examples, of size M x N, where M is the dimension of the feature vector, and N the number of samples. Since the perceptron model for prediction is Y=w*X+b, you have to supply one extra dimension in X which is constant, usually set to 1, so the b term is "built-in" into X. In the example below for X, I set the last entry of X to be 1 in all samples.
• Y is the correct classification for each sample from X (the classification you want the perceptron to learn), so it should be a N dimensional row vector - one output for each input example. Since the perceptron is a binary classifier, it should have only 2 distinct possible values. Looking in the code, you see that it checks for the sign of the prediction, which tells you that the allowed values of Y should be -1,+1 (and not 0,1 for example).
• w is the weight vector you are trying to learn.

So, try to call the function with:

X=[0 0; 0 1; 1 1];
Y=[1 -1];
w=[.5; .5; .5];

EDIT

Use the following code to call the perceptron alg and see the results graphically:

% input samples
X1=[rand(1,100);rand(1,100);ones(1,100)];   % class '+1'
X2=[rand(1,100);1+rand(1,100);ones(1,100)]; % class '-1'
X=[X1,X2];

% output class [-1,+1];
Y=[-ones(1,100),ones(1,100)];

% init weigth vector
w=[.5 .5 .5]';

% call perceptron
wtag=perceptron(X,Y,w);
% predict
ytag=wtag'*X;


% plot prediction over origianl data
figure;hold on
plot(X1(1,:),X1(2,:),'b.')
plot(X2(1,:),X2(2,:),'r.')

plot(X(1,ytag<0),X(2,ytag<0),'bo')
plot(X(1,ytag>0),X(2,ytag>0),'ro')
legend('class -1','class +1','pred -1','pred +1')