artificial intelligence - 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  %<- in practice, use some stopping criterion!
  for ii = 1 : size(X,2)         %cycle through training set
    if sign(w'*X(:,ii)) ~= Y(ii) %wrong decision?
      w = w + X(:,ii) * Y(ii);   %then add (or subtract) this point to w
    end
  end
  sum(sign(w'*X)~=Y)/size(X,2)   %show misclassification rate
end

So I was reading how to apply this function to data matrix X, and target Y, but, do not know how to use this function, I understand, it returns a vector of weights, so it can classify.

Could you please give an example, and explain it??

I′ve tried

X=[0 0; 0 1; 1 1]
Y=[1 0; 2 1]
w=[1 1 1]
Result = perceptron( X, Y, w )

??? Error using ==> mtimes
Inner matrix dimensions must agree.

Error in ==> perceptron at 15
            if sign(w'*X(:,ii)) ~= Y(ii) 

    Result = perceptron( X, Y, w' )

??? Error using ==> ne
Matrix dimensions must agree.

Error in ==> perceptron at 19
        sum(sign(w'*X)~=Y) / size(X,2);     

Thanks

Thank you for the anwers, I got one more, If I change the Y = [0, 1], what happens to the algorithm?.

So, Any input data will not work with Y = [0,1] with this code of the perceptron right?,

-----------------------------EDIT------------------------

One more question, if I want to plot the line that divides the 2 classes, I know we can get that the line solving linear equation system that has to do with weights, but how, what could I do?, I'm trying something like

% the initial weights
w_init = [ 1 1 1]';  
% the weights returned from perceptron    
wtag   = perceptron(X,Y,w_init,15);

% concatenate both
Line = [wtag,w_init] 

% solve the linear system, am I correct doing this?
rref(Line')

% plot???

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')