learn_perceptron.m

Perceptron matlab code

function [beta_hat,beta_zero_hat] = Learn_Perceptron(X,Y,rho,itr_max)

[N,d] = size(X);

% Initialize betas 
beta_hat = zeros(d,1);
beta_hat(1) = 1;
beta_zero_hat = -0.5;


cont = 1;
itr = 0;

PLOT = 1;
if PLOT == 1
    max_x = max(X);
    min_x = min(X);
    X_plot = [min_x;max_x];
    ind_1 = find(Y >0);
    ind_2 = find(Y<=0);
end


while cont == 1
    num_miss = 0;
    for i = 1:N
        val = (beta_zero_hat + X(i,:) * beta_hat) * Y(i);
        if val <= 0
            num_miss = num_miss + 1;
            beta_hat = beta_hat + rho * Y(i) * X(i,:)';
            beta_zero_hat = beta_zero_hat + rho * Y(i);
            if PLOT == 1
                figure(1000);
                plot(X(ind_1,1),X(ind_1,2),'rs');
                hold on
                plot(X(ind_2,1),X(ind_2,2),'bo');
                if abs(beta_hat(2)) > abs(beta_hat(1))
                    zx = X_plot(:,1);
                    yy = -(zx * beta_hat(1) + beta_zero_hat)/beta_hat(2);
                    plot(zx,yy,'k-');
                    
                else
                    zx = X_plot(:,2);
                    yy = -(zx * beta_hat(2) + beta_zero_hat)/beta_hat(1);
                    plot(yy,zx,'k-');
                end
                %axis([min_x(1) max_x(1) min_x(2) max_x(2)]);
                axis([0 1.3 0 1.3]);
                xlabel('x_1');
                ylabel('x_2');
                legend(': y=+1',': y=-1');
                hold off;
                pause
            end
        end
    end
    itr = itr + 1;
    val_all = (beta_zero_hat + X * beta_hat).*Y;
    ind_e = find(val_all<=0);
    if ~isempty(ind_e)
        val_itr(itr) = mean(val_all(ind_e));
    else
        val_itr(itr) = 0;
    end
    if num_miss == 0
        if PLOT == 1
            figure(1000);
            plot(X(ind_1,1),X(ind_1,2),'rs');
            hold on
            plot(X(ind_2,1),X(ind_2,2),'bo');
            if abs(beta_hat(2)) > abs(beta_hat(1))
                zx = X_plot(:,1);
                yy = -(zx * beta_hat(1) + beta_zero_hat)/beta_hat(2);
                plot(zx,yy,'r-');
                
            else
                zx = X_plot(:,2);
                yy = -(zx * beta_hat(2) + beta_zero_hat)/beta_hat(1);
                plot(yy,zx,'r-');
            end
            %axis([min_x(1) max_x(1) min_x(2) max_x(2)]);
            axis([0 1.3 0 1.3]);
            xlabel('x_1');
            ylabel('x_2');
            legend(': y=+1',': y=-1');
            hold off;
            pause
        end
        
        cont = 0;
        
    end
   
    if itr > itr_max
        cont = 0;
    end
    
end