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Kernel_Methods/rosenblatt_perceptron.m

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+% This is an implementation of Rosenblatt's Perceptron
+% from Cristianini and Shawe-Taylor (2000). "Support Vector Machines
+% and Other Kernel-based Learning Methods", Table 2.1:
+% The Perceptron Algorithm (primal form) with a slight change
+% in the definition of a mistake (see "if" statement).
+
+clc; close all;
+x = [0.248,	0.564; 0.103, 0.637; 0.119, 0.489;
+     0.458, 0.281; 0.268, 0.378; 0.267, 0.253;
+     0.156, 0.311; 0.077, 0.350; 0.109, 0.191;
+     0.344, 0.133; 0.494, 0.110; 0.360, 0.886;
+     0.492, 0.740; 0.523, 0.895; 0.719, 0.820;
+     0.926, 0.764; 0.714, 0.603; 0.548, 0.566;
+     0.746, 0.335; 0.852, 0.547];               % Data set: [x1, x2]
+y = ones(20,1); y(1:11) = -1;                   % Data set: y = {+1,-1}
+
+w = [0; 0]; b = 0;          % Initialize parameters w, b
+R = max(vecnorm(x'));       % Distance of farthest data pt. from origin
+eta = 0.1; k = Inf;         % eta = learning rate
+[X,Y] = meshgrid(0:0.01:1); % For plotting the decision boundary
+while k > 0
+    k = 0;                  % Reset counter for no. of mistakes
+    for j = 1:size(x,1)
+        if y(j)*(w'*x(j,:)' + b) < 1    % < 0 instead of < 1 in the book
+            w = w + eta*y(j)*x(j,:)';   % Update w
+            b = b + eta*y(j)*R^2;       % Update b
+            k = k + 1;                  % Increment counter
+        end
+    end
+    Z = reshape([X(:) Y(:)]*w + b,size(X));
+    contourf(X,Y,Z,50,'FaceAlpha',0.3,'LineColor','none');
+    colormap(redblue); hold on; set(gcf,'Color','w');
+    scatter(x(y == 1,1),x(y == 1,2),100,'rx','LineWidth',2.5);
+    scatter(x(y == -1,1),x(y == -1,2),40,'bo','filled');
+    box on; grid on; axis([0 1 0 1]);
+    x2 = [(-b+w(1))/w(2), -(b+w(1))/w(2)];
+    plot([-1 1],x2,'k-','LineWidth',1.5);       % <w,x> + b = 0
+    x2 = [(1-b+w(1))/w(2), (1-b-w(1))/w(2)];
+    plot([-1 1],x2,'k--','LineWidth',1.5);      % <w,x> + b = 1
+    x2 = [(-1-b+w(1))/w(2), -(1+b+w(1))/w(2)];
+    plot([-1 1],x2,'k--','LineWidth',1.5);      % <w,x> + b = -1
+    title(sprintf('w = [%.3f; %.3f], b = %.3f, Margin = %.3f',...
+        w, b, 1./norm(w))); xlabel('x1'); ylabel('x2');
+    legend({'','Positive samples','Negative samples','','',''},...
+        'Location','southeast','Box','off');
+    % for rep = 1:(k>0)+20*(k==0)
+    %     exportgraphics(gcf,'rosenblatt_perceptron.gif','Append',true);
+    % end
+    pause(0.1); clf;
+end
+
+function c = redblue
+% redblue gives a colormap within [cl(1) cl(2)] from
+%   Blue [0 0 1] to White [0 0 0] to Red [1 0 0]
+    m = size(get(gcf,'colormap'),1);        % Get size of colormap
+    cl = clim;                              % Get colormap limits
+    m1 = round(-m*cl(1)/diff(cl));          % Get ratio of (-1), blue
+    m2 = m - m1;                            %  the rest are (+1), red
+    up = (0:m1-1)'/max(m1-1,1);             % up = [0,...,1] 
+    dn = (m2-1:-1:0)'/max(m2-1,1);          % dn = [1,...,0]
+    r = [up; ones(m2,1)];                   % red vector
+    g = [up; dn];                           % green vector
+    b = [ones(m1,1); dn];                   % blue vector
+    c = [r g b];
+end