Consider this classification problem (using the Iris dataset ):
As you can see, in addition to easily divided clusters, for which you know the boundary equation in advance, finding the boundary is not a trivial task ...
One idea is to use the classify discriminant analysis function to find the border (you have the choice between linear and quadratic border).
The following is a complete example illustrating the procedure. This code requires the Statistics toolbar:
%# load Iris dataset (make it binary-class with 2 features) load fisheriris data = meas(:,1:2); labels = species; labels(~strcmp(labels,'versicolor')) = {'non-versicolor'}; NUM_K = numel(unique(labels)); %# number of classes numInst = size(data,1); %# number of instances %# visualize data figure(1) gscatter(data(:,1), data(:,2), labels, 'rb', '*o', ... 10, 'on', 'sepal length', 'sepal width') title('Iris dataset'), box on, axis tight %# params classifierType = 'quadratic'; %# 'quadratic', 'linear' npoints = 100; clrLite = [1 0.6 0.6 ; 0.6 1 0.6 ; 0.6 0.6 1]; clrDark = [0.7 0 0 ; 0 0.7 0 ; 0 0 0.7]; %# discriminant analysis %# classify the grid space of these two dimensions mn = min(data); mx = max(data); [X,Y] = meshgrid( linspace(mn(1),mx(1),npoints) , linspace(mn(2),mx(2),npoints) ); X = X(:); Y = Y(:); [C,err,P,logp,coeff] = classify([XY], data, labels, classifierType); %# find incorrectly classified training data [CPred,err] = classify(data, data, labels, classifierType); bad = ~strcmp(CPred,labels); %# plot grid classification color-coded figure(2), hold on image(X, Y, reshape(grp2idx(C),npoints,npoints)) axis xy, colormap(clrLite) %# plot data points (correctly and incorrectly classified) gscatter(data(:,1), data(:,2), labels, clrDark, '.', 20, 'on'); %# mark incorrectly classified data plot(data(bad,1), data(bad,2), 'kx', 'MarkerSize',10) axis([mn(1) mx(1) mn(2) mx(2)]) %# draw decision boundaries between pairs of clusters for i=1:NUM_K for j=i+1:NUM_K if strcmp(coeff(i,j).type, 'quadratic') K = coeff(i,j).const; L = coeff(i,j).linear; Q = coeff(i,j).quadratic; f = sprintf('0 = %g + %g*x + %g*y + %g*x^2 + %g*x.*y + %g*y.^2',... K,L,Q(1,1),Q(1,2)+Q(2,1),Q(2,2)); else K = coeff(i,j).const; L = coeff(i,j).linear; f = sprintf('0 = %g + %g*x + %g*y', K,L(1),L(2)); end h2 = ezplot(f, [mn(1) mx(1) mn(2) mx(2)]); set(h2, 'Color','k', 'LineWidth',2) end end xlabel('sepal length'), ylabel('sepal width') title( sprintf('accuracy = %.2f%%', 100*(1-sum(bad)/numInst)) ) hold off
