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- % Local Regression and Likelihood, Figure 8.2.
- %
- % Discrimination/Classification, simple example using
- % density estimation.
- %
- % First, compute density estimates fit0, fit1 ('family','rate'
- % - output is in events per unit area) for each class in the
- % training sample. The ratio fit1/(fit1+fit0) estimates the
- % posterior probability that an observation comes from population 1.
- %
- % plotting the classification boundary is slightly tricky - it depends
- % on both fits, so lfplot() can't be used. Instead, both fits must be
- % evaluated on the same grid of values, which is then used to make a
- % contour plot.
- %
- % Author: Catherine Loader
- load cltrain;
- u0 = find(y==0);
- u1 = find(y==1);
- fit0 = locfit([x1(u0) x2(u0)],y(u0),'family','rate','scale',0);
- fit1 = locfit([x1(u1) x2(u1)],y(u1),'family','rate','scale',0);
- v0 = -3+6*(0:50)'/50;
- v1 = -2.2+4.2*(0:49)'/49;
- % predict returns log(rate)
- z = predict(fit0,{v0 v1})-predict(fit1,{v0 v1});
- z = reshape(z,51,50);
- figure('Name','fig8_2: classification');
- contour(v0,v1,z',[0 0]);
- hold on;
- plot(x1(u0),x2(u0),'.');
- plot(x1(u1),x2(u1),'.','color','red');
- hold off;
- p0 = predict(fit0,[x1 x2]);
- p1 = predict(fit1,[x1 x2]);
- py = (p1 > p0);
- disp('Classification table for training data');
- tabulate(10*y+py);
- load cltest;
- p0 = predict(fit0,[x1 x2]);
- p1 = predict(fit1,[x1 x2]);
- py = (p1 > p0);
- disp('Classification table for test data');
- tabulate(10*y+py);
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