SVM(支持向量机)实现数据的三分类

clear; irisData = dlmread('iris.data'); plotAxis = [min(irisData(:, 3)) max(irisData(:, 3)) min(irisData(:, 4)) max(irisData(:, 4))]; kernel = 'rbf'; c = [1 10 100 1000 10000]; sigma = 1 : 0.5: 3; [C, Sigma] = meshgrid(c, sigma); C = C(:); Sigma = Sigma(:); Err = zeros(size(C)); n = length(Err); Xtest = irisData(1 : 150, 3 : 4); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % First train Isis-setosa(1) and Isis-versicolor(2) using grid search. % disp('.....................................................................') X = irisData(1 : 100, 3 : 4); Y = irisData(1 : 100, 5); Y(find(Y==1)) = 1; Y(find(Y==2)) = -1; Xtrain = X; disp('Training Isis-setosa(1) and Isis-versicolor(2) using grid search.') disp('Please wait a while.'); for i = 1 : n [alphaStar, bStar, SVIndex] = yxcSVMtrain(X, Y, C(i), kernel, Sigma(i)); [YClassified, Z, Err(i)] = yxcSVMclassifer(Xtrain, Xtrain, Y, alphaStar, bStar, kernel, Sigma(i)); end [mErr, i] = min(Err); %Compute the minimum one again, using the optimal C and Sigma. [alphaStar, bStar, SVIndex] = yxcSVMtrain(X, Y, C(i), kernel, Sigma(i)); [YClassified, Z, Err(i)] = yxcSVMclassifer(Xtrain, Xtrain, Y, alphaStar, bStar, kernel, Sigma(i)); disp(sprintf('Error rate is %%%d, with C = %d, sigma = %d', mErr*100, C(i), Sigma(i))); disp(sprintf('There are %d support vectors, %d out of %d are wrongly classified', ... length(SVIndex), mErr*length(Y), length(Y))); yxcSVMplot(X, Y, SVIndex, alphaStar, bStar, kernel, Sigma(i), plotAxis); title(sprintf('Isis-setosa(1) and Isis-versicolor(2), SV = %d, Err = %%%d, C = %d, Sigma = %d', ... length(SVIndex), mErr*100, C(i), Sigma(i))); % Test all data on the Isis-setosa(1) and Isis-versicolor(2) data set. [Y12, Z] = yxcSVMclassifer(Xtrain, Xtest, Y, alphaStar, bStar, kernel, Sigma(i)); Y12(find(Y12==1)) = 1; Y12(find(Y12==-1)) = 2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Then train Isis-versicolor(2) and Isis-virginica(3) using grid search. % disp('.....................................................................') X = irisData(51 : 150, 3 : 4); Y = irisData(51 : 150, 5); Y(find(Y==2)) = 1; Y(find(Y==3)) = -1; Xtrain = X; disp('Training Isis-versicolor(2) and Isis-virginica(3) using grid search.') disp('Please wait a while.'); for i = 1 : n [alphaStar, bStar, SVIndex] = yxcSVMtrain(X, Y, C(i), kernel, Sigma(i)); [YClassified, Z, Err(i)] = yxcSVMclassifer(Xtrain, Xtrain, Y, alphaStar, bStar, kernel, Sigma(i)); %disp(sprintf('Cross Validation: %d in %d', i, n)); end [mErr, i] = min(Err); %Compute the minimum one again, using the optimal C and Sigma. [alphaStar, bStar, SVIndex] = yxcSVMtrain(X, Y, C(i), kernel, Sigma(i)); [YClassified, Z, Err(i)] = yxcSVMclassifer(Xtrain, Xtrain, Y, alphaStar, bStar, kernel, Sigma(i)); disp(sprintf('Error rate is %%%d, with C = %d, sigma = %d', mErr*100, C(i), Sigma(i))); disp(sprintf('There are %d support vectors, %d out of %d are wrongly classified', ... length(SVIndex), mErr*length(Y), length(Y))); yxcSVMplot(X, Y, SVIndex, alphaStar, bStar, kernel, Sigma(i), plotAxis); title(sprintf('Isis-versicolor(2) and Isis-virginica(3), SV = %d, Err = %%%d, C = %d, Sigma = %d', ... length(SVIndex), mErr*100, C(i), Sigma(i))); % Test all data on the Isis-versicolor(2) and Isis-virginica(3) data set. [Y23, Z] = yxcSVMclassifer(Xtrain, Xtest, Y, alphaStar, bStar, kernel, Sigma(i)); Y23(find(Y23==1)) = 2; Y23(find(Y23==-1)) = 3; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Last train Isis-setosa(1) and Isis-virginica(3) using grid search. % disp('.....................................................................') X = irisData([1:50 101 : 150], 3 : 4); Y = irisData([1:50 101 : 150], 5); Y(find(Y==1)) = 1; Y(find(Y==3)) = -1; Xtrain = X; disp('Training Isis-setosa(1) and Isis-virginica(3) using grid search.') disp('Please wait a while.'); for i = 1 : n [alphaStar, bStar, SVIndex] = yxcSVMtrain(X, Y, C(i), kernel, Sigma(i)); [YClassified, Z, Err(i)] = yxcSVMclassifer(Xtrain, Xtrain, Y, alphaStar, bStar, kernel, Sigma(i)); %disp(sprintf('Cross Validation: %d in %d', i, n)); end [mErr, i] = min(Err); %Compute the minimum one again, using the optimal C and Sigma. [alphaStar, bStar, SVIndex] = yxcSVMtrain(X, Y, C(i), kernel, Sigma(i)); [YClassified, Z, Err(i)] = yxcSVMclassifer(Xtrain, Xtrain, Y, alphaStar, bStar, kernel, Sigma(i)); disp(sprintf('Error rate is %%%d, with C = %d, sigma = %d', mErr*100, C(i), Sigma(i))); disp(sprintf('There are %d support vectors, %d out of %d are wrongly classified', ... length(SVIndex), mErr*length(Y), length(Y))); yxcSVMplot(X, Y, SVIndex, alphaStar, bStar, kernel, Sigma(i), plotAxis); title(sprintf('Isis-setosa(1) and Isis-virginica(3), SV = %d, Err = %%%d, C = %d, Sigma = %d', ... length(SVIndex), mErr*100, C(i), Sigma(i))); % Test all data on the Isis-versicolor(2) and Isis-virginica(3) data set. [Y13, Z] = yxcSVMclassifer(Xtrain, Xtest, Y, alphaStar, bStar, kernel, Sigma(i)); Y13(find(Y13==1)) = 1; Y13(find(Y13==-1)) = 3; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % We use a little trick to find out which class the points belong to Y123 = sort([Y12 Y23 Y13], 2); Y123 = Y123(:, 2); % Plot the classified data. iY1 = find(Y123 == 1); iY2 = find(Y123 == 2); iY3 = find(Y123 == 3); x = irisData(:, 3); y = irisData(:, 4); figure plot(x(iY1), y(iY1), 'g+'); axis(plotAxis); hold on; plot(x(iY2), y(iY2), 'r*'); hold on; plot(x(iY3), y(iY3), 'y.'); hold on; % Find out the wrongly classified data. Y = irisData(:, 5); iYwrong = find(Y123 ~= Y); plot(x(iYwrong), y(iYwrong), 'ko'); legend('Isis-setosa(1)', 'Isis-versicolor(2)', 'Isis-virginica(3)', 'Wrong ones',... 'Location', 'NorthWest'); title('The Final Job.'); hold off;