[示例] SVM(支持向量机)应用于分类问题

xjzuo

这是一个支持向量机应用于分类问题的演示程序，分为线性与非线性两部分，希望对做这方面研究的人有用。
（请先安装SVM工具箱，然后运行之）

1. %%%%%%%%%%%%%%%%%%%%%%%
   
2. function demsvm1()
   
3. % DEMSVM1 - Demonstrate basic Support Vector Machine classification
   
4. %
   
5. %   DEMSVM1 demonstrates the classification of a simple artificial data
   
6. %   set by a Support Vector Machine classifier, using different kernel
   
7. %   functions.
   
8. %
   
9. %   See also
   
10. %   SVM, SVMTRAIN, SVMFWD, SVMKERNEL, DEMSVM2
    
11. %
    
12. %
    
13. % Copyright (c) Anton Schwaighofer (2001)
    
14. % This program is released unter the GNU General Public License.
    
15. %
    
16. X = [2 7; 3 6; 2 2; 8 1; 6 4; 4 8; 9 5; 9 9; 9 4; 6 9; 7 4];
    
17. Y = [ +1;  +1;  +1;  +1;  +1;  -1;  -1;  -1;  -1;  -1;  -1];
    
18. % define a simple artificial data set
    
19. x1ran = [0 10];
    
20. x2ran = [0 10];
    
21. % range for plotting the data set and the decision boundary
    
22. disp(' ');
    
23. disp('This demonstration illustrates the use of a Support Vector Machine');
    
24. disp('(SVM) for classification. The data is a set of 2D points, together');
    
25. disp('with target values (class labels) +1 or -1.');
    
26. disp(' ');
    
27. disp('The data set consists of the points');
    
28. ind = [1:length(Y)]';
    
29. fprintf('X%2i = (%2i, %2i) with label Y%2i = %2i\n', [ind, X, ind, Y]');
    
30. disp(' ')
    
31. disp('Press any key to plot the data set');
    
32. pause
    
33. f1 = figure;
    
34. plotdata(X, Y, x1ran, x2ran);
    
35. title('Data from class +1 (squares) and class -1 (crosses)');
    
36. fprintf('\n\n\n\n');
    
37. fprintf('The data is plotted in figure %i, where\n', f1);
    
38. disp('  squares stand for points with label Yi = +1');
    
39. disp('  crosses stand for points with label Yi = -1');
    
40. disp(' ')
    
41. disp(' ');
    
42. disp('Now we train a Support Vector Machine classifier on this data set.');
    
43. disp('We use the most simple kernel function, namely the inner product');
    
44. disp('of points Xi, Xj (linear kernel K(Xi,Xj) = Xi''*Xj )');
    
45. disp(' ');
    
46. disp('Press any key to start training')
    
47. pause
    
48. net = svm(size(X, 2), 'linear', [], 10);
    
49. net = svmtrain(net, X, Y);
    
50. f2 = figure;
    
51. plotboundary(net, x1ran, x2ran);
    
52. plotdata(X, Y, x1ran, x2ran);
    
53. plotsv(net, X, Y);
    
54. title(['SVM with linear kernel: decision boundary (black) plus Support' ...
    
55.        ' Vectors (red)']);
    
56. fprintf('\n\n\n\n');
    
57. fprintf('The resulting decision boundary is plotted in figure %i.\n', f2);
    
58. disp('The contour plotted in black separates class +1 from class -1');
    
59. disp('(this is the actual decision boundary)');
    
60. disp('The contour plotted in red are the points at distance +1 from the');
    
61. disp('decision boundary, the blue contour are the points at distance -1.');
    
62. disp(' ');
    
63. disp('All examples plotted in red are found to be Support Vectors.');
    
64. disp('Support Vectors are the examples at distance +1 or -1 from the ');
    
65. disp('decision boundary and all the examples that cannot be classified');
    
66. disp('correctly.');
    
67. disp(' ');
    
68. disp('The data set shown can be correctly classified using a linear');
    
69. disp('kernel. This can be seen from the coefficients alpha associated');
    
70. disp('with each example: The coefficients are');
    
71. ind = [1:length(Y)]';
    
72. fprintf('  Example %2i: alpha%2i = %5.2f\n', [ind, ind, net.alpha]');
    
73. disp('The upper bound C for the coefficients has been set to');
    
74. fprintf('C = %5.2f. None of the coefficients are at the bound,\n', ...
    
75. net.c(1));
    
76. disp('this means that all examples in the training set can be correctly');
    
77. disp('classified by the SVM.')
    
78. disp(' ');
    
79. disp('Press any key to continue')
    
80. pause
    
81. X = [X; [4 4]];
    
82. Y = [Y; -1];
    
83. net = svm(size(X, 2), 'linear', [], 10);
    
84. net = svmtrain(net, X, Y);
    
85. f3 = figure;
    
86. plotboundary(net, x1ran, x2ran);
    
87. plotdata(X, Y, x1ran, x2ran);
    
88. plotsv(net, X, Y);
    
89. title(['SVM with linear kernel: decision boundary (black) plus Support' ...
    
90.        ' Vectors (red)']);
    
91. fprintf('\n\n\n\n');
    
92. disp('Adding an additional point X12 with label -1 gives a data set');
    
93. disp('that can not be linearly separated. The SVM handles this case by');
    
94. disp('allowing training points to be misclassified.');
    
95. disp(' ');
    
96. disp('Training the SVM on this modified data set we see that the points');
    
97. disp('X5, X11 and X12 can not be correctly classified. The decision');
    
98. fprintf('boundary is shown in figure %i.\n', f3);
    
99. disp('The coefficients alpha associated with each example are');
    
100. ind = [1:length(Y)]';
     
101. fprintf('  Example %2i: alpha%2i = %5.2f\n', [ind, ind, net.alpha]');
     
102. disp('The coefficients of the misclassified points are at the upper');
     
103. disp('bound C.');
     
104. disp(' ')
     
105. disp('Press any key to continue')
     
106. pause
     
107. 
     
108. fprintf('\n\n\n\n');
     
109. disp('Adding the new point X12 has lead to a more difficult data set');
     
110. disp('that can no longer be separated by a simple linear kernel.');
     
111. disp('We can now switch to a more powerful kernel function, namely');
     
112. disp('the Radial Basis Function (RBF) kernel.');
     
113. disp(' ')
     
114. disp('The RBF kernel has an associated parameter, the kernel width.');
     
115. disp('We will now show the decision boundary obtained from a SVM with');
     
116. disp('RBF kernel for 3 different values of the kernel width.');
     
117. disp(' ');
     
118. disp('Press any key to continue')
     
119. pause
     
120. net = svm(size(X, 2), 'rbf', [8], 100);
     
121. net = svmtrain(net, X, Y);
     
122. f4 = figure;
     
123. plotboundary(net, x1ran, x2ran);
     
124. plotdata(X, Y, x1ran, x2ran);
     
125. plotsv(net, X, Y);
     
126. title(['SVM with RBF kernel, width 8: decision boundary (black)' ...
     
127.        ' plus Support Vectors (red)']);
     
128. fprintf('\n\n\n\n');
     
129. fprintf('Figure %i shows the decision boundary obtained from a SVM\n', ...
     
130. f4);
     
131. disp('with Radial Basis Function kernel, the kernel width has been');
     
132. disp('set to 8.');
     
133. disp('The SVM now interprets the new point X12 as evidence for a');
     
134. disp('cluster of points from class -1, the SVM builds a small ''island''');
     
135. disp('around X12.');
     
136. disp(' ')
     
137. disp('Press any key to continue')
     
138. pause
     
139. 
     
140. net = svm(size(X, 2), 'rbf', [1], 100);
     
141. net = svmtrain(net, X, Y);
     
142. f5 = figure;
     
143. plotboundary(net, x1ran, x2ran);
     
144. plotdata(X, Y, x1ran, x2ran);
     
145. plotsv(net, X, Y);
     
146. title(['SVM with RBF kernel, width 1: decision boundary (black)' ...
     
147.        ' plus Support Vectors (red)']);
     
148. fprintf('\n\n\n\n');
     
149. fprintf('Figure %i shows the decision boundary obtained from a SVM\n', ...
     
150. f5);
     
151. disp('with radial basis function kernel, kernel width 1.');
     
152. disp('The decision boundary is now highly shattered, since a smaller');
     
153. disp('kernel width allows the decision boundary to be more curved.');
     
154. disp(' ')
     
155. disp('Press any key to continue')
     
156. pause
     
157. 
     
158. net = svm(size(X, 2), 'rbf', [36], 100);
     
159. net = svmtrain(net, X, Y);
     
160. f6 = figure;
     
161. plotboundary(net, x1ran, x2ran);
     
162. plotdata(X, Y, x1ran, x2ran);
     
163. plotsv(net, X, Y);
     
164. title(['SVM with RBF kernel, width 36: decision boundary (black)' ...
     
165.        ' plus Support Vectors (red)']);
     
166. fprintf('\n\n\n\n');
     
167. fprintf('Figure %i shows the decision boundary obtained from a SVM\n', ...
     
168. f6);
     
169. disp('with radial basis function kernel, kernel width 36.');
     
170. disp('This gives a decision boundary similar to the one shown in');
     
171. fprintf('Figure %i for the SVM with linear kernel.\n', f2);
     
172. 
     
173. fprintf('\n\n\n\n');
     
174. disp('Press any key to end the demo')
     
175. pause
     
176. delete(f1);
     
177. delete(f2);
     
178. delete(f3);
     
179. delete(f4);
     
180. delete(f5);
     
181. delete(f6);
     
182. 
     
183. function plotdata(X, Y, x1ran, x2ran)
     
184. % PLOTDATA - Plot 2D data set
     
185. %
     
186. hold on;
     
187. ind = find(Y>0);
     
188. plot(X(ind,1), X(ind,2), 'ks');
     
189. ind = find(Y<0);
     
190. plot(X(ind,1), X(ind,2), 'kx');
     
191. text(X(:,1)+.2,X(:,2), int2str([1:length(Y)]'));
     
192. axis([x1ran x2ran]);
     
193. axis xy;
     
194. 
     
195. function plotsv(net, X, Y)
     
196. % PLOTSV - Plot Support Vectors
     
197. %
     
198. hold on;
     
199. ind = find(Y(net.svind)>0);
     
200. plot(X(net.svind(ind),1),X(net.svind(ind),2),'rs');
     
201. ind = find(Y(net.svind)<0);
     
202. plot(X(net.svind(ind),1),X(net.svind(ind),2),'rx');
     
203. 
     
204. function [x11, x22, x1x2out] = plotboundary(net, x1ran, x2ran)
     
205. % PLOTBOUNDARY - Plot SVM decision boundary on range X1RAN and X2RAN
     
206. %
     
207. hold on;
     
208. nbpoints = 100;
     
209. x1 = x1ran(1):(x1ran(2)-x1ran(1))/nbpoints:x1ran(2);
     
210. x2 = x2ran(1):(x2ran(2)-x2ran(1))/nbpoints:x2ran(2);
     
211. [x11, x22] = meshgrid(x1, x2);
     
212. [dummy, x1x2out] = svmfwd(net, [x11(:),x22(:)]);
     
213. x1x2out = reshape(x1x2out, [length(x1) length(x2)]);
     
214. contour(x11, x22, x1x2out, [-0.99 -0.99], 'b-');
     
215. contour(x11, x22, x1x2out, [0 0], 'k-');
     
216. contour(x11, x22, x1x2out, [0.99 0.99], 'g-');
     
217. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

复制代码

kevin19821

看起来还是有点迷糊

kevin19821

我怎只看到训练的样本了，没有分类呢？

ncepu_ly

好贴,谢谢,学习学习!

frogfish

原帖由 kevin19821 于 2007-11-13 21:37 发表

                               
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我怎只看到训练的样本了，没有分类呢？

呵呵，那是你没自己看全代码

koihime

这就说明了程序写好注释的重要性

frogfish

原帖由 koihime 于 2008-1-8 09:06 发表

                               
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这就说明了程序写好注释的重要性

一般看别人代码比自己写代码还要类，当然注释是一方面，思路的不同也是很大的原因

lis76

拷回去研究下

xiaofour1983

看看!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

若菱

xjzuo，你这个svm的工具箱是从哪里下载的？ 很需要

frogfish

原帖由 若菱 于 2008-8-29 10:59 发表

                               
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xjzuo，你这个svm的工具箱是从哪里下载的？ 很需要

http://www.chinavib.com/forum/viewthread.php?tid=36029
这个帖子有各种svm工具箱的说明和相关连接

不知道xjzuo用的是哪个

whitebaby323

对阿你用的工具箱是哪个为什么运行到训练的时候就出错了，找不到
net = svm(size(X, 2), 'linear', [], 10);这条语句

Ella_1000

我也出现了12的问题，请问怎么解决？

baihewuji

错误
??? Undefined command/function 'svm'.

Error in ==> demsvm1 at 48
net = svm(size(X, 2), 'linear', [], 10);

蓝白允诺

:loveliness: 下来试试再评论，呵呵。