[转载]数据挖掘SVM的MATLAB实现

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数据挖掘中SVM算法的MATLAB的实现

代码如下：

本帖隐藏的内容

1. function [D, a_star] = SVM(train_features, train_targets, params, region)
   
2. 
   
3. % Classify using (a very simple implementation of) the support vector machine algorithm
   
4. %
   
5. % Inputs:
   
6. % features- Train features
   
7. % targets - Train targets
   
8. % params - [kernel, kernel parameter, solver type, Slack]
   
9. %               Kernel can be one of: Gauss, RBF (Same as Gauss), Poly, Sigmoid, or Linear
   
10. %               The kernel parameters are:
    
11. %                   RBF kernel  - Gaussian width (One parameter)
    
12. %                   Poly kernel - Polynomial degree
    
13. %                   Sigmoid     - The slope and constant of the sigmoid (in the format [1 2], with no separating commas)
    
14. %   Linear   - None needed
    
15. %               Solver type can be one of: Perceptron, Quadprog
    
16. % region - Decision region vector: [-x x -y y number_of_points]
    
17. %
    
18. % Outputs
    
19. % D - Decision sufrace
    
20. % a - SVM coeficients
    
21. %
    
22. % Note: The number of support vectors found will usually be larger than is actually
    
23. % needed because both solvers are approximate.
    
24. 
    
25. [Dim, Nf]       = size(train_features);
    
26. Dim             = Dim + 1;
    
27. train_features(Dim,:) = ones(1,Nf);
    
28. z = 2*(train_targets>0) - 1;
    
29. 
    
30. %Get kernel parameters
    
31. [kernel, ker_param, solver, slack] = process_params(params);
    
32. 
    
33. %Transform the input features
    
34. y = zeros(Nf);
    
35. switch kernel,
    
36. case {
    
37. 'Gauss','RBF'
    
38. },
    
39.    for i = 1:Nf,
    
40.       y(:,i)    = exp(-sum((train_features-train_features(:,i)*ones(1,Nf)).^2)'/(2*ker_param^2));
    
41.    end
    
42. case {
    
43. 'Poly', 'Linear'
    
44. }
    
45.    if strcmp(kernel, 'Linear')
    
46.       ker_param = 1;
    
47.    end
    
48.    
    
49.    for i = 1:Nf,
    
50.       y(:,i) = (train_features'*train_features(:,i) + 1).^ker_param;
    
51.    end
    
52. case 'Sigmoid'
    
53.     if (length(ker_param) ~= 2)
    
54.         error('This kernel needs two parameters to operate!')
    
55.     end
    
56.      
    
57.    for i = 1:Nf,
    
58.       y(:,i) = tanh(train_features'*train_features(:,i)*ker_param(1)+ker_param(2));
    
59.    end
    
60. otherwise
    
61.    error('Unknown kernel. Can be Gauss, Linear, Poly, or Sigmoid.')
    
62. end
    
63. 
    
64. %Find the SVM coefficients
    
65. switch solver
    
66. case 'Quadprog'
    
67.    %Quadratic programming
    
68.    if ~isfinite(slack)
    
69.        alpha_star = quadprog((z'*z).*(y'*y), -ones(1, Nf), [], [], z, 0, 0)';
    
70.    else
    
71.        alpha_star = quadprog((z'*z).*(y'*y), -ones(1, Nf), [], [], z, 0, 0, slack)';
    
72.    end
    
73.    a_star = (alpha_star.*z)*y';
    
74.    
    
75.    %Find the bias
    
76.    in           = find((alpha_star > 0) & (alpha_star < slack));
    
77.    if isempty(in),
    
78.        bias = 0;
    
79.    else
    
80.     B            = z(in) - a_star * y(:,in);
    
81.        bias         = mean(B(in));
    
82.    end
    
83.    
    
84. case 'Perceptron'
    
85.    max_iter = 1e5;
    
86.    iter = 0;
    
87.    rate        = 0.01;
    
88.    xi = ones(1,Nf)/Nf*slack;
    
89.    
    
90.    if ~isfinite(slack),
    
91.        slack = 0;
    
92.    end
    
93.    
    
94.    %Find a start point
    
95.    processed_y = [y; ones(1,Nf)] .* (ones(Nf+1,1)*z);
    
96.    a_star = mean(processed_y')';
    
97.    
    
98.    while ((sum(sign(a_star'*processed_y+xi)~=1)>0) & (iter < max_iter))
    
99.       iter = iter + 1;
    
100.       if (iter/5000 == floor(iter/5000)),
     
101.          disp(['Working on iteration number ' num2str(iter)])
     
102.       end
     
103.       
     
104.       %Find the worse classified sample (That farthest from the border)
     
105.       dist = a_star'*processed_y+xi;
     
106.       [m, indice] = min(dist);
     
107.       a_star = a_star + rate*processed_y(:,indice);
     
108.       
     
109.       %Calculate the new slack vector
     
110.       xi(indice)  = xi(indice) + rate;
     
111.       xi = xi / sum(xi) * slack;
     
112.    end
     
113.    
     
114.    if (iter == max_iter),
     
115.       disp(['Maximum iteration (' num2str(max_iter) ') reached']);
     
116.    else
     
117.       disp(['Converged after ' num2str(iter) ' iterations.'])
     
118. end
     
119.    
     
120.    bias   = 0;
     
121.    a_star = a_star(1:Nf)';
     
122.    
     
123. case 'Lagrangian'
     
124.     %Lagrangian SVM (See Mangasarian & Musicant, Lagrangian Support Vector Machines)
     
125.     tol         = 1e-5;
     
126.     max_iter    = 1e5;
     
127.     nu          = 1/Nf;
     
128.     iter        = 0;
     
129. 
     
130.     D           = diag(z);
     
131.     alpha       = 1.9/nu;
     
132.      
     
133.     e           = ones(Nf,1);
     
134.     I           = speye(Nf);
     
135.     Q           = I/nu + D*y'*D;
     
136.     P           = inv(Q);
     
137.     u           = P*e;
     
138.     oldu        = u + 1;
     
139.      
     
140.     while ((iter<max_iter) & (sum(sum((oldu-u).^2)) > tol)),
     
141.         iter    = iter + 1;
     
142.         if (iter/5000 == floor(iter/5000)),
     
143.            disp(['Working on iteration number ' num2str(iter)])
     
144.         end
     
145.         oldu    = u;
     
146.         f       = Q*u-1-alpha*u;
     
147.         u       = P*(1+(abs(f)+f)/2);
     
148.     end
     
149.    
     
150.     a_star    = y*D*u(1:Nf);
     
151.     bias      = -e'*D*u;
     
152.      
     
153. otherwise
     
154.    error('Unknown solver. Can be either Quadprog or Perceptron')
     
155. end
     
156. 
     
157. %Find support verctors
     
158. sv = find(abs(a_star) > 1e-10);
     
159. Nsv = length(sv);
     
160. if isempty(sv),
     
161.    error('No support vectors found');
     
162. else
     
163.    disp(['Found ' num2str(Nsv) ' support vectors'])
     
164. end
     
165. 
     
166. %Margin
     
167. b = 1/sqrt(sum(a_star.^2));
     
168. disp(['The margin is ' num2str(b)])
     
169. 
     
170. %Now build the decision region
     
171. N           = region(5);
     
172. xx          = linspace (region(1),region(2),N);
     
173. yy          = linspace (region(3),region(4),N);
     
174. D = zeros(N);
     
175. 
     
176. for j = 1:N,
     
177.    y = zeros(N,1);
     
178.    for i = 1:Nsv,
     
179.       data = [xx(j)*ones(1,N); yy; ones(1,N)];
     
180.       
     
181.       switch kernel,
     
182. case {
     
183. 'Gauss','RBF'
     
184. },
     
185.          y     = y + a_star(i) * exp(-sum((data-train_features(:,sv(i))*ones(1,N)).^2)'/(2*ker_param^2));
     
186. case {
     
187. 'Poly', 'Linear'
     
188. }
     
189.          y     = y + a_star(i) * (data'*train_features(:,sv(i))+1).^ker_param;
     
190. case 'Sigmoid'
     
191.          y     = y + a_star(i) * tanh(data'*train_features(:,sv(i))*ker_param(1)+ker_param(2));
     
192.       end
     
193.    end
     
194.    D(:,j) = (y + bias);
     
195. end
     
196. 
     
197. 
     
198. D = D>0;

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[转载]数据挖掘SVM的MATLAB实现

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