[专题汇总]模式识别

Parzen Window Density Estimation

1. close all; clc; clear;
   
2. 
   
3. rand('seed',0);
   
4. randn('seed',0);
   
5. 
   
6. x_truth = linspace( -1, 3, 1000 );
   
7. indsGT  = x_truth>0.0;
   
8. indsLT  = x_truth<2.0;
   
9. inds    = find( indsGT & indsLT );
   
10. p_truth = zeros( 1, 1000 );
    
11. p_truth(inds) = 1/2;
    
12. 
    
13. % Generate some data from the true distribution:
    
14. %
    
15. 
    
16. 
    
17. N_values = [ 32, 256, 5000 ];
    
18. h_values = [ 0.05, 0.2 ];
    
19. 
    
20. n_hs = length(h_values);
    
21. colors = 'rb';
    
22. for ni = 1:length(N_values)
    
23.   N = N_values(ni);
    
24.   X = unifrnd( 0, 2, N, 1 );
    
25. 
    
26.   figure;
    
27.   pt = plot( x_truth, p_truth, '-g' ); hold on;
    
28.   ph = zeros(n_hs,1); % handles for each Parzen density estimation
    
29.   
    
30.   for hi = 1:length(h_values)
    
31.     h = h_values(hi);     
    
32. 
    
33.     % For each possible h plot the Parzen approximation on top of the truth:
    
34.     %   
    
35.     x_grid = linspace(-1,3,100); % where we will sample our density \hat{p}
    
36. 
    
37.     p_hat = [];
    
38.     for xi = 1:length(x_grid)
    
39.       x = x_grid(xi);
    
40.       p = mean( normpdf( ( repmat( x, N, 1 ) - X ) / h ) )/h;
    
41. 
    
42.       p_hat = [ p_hat, p ];  
    
43.     end
    
44. 
    
45.     ph(hi) = plot( x_grid, p_hat, ['-',colors(hi)] );
    
46.    
    
47.   end
    
48.   
    
49.   legend( [pt,ph(1),ph(2)], {'truth',['N=',num2str(N),'; h=0.05'],['N=',num2str(N), '; h=0.2']} );
    
50.   fn = ['chap_2_prob_31_N_',num2str(N),'.eps'];
    
51.   saveas(gcf,['../../WriteUp/Graphics/Chapter2/',fn],'epsc');
    
52.   
    
53. end
    
54. http://waxworksmath.com/Authors/N_Z/Theodoridis/WWW/chapter_2.html

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K Nearest Neighbor Density Estimation using Matlab

1. close all; clc; clear;
   
2. 
   
3. rand('seed',0);
   
4. randn('seed',0);
   
5. 
   
6. x_truth = linspace( -1, 3, 1000 );
   
7. indsGT  = x_truth>0.0;
   
8. indsLT  = x_truth<2.0;
   
9. inds    = find( indsGT & indsLT );
   
10. p_truth = zeros( 1, 1000 );
    
11. p_truth(inds) = 1/2;
    
12. 
    
13. % Generate some data from the true distribution:
    
14. %
    
15. N = 5000;
    
16. X = unifrnd( 0, 2, N, 1 );
    
17. 
    
18. k_values = [ 32, 64, 256 ];
    
19. 
    
20. n_ks = length(k_values);
    
21. colors = 'rbk';
    
22. 
    
23. figure;
    
24. pt = plot( x_truth, p_truth, '-g' ); hold on;
    
25. ph = zeros(n_ks,1); % handles for each Parzen density estimation
    
26. 
    
27. for ki = 1:length(k_values)
    
28.   k = k_values(ki);     
    
29.   
    
30.   % For each possible h plot the K-NN density approximation on top of the truth:
    
31.   %   
    
32.   x_grid = linspace(0,2,100); % where we will sample our density \hat{p}
    
33.   
    
34.   p_hat = [];
    
35.   for xi = 1:length(x_grid)
    
36.     x = x_grid(xi);
    
37.    
    
38.     % find the K-NN of x and the volume around them:
    
39.     %
    
40.     [dum,inds] = sort(abs(X - x));
    
41.     nn     = inds(1:k);
    
42.     xnn    = X(nn);
    
43.     V_of_x = max(xnn) - min(xnn);
    
44.    
    
45.     p = k/(N*V_of_x);
    
46.    
    
47.     p_hat = [ p_hat, p ];  
    
48.   end
    
49.   
    
50.   ph(ki) = plot( x_grid, p_hat, ['-',colors(ki)] );
    
51.   
    
52. end
    
53. 
    
54. legend( [pt,ph(1),ph(2),ph(3)], {'truth','k=32','k=64','k=256'} );
    
55. fn = ['chap_2_prob_32.eps'];
    
56. saveas(gcf,['../../WriteUp/Graphics/Chapter2/',fn],'epsc');
    
57. http://waxworksmath.com/Authors/N_Z/Theodoridis/WWW/chapter_2.html

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