[专题汇总]模式识别

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• Scalable Pattern Recognition Algorithms
• Introduction to Pattern Recognition: A Matlab Approach, 1st
• Pattern Recognition with Neural Networks in C++
• Pattern Recognition Algorithms for Data Mining
• Applied Pattern Recognition: Algorithms and Implementation in C++
• Pattern.Recognition.and.Machine.Learning.Solutions.Exercises,.Christ
• Technical Analysis for Algorithmic Pattern Recognition
• Introduction To Pattern Recognition And Machine Learning
• Neural Networks for Pattern Recognition Oxford University Press (1995)
• Image Processing and Pattern Recognition 2010
• Pattern Recognition and Machine Learning Information Science and Statistics
• Pattern Recognition and Machine Learning 完整答案
• Discriminant Analysis and Statistical Pattern Recognition, Wiley
• Pattern.Recognition Theodoridis,.Koutroumbas,.文字版
• Data Analysis and Pattern Recognition in Multiple Databases
• Markov Models for Pattern Recognition:From Theory to Applications 2nd Edition
• Introduction to Statistical Pattern Recognition~Fukunaga, Keinosuke.2nd
• A Probabilistic Theory of Pattern Recognition
• Fibonacci Ratios with Pattern Recognition
• Pattern Recognition and Machine Learning - Bishop, PRML
• A Tutorial on Support Vector Machines for Pattern Recognition（英文+中文翻译）
• Supervised and Unsupervised Pattern Recognition: Feature Extraction and Computat
• Data Analysis & Pattern Recognition in Multiple Databases
• Data Complexity in Pattern Recognition
• Pattern Recognition and Machine Learning原版及习题答案
• Random Graphs for Statistical Pattern Recognition
• Pattern Recognition and Machine Learning课后习题答案
• Pattern Recognition and Machine Intelligence
• Introduction to Pattern Recognition and Machine Learning
• Data Analysis and Pattern Recognition in Multiple Databases
• Applied Pattern Recognition, Fourth Edition
• Probabilistic Theory of Pattern Recognition~Springer.1996
• Statistical Pattern Recognition (Second Edition)等四本书
• Pattern Recognition and Machine Learning Solutions to the Exercises
• Price-Pattern Recognition Using a Local Polynomial Regression
• Pattern Recognition in Bioinformatics
• Introduction to Statistical Pattern Recognition
• Matrix Methods in Data Mining and Pattern Recognition
• Pattern Recognition with Neural Networks in C++
• Pattern Recognition Using Neural and Functional Networks
• Random Graphs for Statistical Pattern Recognition
• Pattern Recognition and Machine Learning by Christopher Bishop
• long memory pattern modelling and recognition system for financial time-series
• Statistical Pattern Recognition, Second Edition
• Pattern Recognition and Machine Learning (Information Science and Statistics)
• Neural.Networks.for.Pattern.Recognition
• Pattern Recognition and Neural Networks
• Pattern Recognition and Machine Learning~C. M. Bishop.Spriger.2007
• Stock Price Pattern Recognition -- A Recurrent Neural Network Approach
• Matrix Methods in Data Mining and Pattern Recognition
• Statistical Pattern Recognition
• Random Graphs for Statistical Pattern Recognition
• Mining Sequential Patterns from Large Data Sets
• Analytic Pattern Matching: From DNA to Twitter
• Data Complexity in Pattern Recognition
• Technical Analysis for Algorithmic Pattern Recognition
• Pattern Theory: The Stochastic Analysis of Real-World Signals
  

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关键词：模式识别 introduction Intelligence discriminant Applications 模式识别

1. % Example 2.2.1
   
2. % "Introduction to Pattern Recognition: A MATLAB Approach"
   
3. % S. Theodoridis, A. Pikrakis, K. Koutroumbas, D. Cavouras
   
4. 
   
5. close('all');
   
6. clear
   
7. 
   
8. rand('seed',0);
   
9. 
   
10. % Generate the dataset X1 as well as the vector containing the class labels of
    
11. % the points in X1
    
12. N=[100 100]; % 100 vectors per class
    
13. l=2; % Dimensionality of the input space
    
14. 
    
15. x=[3 3]';
    
16. % x=[2 2]'; for X2
    
17. % x=[0 2]'; for X3
    
18. % x=[1 1]'; for X4
    
19. 
    
20. X1=[2*rand(l,N(1)) 2*rand(l,N(2))+x*ones(1,N(2))];
    
21. X1=[X1; ones(1,sum(N))];
    
22. y1=[-ones(1,N(1)) ones(1,N(2))];
    
23. 
    
24. % 1. Plot X1, where points of different classes are denoted by different colors,
    
25. figure(1), plot(X1(1,y1==1),X1(2,y1==1),'bo',...
    
26. X1(1,y1==-1),X1(2,y1==-1),'r.')
    
27. figure(1), axis equal
    
28. 
    
29. % 2. Run the perceptron algorithm for X1 with learning parameter 0.01
    
30. rho=0.01; % Learning rate
    
31. w_ini=[1 1 -0.5]';
    
32. [w,iter,mis_clas]=perce(X1,y1,w_ini,rho)

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1. % Example 2.2.2
   
2. % "Introduction to Pattern Recognition: A MATLAB Approach"
   
3. % S. Theodoridis, A. Pikrakis, K. Koutroumbas, D. Cavouras
   
4. 
   
5. close('all');
   
6. clear
   
7. 
   
8. rand('seed',0);
   
9. 
   
10. % Generate the dataset X1 as well as the vector containing the class labels of
    
11. % the points in X1
    
12. N=[100 100]; % 100 vectors per class
    
13. l=2; % Dimensionality of the input space
    
14. 
    
15. x=[3 3]';
    
16. % x=[2 2]'; for X2
    
17. % x=[0 2]'; for X3
    
18. % x=[1 1]'; for X4
    
19. 
    
20. X1=[2*rand(l,N(1)) 2*rand(l,N(2))+x*ones(1,N(2))];
    
21. X1=[X1; ones(1,sum(N))];
    
22. y1=[-ones(1,N(1)) ones(1,N(2))];
    
23. 
    
24. % 1. Plot X1, where points of different classes are denoted by different
    
25. % colors
    
26. figure(1), plot(X1(1,y1==1),X1(2,y1==1),'bo',...
    
27. X1(1,y1==-1),X1(2,y1==-1),'r.')
    
28. figure(1), axis equal
    
29. 
    
30. % 2. Run the perceptron algorithm for X1 with learning parameter 0.01
    
31. rho=0.01; % Learning rate
    
32. %rho=0.05
    
33. w_ini=[1 1 -0.5]';
    
34. [w,iter,mis_clas]=perce_online(X1,y1,w_ini,rho)

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1. % Example 2.3.1
   
2. % "Introduction to Pattern Recognition: A MATLAB Approach"
   
3. % S. Theodoridis, A. Pikrakis, K. Koutroumbas, D. Cavouras
   
4. 
   
5. close('all');
   
6. clear;
   
7. 
   
8. % 1.
   
9. m(:,1)=[0 0 0 0 0]';
   
10. m(:,2)=[1 1 1 1 1]';
    
11. S=[.9 .3 .2 .05 .02;
    
12.      .3 .8 .1 .2 .05;
    
13.      .2 .1 .7 .015 .07;
    
14.      .05 .2 .015 .8 .01;
    
15.      .02 .05 .07 .01 .75];
    
16. P=[1/2 1/2];
    
17. 
    
18. % Generate X1 and the required class labels
    
19. N1=200;
    
20. randn('seed',0)
    
21. X1=[mvnrnd(m(:,1),S,fix(N1/2)); mvnrnd(m(:,2),S,N1-fix(N1/2))]';
    
22. z1=[ones(1,fix(N1/2)) 2*ones(1,N1-fix(N1/2))];
    
23. 
    
24. % Generate X2 and the required class labels
    
25. N2=200;
    
26. % N2=10000 % for X3
    
27. % N2=100000 % for X4
    
28. randn('seed',100)
    
29. X2=[mvnrnd(m(:,1),S,fix(N2/2)); mvnrnd(m(:,2),S,N2-fix(N2/2))]';
    
30. z2=[ones(1,fix(N2/2)) 2*ones(1,N2-fix(N2/2))];
    
31. 
    
32. % Compute the Bayesian classification error based on X2
    
33. S_true(:,:,1)=S;
    
34. S_true(:,:,2)=S;
    
35. [z]=bayes_classifier(m,S_true,P,X2);
    
36. err_Bayes_true=sum(z~=z2)/sum(N2)
    
37. 
    
38. 
    
39. % 2. Augment the data vectors of X1
    
40. X1=[X1; ones(1,sum(N1))];
    
41. y1=2*z1-3;
    
42. 
    
43. % Augment the data vectors of X2
    
44. X2=[X2; ones(1,sum(N2))];
    
45. y2=2*z2-3;
    
46. 
    
47. % Compute the classification error of the LS classifier based on X2
    
48. [w]=SSErr(X1,y1,0);
    
49. SSE_out=2*(w'*X2>0)-1;
    
50. err_SSE=sum(SSE_out.*y2<0)/sum(N2)

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1. % Example 2.3.2
   
2. % "Introduction to Pattern Recognition: A MATLAB Approach"
   
3. % S. Theodoridis, A. Pikrakis, K. Koutroumbas, D. Cavouras
   
4. 
   
5. close('all');
   
6. clear;
   
7. 
   
8. m=[0 0 0 0 0; 2 2 0 2 2]';
   
9. S=[1 0 0 0 0; 0 1 0 0 0; 0 0 10^(-350) 0 0; 0 0 0 1 0; 0 0 0 0 1];
   
10. [l,l]=size(S);
    
11. 
    
12. % Generate X1
    
13. N1=1000;
    
14. randn('seed',0)
    
15. X1=[mvnrnd(m(:,1),S,fix(N1/2)); mvnrnd(m(:,2),S,N1-fix(N1/2))]';
    
16. X1=[X1; ones(1,N1)];
    
17. y1=[ones(1,fix(N1/2)) -ones(1,N1-fix(N1/2))];
    
18. 
    
19. % Generate X2
    
20. N2=10000;
    
21. randn('seed',100)
    
22. X2=[mvnrnd(m(:,1),S,fix(N2/2)); mvnrnd(m(:,2),S,N2-fix(N2/2))]';
    
23. X2=[X2; ones(1,N2)];
    
24. y2=[ones(1,fix(N2/2)) -ones(1,N2-fix(N2/2))];
    
25. 
    
26. % 1. Compute the condition number of X1*X1'and the solution vector, w, for
    
27. % the original version of the LS classifier
    
28. cond_num=cond(X1*X1')
    
29. w=SSErr(X1,y1,0)
    
30. % Note: cond_num=1.4767e+017 and w is a vector of NaN (Not-A-Number)
    
31. 
    
32. % 2. Repeat step 1 for the regularized version of the LS classifier
    
33. C=0.1;
    
34. cond_num=cond(X1*X1'+C*eye(l+1))
    
35. w=SSErr(X1,y1,C)
    
36. 
    
37. % 4. Compute the classification error on X2 for the gicen w
    
38. SSE_out=2*(w'*X2>0)-1;
    
39. err_SSE=sum(SSE_out.*y2<0)/N2

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1. %
   
2. % Written by:
   
3. % --
   
4. % John L. Weatherwax                2007-07-01
   
5. %
   
6. % email: wax@alum.mit.edu
   
7. %
   
8. % Please send comments and especially bug reports to the
   
9. % above email address.
   
10. %
    
11. %-----
    
12. 
    
13. close all; clc; clear;
    
14. 
    
15. mu1 = [ 0.1, 0.1 ].';
    
16. mu2 = [ 2.1, 1.9 ].';
    
17. mu3 = [ -1.5, 2.0 ].';
    
18. 
    
19. S = [ [ 1.2, 0.4 ]; [ 0.4, 1.8 ] ];
    
20. w1 = S \ mu1;
    
21. w2 = S \ mu2;
    
22. w3 = S \ mu3;
    
23. 
    
24. P = 1/3;
    
25. w10 = log(1/3) - 0.5 * (mu1.') * w1;
    
26. w20 = log(1/3) - 0.5 * (mu2.') * w2;
    
27. w30 = log(1/3) - 0.5 * (mu3.') * w3;
    
28. 
    
29. x = [ 2.1; 1.9 ];
    
30. 
    
31. % Compute the three discriminant values:
    
32. %
    
33. g1 = (w1.')*x + w10;
    
34. g2 = (w2.')*x + w20;
    
35. g3 = (w3.')*x + w30;
    
36. 
    
37. [m, class] = max( [g1, g2, g3] );
    
38. http://waxworksmath.com/Authors/N_Z/Theodoridis/Code/Chapter2/chap_2_prob_7.m

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1. %
   
2. % Written by:
   
3. % --
   
4. % John L. Weatherwax                2007-07-01
   
5. %
   
6. % email: wax@alum.mit.edu
   
7. %
   
8. % Please send comments and especially bug reports to the
   
9. % above email address.
   
10. %
    
11. %-----
    
12. 
    
13. close all; clc; clear;
    
14. 
    
15. S = [ [ 0.3, 0.1, 0.1 ]; [ 0.1, 0.3, -0.1 ]; [ 0.1, -0.1, 0.3] ];
    
16. mu1 = [ 0; 0; 0 ];
    
17. mu2 = [ 0.5; 0.5; 0.5 ];
    
18. mu_diff = mu1 - mu2;
    
19. w = S \ mu_diff;
    
20. 
    
21. P1 = 0.3;
    
22. P2 = 1-P1;
    
23. 
    
24. norm_mu_diff = sqrt( mu_diff.' * ( S \ mu_diff ) );
    
25. x0 = 0.5 * mu_diff - log( P1 / P2 ) * ( mu_diff / norm_mu_diff^2 );

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http://waxworksmath.com/Authors/N_Z/Theodoridis/Code/Chapter2/chap_2_prob_7.m

1. %
   
2. close all; clc; clear;
   
3. 
   
4. rand('seed',0);
   
5. randn('seed',0);
   
6. 
   
7. mu1 = [ 1, 1 ].';
   
8. mu2 = [ 1.5, 1.5 ].';
   
9. sigmasSquared = 0.2;
   
10. d = size(mu1,1);
    
11. 
    
12. nFeats = 10000;
    
13. 
    
14. X1 = mvnrnd( mu1, sigmasSquared*eye(d), nFeats );
    
15. X2 = mvnrnd( mu2, sigmasSquared*eye(d), nFeats );
    
16. 
    
17. h1 = plot( X1(:,1), X1(:,2), '.b' ); hold on;
    
18. h2 = plot( X2(:,1), X2(:,2), '.r' ); hold on;
    
19. legend( [h1,h2], {'class 1', 'class 2'} );
    
20. 
    
21. mean_diff = mu1 - mu2;
    
22. 
    
23. X = [ X1; X2 ];
    
24. labels = [ ones(nFeats,1); 2*ones(nFeats,1) ];
    
25. 
    
26. 
    
27. % Part (a): classify each of the vectors in X1 and X2 using the algebraically simplified notation:
    
28. %
    
29. rhs = 0.5 * ( dot(mu1,mu1) - dot(mu2,mu2) );
    
30. lhs = mean_diff' * X';
    
31. 
    
32. % If lhs > rhs we are selecting this sample from class #1 otherwise from class #2:
    
33. %
    
34. class_decision = lhs > rhs;
    
35. choosen_class = zeros(2*nFeats,1);
    
36. choosen_class(find(class_decision==1)) = 1;
    
37. choosen_class(find(class_decision~=1)) = 2;
    
38. 
    
39. P_correct = sum(choosen_class == labels)/(2*nFeats);
    
40. P_error   = 1 - P_correct;
    
41. 
    
42. % Calculate the optimal Bayes error rate (using the results from Problem~2.9):
    
43. %
    
44. addpath('../../../Duda_Hart_Stork/Code/Chapter2/ComputerExercises');
    
45. dm = mahalanobis(mu1,mu2,sigmasSquared*eye(d));
    
46. P_B = 1 - normcdf( 0.5 * dm );
    
47. 
    
48. fprintf('empirical P_e= %10.6f; analytic Bayes P_e= %10.6f\n',P_error,P_B);
    
49. 
    
50. 
    
51. % Part (b): classify each of the vectors in X1 and X2 (using the algebraically simplified notation):
    
52. %
    
53. rhs = 0.5 * ( dot(mu1,mu1) - dot(mu2,mu2) ) + sigmasSquared * log(2);
    
54. lhs = mean_diff' * X';
    
55. 
    
56. % If lhs > rhs we are selecting this sample from class #1 otherwise from class #2:
    
57. %
    
58. class_decision = lhs > rhs;
    
59. choosen_class = zeros(2*nFeats,1);
    
60. choosen_class(find(class_decision==1)) = 1;
    
61. choosen_class(find(class_decision~=1)) = 2;
    
62. 
    
63. P_correct = sum(choosen_class == labels)/(2*nFeats);
    
64. P_error   = 1 - P_correct;
    
65. 
    
66. % extract the expected loss using this classifier:
    
67. %
    
68. L_12 = sum( choosen_class(1:nFeats)~=1 );
    
69. L_21 = sum( choosen_class(nFeats+1:end)~=2 );
    
70. r_hat = ( L_12 + 0.5 * L_21 )/(2*nFeats);
    
71. 
    
72. fprintf('P_correct= %10.6f; r_hat= %10.6f\n',P_correct,r_hat);
    
73. http://waxworksmath.com/Authors/N_Z/Theodoridis/WWW/chapter_2.html

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1. close all; clc; clear;
   
2. 
   
3. rand('seed',0);
   
4. randn('seed',0);
   
5. 
   
6. mu1 = [ 1, 1 ].';
   
7. mu2 = [ 1.5, 1.5 ].';
   
8. sigmaCov = [ 1.01, 0.2; 0.2, 1.01 ];
   
9. 
   
10. nFeats = 10000;
    
11. 
    
12. X1 = mvnrnd( mu1, sigmaCov, nFeats );
    
13. X2 = mvnrnd( mu2, sigmaCov, nFeats );
    
14. 
    
15. h1 = plot( X1(:,1), X1(:,2), '.b' ); hold on;
    
16. h2 = plot( X2(:,1), X2(:,2), '.r' ); hold on;
    
17. legend( [h1,h2], {'class 1', 'class 2'} );
    
18. 
    
19. X = [ X1; X2 ];
    
20. labels = [ ones(nFeats,1); 2*ones(nFeats,1) ];
    
21. 
    
22. % Part (a): classify each of the vectors in X1 and X2 (directly using the likelihood ratio)
    
23. %
    
24. lratio = mvnpdf( X, mu1.', sigmaCov ) ./ mvnpdf( X, mu2.', sigmaCov );
    
25. 
    
26. % If lratio > 1 we are selecting this sample from class #1 otherwise from class #2:
    
27. %
    
28. class_decision = lratio > 1;
    
29. choosen_class = zeros(2*nFeats,1);
    
30. choosen_class(find(class_decision==1)) = 1;
    
31. choosen_class(find(class_decision~=1)) = 2;
    
32. 
    
33. P_correct = sum(choosen_class == labels)/(2*nFeats);
    
34. P_error   = 1 - P_correct;
    
35. 
    
36. % Calculate the optimal Bayes error rate (using the results from Problem~2.9):
    
37. %
    
38. addpath('../../../Duda_Hart_Stork/Code/Chapter2/ComputerExercises');
    
39. dm = mahalanobis(mu1,mu2,sigmaCov);
    
40. P_B = 1 - normcdf( 0.5 * dm );
    
41. 
    
42. fprintf('empirical P_e= %10.6f; analytic Bayes P_e= %10.6f\n',P_error,P_B);
    
43. 
    
44. % Part (b): classify each of the vectors in X1 and X2 (directly using the likelihood ratio)
    
45. %
    
46. 
    
47. % If lratio > 1/2 we are selecting this sample from class #1 otherwise from class #2:
    
48. %
    
49. class_decision = lratio > 1/2;
    
50. choosen_class = zeros(2*nFeats,1);
    
51. choosen_class(find(class_decision==1)) = 1;
    
52. choosen_class(find(class_decision~=1)) = 2;
    
53. 
    
54. P_correct = sum(choosen_class == labels)/(2*nFeats);
    
55. P_error   = 1 - P_correct;
    
56. 
    
57. % extract the expected loss using this classifier:
    
58. %
    
59. L_12 = sum( choosen_class(1:nFeats)~=1 );
    
60. L_21 = sum( choosen_class(nFeats+1:end)~=2 );
    
61. r_hat = ( L_12 + 0.5 * L_21 )/(2*nFeats);
    
62. 
    
63. fprintf('P_correct= %10.6f; r_hat= %10.6f\n',P_correct,r_hat);
    
64. http://waxworksmath.com/Authors/N_Z/Theodoridis/WWW/chapter_2.html

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Nearest Neighbors Classification using Matlab

1. close all; clc; clear;
   
2. 
   
3. rand('seed',0);
   
4. randn('seed',0);
   
5. 
   
6. nTraining = 50;
   
7. nTesting  = 50;
   
8. 
   
9. % Generate training data like for Problem 2.12:
   
10. %
    
11. mu1 = [ 1, 1 ].';
    
12. mu2 = [ 1.5, 1.5 ].';
    
13. sigmasSquared = 0.2;
    
14. d = size(mu1,1);
    
15. 
    
16. nFeats = nTraining;
    
17. 
    
18. X1 = mvnrnd( mu1, sigmasSquared*eye(d), nFeats );
    
19. X2 = mvnrnd( mu2, sigmasSquared*eye(d), nFeats );
    
20. 
    
21. if( 0 )
    
22.   h1 = plot( X1(:,1), X1(:,2), '.b' ); hold on;
    
23.   h2 = plot( X2(:,1), X2(:,2), '.r' ); hold on;
    
24.   legend( [h1,h2], {'class 1', 'class 2'} );
    
25. end
    
26. 
    
27. X_train = [ X1; X2 ];
    
28. labels_train = [ ones(nFeats,1); 2*ones(nFeats,1) ];
    
29. 
    
30. % Generate 100 new points from each class to classify:
    
31. %
    
32. nFeats = nTesting;
    
33. 
    
34. X1 = mvnrnd( mu1, sigmasSquared*eye(d), nFeats );
    
35. X2 = mvnrnd( mu2, sigmasSquared*eye(d), nFeats );
    
36. 
    
37. X_test = [ X1; X2 ];
    
38. labels_test = [ ones(nFeats,1); 2*ones(nFeats,1) ];  
    
39. 
    
40. % Classify each of the vectors in X_test using the NN and 3NN rules
    
41. %
    
42. addpath('../../../Duda_Hart_Stork/BookSupplements/ClassificationToolbox/Src');
    
43. for nni = 1:11
    
44.   test_targets = Nearest_Neighbor( X_train.', labels_train, X_test.', nni);
    
45.   P_NN_error = sum( test_targets(:) ~= labels_test(:) )/length(test_targets);
    
46.   fprintf('P_e %2dNN= %10.6f; \n',nni,P_NN_error);
    
47. end
    
48. 
    
49. % Calculate the optimal Bayes error rate (using the results from Problem~2.9):
    
50. %
    
51. addpath('../../../Duda_Hart_Stork/Code/Chapter2/ComputerExercises');
    
52. dm = mahalanobis(mu1,mu2,sigmasSquared*eye(d));
    
53. P_B = 1 - normcdf( 0.5 * dm );
    
54. 
    
55. fprintf('P_B= %10.6f\n',P_B);

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