% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Problem: Epage 71
%
%-----

close all; clc; clear; 

rand('seed',0);
randn('seed',0);

nTraining = 50;
nTesting  = 50;

% Generate training data like for Problem 2.12:
%
mu1 = [ 1, 1 ].';
mu2 = [ 1.5, 1.5 ].';
sigmasSquared = 0.2; 
d = size(mu1,1); 

nFeats = nTraining; 

X1 = mvnrnd( mu1, sigmasSquared*eye(d), nFeats ); 
X2 = mvnrnd( mu2, sigmasSquared*eye(d), nFeats ); 

if( 0 ) 
  h1 = plot( X1(:,1), X1(:,2), '.b' ); hold on; 
  h2 = plot( X2(:,1), X2(:,2), '.r' ); hold on; 
  legend( [h1,h2], {'class 1', 'class 2'} ); 
end

X_train = [ X1; X2 ]; 
labels_train = [ ones(nFeats,1); 2*ones(nFeats,1) ]; 

% Generate 100 new points from each class to classify: 
%
nFeats = nTesting; 

X1 = mvnrnd( mu1, sigmasSquared*eye(d), nFeats ); 
X2 = mvnrnd( mu2, sigmasSquared*eye(d), nFeats ); 

X_test = [ X1; X2 ]; 
labels_test = [ ones(nFeats,1); 2*ones(nFeats,1) ];  

% Classify each of the vectors in X_test using the NN and 3NN rules
%
addpath('../../../Duda_Hart_Stork/BookSupplements/ClassificationToolbox/Src');
for nni = 1:11
  test_targets = Nearest_Neighbor( X_train.', labels_train, X_test.', nni);
  P_NN_error = sum( test_targets(:) ~= labels_test(:) )/length(test_targets);
  fprintf('P_e %2dNN= %10.6f; \n',nni,P_NN_error);
end

% Calculate the optimal Bayes error rate (using the results from Problem~2.9): 
%
addpath('../../../Duda_Hart_Stork/Code/Chapter2/ComputerExercises'); 
dm = mahalanobis(mu1,mu2,sigmasSquared*eye(d));
P_B = 1 - normcdf( 0.5 * dm );

fprintf('P_B= %10.6f\n',P_B);