ele 888 lab 1 part 1, C (gcc)

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% ELE 888/ EE 8209: LAB 1: Bayesian Decision Theory
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [posteriors_x,g_x]=lab1(x,Training_Data,x2)

% x = individual sample to be tested (to identify its probable class label)
% featureOfInterest = index of relevant feature (column) in Training_Data 
% Train_Data = Matrix containing the training samples and numeric class labels
% posterior_x  = Posterior probabilities
% g_x = value of the discriminant function

D=Training_Data;

% D is MxN (M samples, N columns = N-1 features + 1 label)
[M,N]=size(D);

feature = 2; %Feature 2 for x2 (Sepal Width) and 1 for x1 (Septal Length)

f=D(:,feature);  % feature samples
la=D(:,N); % class labels

%% %%%%Prior Probabilities%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Hint: use the commands "find" and "length"
class1 = la==1; %Iris Setosa
class2 = la==2; %Iris Versicolour

disp('Prior probabilities:');
Pr1 = sum(class1)/length(la)
Pr2 = sum(class2)/length(la)

%% %%%%%Class-conditional probabilities%%%%%%%%%%%%%%%%%%%%%%%

disp('Mean & Std for class 1 & 2');
m11 = mean(f(class1))  % mean of the class conditional density p(x/w1)
std11 = std(f(class1)) % Standard deviation of the class conditional density p(x/w1)

m12 = mean(f(class2)) % mean of the class conditional density p(x/w2)
std12= std(f(class2)) % Standard deviation of the class conditional density p(x/w2)

findfeature = x;

disp(['Conditional probabilities for x=' num2str(x)]);
cp11= 1/(sqrt(2*pi)*std11)*exp(-0.5*((findfeature-m11)/std11)^2) % use the above mean, std and the test feature to calculate p(x/w1)

cp12= 1/(sqrt(2*pi)*std12)*exp(-.5*((findfeature-m12)/std12)^2) % use the above mean, std and the test feature to calculate p(x/w2)

%% %%%%%%Compute the posterior probabilities%%%%%%%%%%%%%%%%%%%%

disp('Posterior prob. for the test feature');

Px = cp11*Pr1 + cp12*Pr2;
pos11= cp11*Pr1/Px % p(w1/x) for the given test feature value

pos12= cp12*Pr2/Px % p(w2/x) for the given test feature value

posteriors_x= [pos11, pos12];

% plot(f*pos11,f*Px);
% figure,
% plot(f*pos12,f*Px);

%% %%%%%%Discriminant function for min error rate classifier%%%

disp('Discriminant function for the test feature');

[C,I]= min(posteriors_x);
g_x= I % compute the g(x) for min err rate classifier.

%% Finding Threshold
 
 thres = sym('thres');
 eq = 1/(sqrt(2*pi)*std11)*exp(-.5*((thres-m11)/std11)^2) * Pr1 == 1/(sqrt(2*pi)*std12)*exp(-.5*((thres-m12)/std12)^2) * Pr2;
 thres = solve(eq, thres);
 thres = double(thres);
 Th1 = thres(thres>0)
 
 
  figure,
  plot(thres)
 %% Unbalanced Loss
% Theta = (0.8/0.9)*(Pr2/Pr1);
 
% thres = sym('thres');
% eq = 1/(sqrt(2*pi)*std11)*exp(-.5*((thres-m11)/std11)^2) * Pr1 == 1/(sqrt(2*pi)*std12)*exp(-.5*((thres-m12)/std12)^2) * Pr2;
% thres = solve(eq, thres);
% thres = double(thres);
% Th1 = thres(thres>Theta)
% 
% %% Bonus
% 
% f=D(:,1:2);  % feature samples
% la=D(:,N); % class labels
% [M,N]=size(la);
% sigma=cov(f);  %Using Covariance matrix, sigma 
% 
% %% 
% class1 = la==1;
% class2 = la==2;
% 
% disp('Mean & Std for class 1 & 2');
% mu1 = mean(f(class1)) % mean of the class conditional density p(x/w1)
% mu2 = mean(f(class2)) % mean of the class conditional density p(x/w2)
% 
% lsigmal = det(sigma)
% isigma=inv(sigma);
% 
% %feature = y2(1);
% %feature2 = y2(2);
% % 
% % disp(['Conditional probabilities for x=' num2str(x)]);
% % cp11 = 1/((2*pi)^((length(sigma))/2)*(lsigmal^0.5))*exp((-1/2)*(transpose(feature-mu1))*isigma*(feature-mu1));% use the above mean, std and the test feature to calculate p(x/w1)
% % cp21 = 1/((2*pi)^((length(sigma))/2)*(lsigmal^0.5))*exp((-1/2)*(transpose(feature2-mu2))*isigma*(feature2-mu2));
% % cp12 = 1/((2*pi)^((length(sigma))/2)*(lsigmal^0.5))*exp((-1/2)*(transpose(feature-mu2))*isigma*(feature-mu2)); % use the above mean, std and the test feature to calculate p(x/w2)
% % cp22 = 1/((2*pi)^((length(sigma))/2)*(lsigmal^0.5))*exp((-1/2)*(transpose(feature2-mu1))*isigma*(feature2-mu1));
% 
% %% 
% 
% disp('Posterior prob. for the test feature');
% 
% Px = cp11*Pr1 + cp12*Pr2;
% Px2 = cp21*Pr1 + cp22*Pr2;
% pos11 = cp11*Pr1/Px% p(w1/x) for the given test feature value
% pos21 = cp21*Pr1/Px2
% pos12= cp12*Pr2/Px% p(w2/x) for the given test feature value
% pos22 = cp22*Pr2/Px2
% posteriors_x = [pos11, pos12, pos21, pos22];
% 
% plot3(pos11,pos12,pos21);hold on 
% figure;
% plot3(pos21,pos22);
% 
% %% 
% 
% disp('Discriminant function for the test feature');
% 
% %[C,I]= min(posteriors_x);

g_x = I  % compute the g(x) for min err rate classifier.

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