888 BONUS LAB 1, C (gcc)

888 BONUS LAB 1

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% ELE 888/ EE 8209: LAB 1: Bayesian Decision Theory
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [posteriors_x,g_x]=lab1(x,Training_Data,y)
%%
% 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);

%TRYING TO GET THE BONUS TO WORK

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

% Hint: use the commands "find" and "length"

%% Bonus

f=D(:,1:2);  % feature samples
la=D(:,N); % class labels
[dee,col]=size(la);
sigma=cov(f);

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

Pr1 = sum(la==1)/length(la);
Pr2 = sum(la==2)/length(la);

disp('Mean & Std for class 1 & 2');
mu1 = mean(f(la==1)) % mean of the class conditional density p(x/w1)
mu2 = mean(f(la==2)) % mean of the class conditional density p(x/w2)

lsigmal = det(sigma);
isigma=inv(sigma);

feature = x(1); %changed from y
feature2 = x(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];

plot(pos11,pos12);hold on 
%figure;
plot(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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