Create A Program to Create Pattern Recognition in Matlab Assignment Solution.

function probability = computeGaussianDensity(mean, stdDev, x)

    probability = 1/(stdDev*sqrt(2*pi)) *exp(-(x-mean)^2 /(2*stdDev^2));

end

clc, clear all, close all

%% Part 2

load partOneData.mat

N1 = length(classOne); % number of samples for class one

N2 = length(classTwo); % "" "" "" class two

N = N1+N2;

%% Part 3

figure

histogram(classOne, 100)

hold on

histogram(classTwo, 100)

xlabel('No. Sample')

ylabel('Value')

title('Histogram for Class One and Class Two')

grid on

legend('class one', 'class two')

%% Part 4

% Probability of class one

prob_one = N1/N;

fprintf("The probability for class one is: %.2f%%\n", prob_one*100);

%% Part 5

prob_two = N2/N;

fprintf("The probability for class two is: %.2f%%\n", prob_two*100);

%% Part 6

test_size = 0.4; % percent of test

training_size = 1-test_size;

n_training = round(training_size*N1);

% Shuffle data

classOne = classOne(randperm(N1));

classTwo = classTwo(randperm(N2));

% Split into train and test

train1 = classOne(1:n_training);

train2 = classTwo(1:n_training);

test1 = classOne(n_training+1:end);

test2 = classTwo(n_training+1:end);

%% part a)

mu1 = mean(train1);

sigma1 = std(train1);

mu2 = mean(train2);

sigma2 = std(train2);

%% Part b)

% We add a new column to each test vector to specify its label (! or 2)

test1 = [test1', ones(length(test1),1)];

test2 = [test2', 2*ones(length(test2),1)];

% We combine both test datasets into one single matrix

test = [test1;test2];

% Calculate the probabilities that a sample belongs to one class and label

% them

labels = [];

for i = 1:length(test)

    x = test(i,1);

    label = test(i,2);

    % Probabilities

    prob = [computeGaussianDensity(mu1, sigma1, x)*prob_one, computeGaussianDensity(mu2, sigma2, x)*prob_two];

    % Pik highest probability and label the sample based on that

    [max_prob, y] = max(prob);

    % Add label

    labels = [labels;y];

end

% Now, compute accuracy

y = test(:,2);

y_pred = labels;

accuracy = sum(y==y_pred)/size(test,1);

fprintf("The accuracy of the Bayesian classifier is: %.2f%%\n", accuracy*100);

clc, clear all, close all

%% Part 2

load partTwoData.mat

N1 = size(classOne,1); % number of samples for class one

N2 = size(classTwo,1); % "" "" "" class two

N = N1+N2;

%% Part 3

% Probability of class one

prob_one = N1/N;

fprintf("The probability for class one is: %.2f%%\n", prob_one*100);

%% Part 4

prob_two = N2/N;

fprintf("The probability for class two is: %.2f%%\n", prob_two*100);

%% Part 5

test_size = 0.4; % percent of test

training_size = 1-test_size;

n_training = round(training_size*N1);

% Shuffle data

classOne = classOne(randperm(N1),:);

classTwo = classTwo(randperm(N2),:);

% Split into train and test

train1 = classOne(1:n_training,:);

train2 = classTwo(1:n_training,:);

test1 = classOne(n_training+1:end,:);

test2 = classTwo(n_training+1:end,:);

%% part a)

mu1 = mean(train1);

E1 = corr(train1);

mu2 = mean(train2);

E2 = corr(train2);

%% Part b)

% We add a new column to each test vector to specify its label (! or 2)

test1 = [test1, ones(length(test1),1)];

test2 = [test2, 2*ones(length(test2),1)];

% We combine both test datasets into one single matrix

test = [test1;test2];

% Calculate the probabilities that a sample belongs to one class and label

% them

labels = [];

for i = 1:length(test)

    x = test(i,1:2);

    label = test(i,3);

    % Probabilities

    prob = [computeGaussianDensityMultivariate(mu1, E1, x)*prob_one, computeGaussianDensityMultivariate(mu2, E2, x)*prob_two];

    % Pik highest probability and label the sample based on that

    [max_prob, y] = max(prob);

    % Add label

    labels = [labels;y];

end

% Now, compute accuracy

y = test(:,3);

y_pred = labels;

accuracy = sum(y==y_pred)/size(test,1);

fprintf("The accuracy of the Bayesian classifier is: %.2f%%\n", accuracy*100);