This commit is contained in:
Michael Zhang 2023-10-21 23:32:00 -05:00
parent ac35e842d8
commit 5e820c4227
8 changed files with 91 additions and 27 deletions

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@ -8,11 +8,13 @@ function [] = Back_Project(training_data, test_data, n_components)
% TODO: perform PCA
% for each number of principal components
for n = 1:length(n_components)
% TODO: perform the back projection algorithm using the first n_components(n) principal components
% TODO: plot first 5 images back projected using the first
% n_components(n) principal components

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@ -3,21 +3,29 @@
% these posterior probabilities are compared using the log odds.
function [predictions] = Classify(data, m1, m2, S1, S2, pc1, pc2)
d = 8;
% calculate P(x|C) * P(C) for both classes
% TODO: calculate P(x|C) * P(C) for both classes
pxC1 = mvnpdf(data, m1, S1);
pxC2 = mvnpdf(data, m2, S2);
pxC1 = exp(-1/2*(data-m1)./S1*(data-m1)') / (power(2*pi,d/2) * sqrt(det(S1)));
pxC2 = exp(-1/2*(data-m2)*(S2\(data-m2).'));
g1 = pxC1 * pc1;
g2 = pxC2 * pc2;
g1 = log(pxC1 * pc1);
g2 = log(pxC2 * pc2);
% TODO: calculate log odds, if > 0 then data(i) belongs to class c1, else, c2
for i = 1:length(data)
data(i)
end
log_odds = g1 - g2;
% for i = 1:length(data)
% if g1 > g2
% predictions(i) = 1;
% else
% predictions(i) = 2;
% end
% end
% TODO: get predictions from log odds calculation
[num_rows, ~] = size(data);
predictions = zeros(num_rows,1);
for i = 1:num_rows
predictions(i) = log_odds(i) > 0;
end
end % Function end

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@ -5,9 +5,14 @@ function [] = Eigenfaces(training_data, test_data)
% stack data
data = vertcat(training_data, test_data);
% TODO: perform PCA
% perform PCA
coeff = pca(data);
% TODO: show the first 5 eigenvectors (see homework for example)
imagesc(reshape(faces_data(i,1:end-1),32,30)')
% show the first 5 eigenvectors (see homework for example)
for i = 1:5
subplot(3,2,i)
imagesc(reshape(coeff(:,i),32,30)');
end
% pause;
end % Function end

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@ -2,6 +2,16 @@
% predicted labels that are incorrrect.
function [] = Error_Rate(predictions, labels)
% TODO: compute error rate and print it out
% compute error rate and print it out
c = 0;
[total_rows, ~] = size(predictions);
for i = 1:total_rows
if predictions(i) == labels(i)
c = c + 1;
end
end
fprintf('Rate: %.1f%% (%d / %d)\n', 100 * c / total_rows, c, total_rows);
end % Function end

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@ -6,18 +6,46 @@ function [test_err] = KNN(k, training_data, test_data, training_labels, test_lab
n = length(test_data(:,1)); % get number of rows in test data
preds = zeros(length(test_labels),1); % predict labels for each test point
% TODO: compute pairwise euclidean distance between the test data and the
% training data
% compute pairwise euclidean distance between the test data and the training data
pairwise_distance = pdist2(training_data, test_data);
unique_classes = unique(training_labels);
% for each data point (row) in the test data
for t = 1:n
% TODO: compute k-nearest neighbors for data point
distances = pairwise_distance(:,t);
[~, smallest_indexes] = sort(distances, 'ascend');
smallest_k_indexes = smallest_indexes(1:k);
distances_by_class = zeros(max(unique_classes), 2);
for i = 1:length(unique_classes)
class = unique_classes(i);
this_class_distances = distances(training_labels == class,:);
distances_by_class(i,1) = class;
distances_by_class(i,2) = mean(this_class_distances);
end
distances_by_class_table = array2table(distances_by_class);
% TODO: classify test point using majority rule. Include tie-breaking
% using whichever class is closer by distance. Fill in preds with the
% predicted label.
smallest_k_labels = training_labels(smallest_k_indexes);
labels_by_count = tabulate(smallest_k_labels);
labels_by_count_sorted = sortrows(labels_by_count, 2);
most_frequent_label = labels_by_count_sorted(1,:);
most_frequent_label_count = most_frequent_label(2);
labels_that_have_most_frequent_count = labels_by_count_sorted(labels_by_count_sorted(:,2) == most_frequent_label_count,1);
if length(labels_that_have_most_frequent_count) > 1
common_indexes = find(ismember(distances_by_class, labels_that_have_most_frequent_count));
common_distances = distances_by_class(common_indexes,:);
sorted_distances = sortrows(common_distances,2);
preds(t) = sorted_distances(1,1);
else
winning_label = mode(smallest_k_labels);
preds(t) = winning_label;
end
end

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@ -2,13 +2,19 @@
% errors for k-nearest neighbors using different values of k.
function [] = KNN_Error(neigenvectors, ks, training_data, test_data, training_labels, test_labels)
% TODO: perform PCA
% perform PCA
% TODO: project data using the number of eigenvectors defined by neigenvectors
% TODO: compute test error for kNN with differents k's. Fill in
% test_errors with the results for each k in ks.
test_errors = zeros(1,length(ks));
for i = 1:length(ks)
k = ks(i);
test_errors(i) = KNN(k, training_data, test_data, training_labels, test_labels);
end
% print error table
fprintf("-----------------------------\n");

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@ -4,7 +4,7 @@
% S2: learned covariance matrix for features of class 2)
function [m1, m2, S1, S2] = Param_Est(training_data, training_labels, part)
[num_rows, num_cols] = size(training_data);
[num_rows, ~] = size(training_data);
class1_data = training_data(training_labels==1,:);
class2_data = training_data(training_labels==2,:);
@ -14,11 +14,14 @@ function [m1, m2, S1, S2] = Param_Est(training_data, training_labels, part)
S1 = cov(class1_data);
S2 = cov(class2_data);
% Parameter estimation for 3 different models described in homework
% Model 3.
% Assume 𝑆1 and 𝑆2 are diagonal (the Naive Bayes model in equation (5.24)).
if(strcmp(part, '3'))
S1 = diag(diag(S1));
S2 = diag(diag(S2));
% Model 2.
% Assume 𝑆1 = 𝑆2. In other words, shared S between two classes (the discriminant function is as equation (5.21) and (5.22) in the textbook).
elseif(strcmp(part, '2'))
P_C1 = length(class1_data) / num_rows;
P_C2 = length(class2_data) / num_rows;
@ -27,6 +30,8 @@ function [m1, m2, S1, S2] = Param_Est(training_data, training_labels, part)
S1 = S;
S2 = S;
% Model 1.
% Assume independent 𝑆1 and 𝑆2 (the discriminant function is as equation (5.17) in the textbook).
elseif(strcmp(part, '1'))
end

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@ -21,7 +21,7 @@ function [] = Problem1(training_file, test_file)
fprintf('Model %s\n', part{i});
% Training for Multivariate Gaussian
[m1 m2 S1 S2] = Param_Est(training_data, training_labels, part(i));
[m1, m2, S1, S2] = Param_Est(training_data, training_labels, part(i));
[predictions] = Classify(training_data, m1, m2, S1, S2, pc1, pc2);
fprintf('training error\n');
Error_Rate(predictions, training_labels);