updates

assignments/hwk02/Back_Project.m

@@ -4,17 +4,19 @@
 function [] = Back_Project(training_data, test_data, n_components)
   
   % stack data 
-   data = vertcat(training_data, test_data);
+  data = vertcat(training_data, test_data);
 
   % 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: 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
+
+    % TODO: plot first 5 images back projected using the first
+    % n_components(n) principal components
 
   end
 

assignments/hwk02/Classify.m

@@ -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

assignments/hwk02/Eigenfaces.m

@@ -2,12 +2,17 @@
 % 5 eigenvectors
 function [] = Eigenfaces(training_data, test_data)
 
-   % stack data 
-   data = vertcat(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

assignments/hwk02/Error_Rate.m

@@ -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

assignments/hwk02/KNN.m

@@ -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
 

assignments/hwk02/KNN_Error.m

@@ -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");

assignments/hwk02/Param_Est.m

@@ -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
   

assignments/hwk02/Problem1.m

@@ -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);