prop var

assignments/hwk02/Eigenfaces.m

@@ -8,5 +8,6 @@ function [] = Eigenfaces(training_data, test_data)
    % TODO: perform PCA
 
    % TODO: show the first 5 eigenvectors (see homework for example)
+   imagesc(reshape(faces_data(i,1:end-1),32,30)')
 
 end % Function end

assignments/hwk02/HW2.typ

@@ -37,4 +37,8 @@
 
   b. #c[*(20 points)* Generate a plot of proportion of variance (see Figure 6.4 (b) in the main textbook) on the training data, and select the minimum number ($K$) of eigenvectors that explain at least 90% of the variance. Show both the plot and $K$ in the report. This can be accomplished by completing the _TODO_ headers in the `ProportionOfVariance.m` script. Project the training and test data to the $K$ principal components and run KNN on the projected data for $k = {1, 3, 5, 7}$. Print out the error rate on the test set. Implement your own version of and K-Nearest Neighbor classifier (KNN) for this problem. Classify each test point using a majority rule i.e., by choosing the most common class among the $k$ training points it is closest to. In the case where two classes are equally as frequent, perform a tie-breaker by choosing whichever class has on average a smaller distance to the test point. This can be accomplished by completing the _TODO_ comment headers in the `KNN.m` and `KNN_Error.m` scripts.]
 
+    #figure(image("images/prop_var.png"))
+
+    I used $K = 41$.
+
   c. #c[*(20 points)* Use the first $K = {10, 50, 100}$ principle components to approximate the first five images of the training set (first row of the data matrix) by projecting the centered data using the first $K$ principal components then "back project" (weighted sum of the components) to the original space and add the mean. For each $K$, plot the reconstructed image. This can be accomplished by completing the _TODO_ comment headers in the `Back_Project.m` script. Explain your observations in the report.]

assignments/hwk02/ProportionOfVariance.m

@@ -4,14 +4,24 @@
 % variance explained.
 function [neigenvectors] = ProportionOfVariance(training_data)
 
-   % stack data
-   data = vertcat(training_data);
+  % stack data
+  data = vertcat(training_data);
 
-  % TODO: perform PCA
+  % perform PCA
+  [~,~,latent] = pca(data);
 
-  % TODO: compute proportion of variance explained
+  % compute proportion of variance explained
+  all_eigs = sum(latent);
+  prop_var = cumsum(latent) / all_eigs;
 
-  % TODO: show figure of proportion of variance explained where the x-axis is the number of eigenvectors and the y-axis is the percentage of
+  % show figure of proportion of variance explained where the x-axis is the number of eigenvectors and the y-axis is the percentage of
   % variance explained
+  subplot(2,1,1);
+  plot(find(latent), latent);
+
+  subplot(2,1,2);
+  plot(find(prop_var), prop_var);
+
+  neigenvectors = find(prop_var > 0.9, 1);
 
 end % Function end