1 function sheet07
   2 % Generate data
   3 centers = [0, 0; 7, 3; -2, 4; 0, 10; -5, -5];
   4 
   5 [X, Y] = generate_data(centers, 50);
   6 
   7 % plot the result
   8 figure(1)
   9 gscatter(X(:,1), X(:,2), Y);
  10 
  11 % cluster the data set with different choices of K
  12 figure(2)
  13 [Y2, M2] = k_means_clustering(2, X);
  14 plot_clustering(X, Y2, M2)
  15 
  16 figure(3)
  17 [Y5, M5] = k_means_clustering(5, X);
  18 plot_clustering(X, Y5, M5)
  19 
  20 figure(4)
  21 [Y8, M8] = k_means_clustering(8, X);
  22 plot_clustering(X, Y8, M8)
  23 
  24 
  25 % 1. Generate data with normally distributed clusters
  26 % with centers given by the rows of C. Generate N
  27 % points from each cluster, and also return a vector K
  28 % which contains the cluster indices for each point.
  29 function [X, K] = generate_data(C, N)
  30 % ...
  31 
  32 % 2. Compute K-means clustering. Randomly select K points
  33 % as initial means. Iterate while the difference
  34 % between the old means and the new means matrix in the 
  35 % Frobenius norm (norm(..., 'fro')) is larger than 1e-10.
  36 %
  37 % Return the cluster indices and the matrix of means (means
  38 % are rows).
  39 function [Y, MEANS] = k_means_clustering(K, X)
  40 % ...
  41 
  42 % Plot the clustering and the centers.
  43 function plot_clustering(X, Y, MEANS)
  44 gscatter(X(:, 1), X(:, 2), Y);
  45 hold on;
  46 plot(MEANS(:, 1), MEANS(:, 2), '+', 'MarkerSize', 10, 'LineWidth', 3);
  47 hold off;
  48 
  49 % Compute all pairwise distances quickly.
  50 function D = pwdist(X, Y)
  51 D = size(X, 2);
  52 N = size(X, 1);
  53 M = size(Y, 1);
  54   
  55 XX = sum(X.*X, 2);
  56 YY = sum(Y.*Y, 2);
  57 D = repmat(XX, 1, M) + repmat(YY', N, 1) - 2*X*Y';