1 function sheet06
   2 
   3 % Generate some data
   4 N = 100;
   5 M1 = [1; 2];
   6 M2 = [-5; 7];
   7 X = [randn(2, N) + repmat(M1, 1, N), ...
   8      randn(2, N) + repmat(M2, 1, N)];
   9 Y = [ones(1, N), -ones(1, N)];
  10 
  11 % Show data
  12 subplot(3,1,1);
  13 plotdata(X, Y);
  14 
  15 % Compute fda direction and another one and show
  16 % the projected data
  17 W = fda(X, Y)
  18 W1 = [1; 0];
  19 
  20 hold on;
  21 plotdata(project(X, W), Y);
  22 plotdata(project(X, W1), Y);
  23 hold off;
  24 
  25 % Histograms for the fda direction
  26 subplot(3,1,2);
  27 show_projected_data(W'*X, Y);
  28 
  29 % Histograms for the other direction
  30 subplot(3,1,3);
  31 show_projected_data(W1'*X, Y);
  32 
  33 % Plot two classes.
  34 function plotdata(X, Y)
  35 P = (Y == 1);
  36 N = (Y == -1);
  37 
  38 plot(X(1, P), X(2, P), 'r+', X(1, N), X(2, N), 'bo');
  39 
  40 axis equal
  41 grid on
  42 
  43 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  44 % Your solutions below
  45 %
  46 
  47 % 1. Return scatter matrix S = (X - M)(X - M)'
  48 function S = scatter(X, M)
  49 % ...
  50 
  51 % 2. Compute FDA direction.
  52 function W = fda(X, Y)
  53 % ...
  54 
  55 % 3. Project X to subspace spanned by W.
  56 function X = project(X, W)
  57 % ...
  58 
  59 % 4. Plot histograms for both classes of a 
  60 % one-dimensional data set X.
  61 function show_projected_data(X, Y)
  62 % ...