function multiclass_gp_1D_example()
% plot GP model outputs for 1D artificial data
% play around with param settings to become familiar with GP models
%
% Copyright (c) by Alexander Freytag, 2013-11-13.

  % get some artificial 1D data
  train_data = [1;2.5;4.5];
  train_labels = [1; 2; 4];
  test_data = (0.1:0.01:5)';

  % some default settings of hyperparameters
  loghyper = [-1 0];
  gpnoise = 0.01;

  
  % learn multi-class GP model
  K = feval('covSEiso', loghyper, train_data);
  model = learn_multiclass_gp(K, train_labels, gpnoise);

  % evaluate model on test data
  Ks = feval('covSEiso', loghyper, train_data, test_data);
  Kss = feval('covSEiso', loghyper, test_data, 'diag');  
  [mu, pred_labels, variance] = test_multiclass_gp(model, Ks, Kss');

  % visualize everything nicely
  f1 = figure(1);
  plot(train_data(1), 1, 'bx');
  title('Mean curve of each binary task');

  hold on
  plot(train_data(2), 1, 'gx');
  plot(train_data(3), 1, 'rx');

  plot(test_data, mu(:,1), 'b');
  plot(test_data, mu(:,2), 'g');
  plot(test_data, mu(:,3), 'r');
  hold off

  f2 = figure(2);
  plot(test_data, pred_labels, 'kx');
  title('Predicted multi-class labels');

  f3 = figure(3);
  title('Multi-class posterior mean and variance');
  colors = {'b', 'g', 'r'};
  hold on
  max_mean = max(mu,[],2);
  lower = max_mean-sqrt(variance);
  upper = max_mean+sqrt(variance);
  p = [test_data, lower; flipdim(test_data,1),flipdim(upper,1)];
  fill(p(:,1), p(:,2), 'y');
  for k=1:length(model.unique_labels)

    tmp_ID = pred_labels == model.unique_labels(k);
    plot(test_data(tmp_ID),mu(tmp_ID,k),colors{k}, 'LineWidth', 2);

  end
  hold off

end