% The farthest point clustering scheme tends to grab points that are evenly
% spaced over the support of the dataset. When there are lots of "outliers"
% there may be very few points where most of the data are.

K = 30;  % Grab K points
D = 2;   % in D dimensions, out of
N = 1e3; % a dataset of size N

alpha = 0.8;
xx = [randn(D, ceil(N*alpha)),...
      bsxfun(@plus, [4;4], 3*exp(randn(D, N-ceil(N*alpha))))];
idx = ceil(N*rand(1,K));
[idx2, yy] = fpc(xx, K);

clf;
subplot(1,2,1); hold on;
plot(xx(1,:), xx(2,:), '+');
plot(xx(1,idx), xx(2,idx), 'rx', 'MarkerSize', 10, 'LineWidth', 2);
axis equal

subplot(1,2,2); hold on;
for kk = 1:K
    color = rand(1,3);
    plot(xx(1,yy==kk), xx(2,yy==kk), '+', 'Color', color);
    plot(xx(1,idx2(kk)), xx(2,idx2(kk)), 'kx', 'MarkerSize', 12, 'LineWidth', 4);
    plot(xx(1,idx2(kk)), xx(2,idx2(kk)), 'x', 'MarkerSize', 8, 'LineWidth', 2, 'Color', color);
end
axis equal