Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / kmeans.m

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+## Copyright (C) 2011 Soren Hauberg <soren@hauberg.org>
+## Copyright (C) 2012 Daniel Ward <dwa012@gmail.com>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{idx}, @var{centers}] =} kmeans (@var{data}, @var{k}, @var{param1}, @var{value1}, @dots{})
+## K-means clustering.
+##
+## @seealso{linkage}
+## @end deftypefn
+
+function [classes, centers, sumd, D] = kmeans (data, k, varargin)
+  [reg, prop] = parseparams (varargin);
+
+  ## defaults for options
+  emptyaction = "error";
+  start       = "sample";
+
+  #used for getting the number of samples
+  nRows = rows (data);
+
+  ## used to hold the distances from each sample to each class
+  D = zeros (nRows, k);
+  
+  #used for convergence of the centroids
+  err = 1;
+  
+  #initial sum of distances
+  sumd = Inf;
+  
+  ## Input checking, validate the matrix and k
+  if (!isnumeric (data) || !ismatrix (data) || !isreal (data))
+    error ("kmeans: first input argument must be a DxN real data matrix");
+  elseif (!isscalar (k))
+    error ("kmeans: second input argument must be a scalar");
+  endif
+  
+  if (length (varargin) > 0)
+    ## check for the 'emptyaction' property
+    found = find (strcmpi (prop, "emptyaction") == 1);
+    switch (lower (prop{found+1}))
+      case "singleton"
+        emptyaction = "singleton";
+      otherwise
+        error ("kmeans: unsupported empty cluster action parameter");
+    endswitch
+  endif
+  
+  ## check for the 'start' property
+  switch (lower (start))
+    case "sample"
+      idx = randperm (nRows) (1:k);
+      centers = data (idx, :);
+    otherwise
+      error ("kmeans: unsupported initial clustering parameter");
+  endswitch
+  
+  ## Run the algorithm
+  while err > .001
+    ## Compute distances
+    for i = 1:k
+      D (:, i) = sumsq (data - repmat (centers(i, :), nRows, 1), 2);
+    endfor
+    
+    ## Classify
+    [tmp, classes] = min (D, [], 2);
+    
+    ## Calcualte new centroids
+    for i = 1:k
+      ## Check for empty clusters
+      if (sum (classes == i) ==0 || length (mean (data(classes == i, :))) == 0)
+      
+        switch emptyaction
+          ## if 'singleton', then find the point that is the
+          ## farthest and add it to the empty cluster
+          case 'singleton'
+            classes(maxCostSampleIndex (data, centers(i,:))) = i;
+         ## if 'error' then throw the error
+          otherwise
+            error ("kmeans: empty cluster created");
+        endswitch
+     endif ## end check for empty clusters
+
+      ## update the centroids
+      centers(i, :) = mean (data(classes == i, :));
+    endfor
+
+    ## calculate the differnece in the sum of distances
+    err  = sumd - objCost (data, classes, centers);
+    ## update the current sum of distances
+    sumd = objCost (data, classes, centers);
+  endwhile
+endfunction
+
+## calculate the sum of distances
+function obj = objCost (data, classes, centers)
+  obj = 0;
+    for i=1:rows (data)
+      obj = obj + sumsq (data(i,:) - centers(classes(i),:));
+    endfor
+endfunction
+
+function index = maxCostSampleIndex (data, centers)
+  cost = 0;
+  for index = 1:rows (data)
+    if cost < sumsq (data(index,:) - centers)
+      cost = sumsq (data(index,:) - centers);
+    endif
+  endfor
+endfunction
+
+%!demo
+%! ## Generate a two-cluster problem
+%! C1 = randn (100, 2) + 1;
+%! C2 = randn (100, 2) - 1;
+%! data = [C1; C2];
+%!
+%! ## Perform clustering
+%! [idx, centers] = kmeans (data, 2);
+%!
+%! ## Plot the result
+%! figure
+%! plot (data (idx==1, 1), data (idx==1, 2), 'ro');
+%! hold on
+%! plot (data (idx==2, 1), data (idx==2, 2), 'bs');
+%! plot (centers (:, 1), centers (:, 2), 'kv', 'markersize', 10);
+%! hold off