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## Copyright (C) 2011-2025 L. Markowsky <lmarkowsky@gmail.com>
##
## This file is part of the fuzzy-logic-toolkit.
##
## The fuzzy-logic-toolkit 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.
##
## The fuzzy-logic-toolkit 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 the fuzzy-logic-toolkit; see the file COPYING. If not,
## see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{Mu} =} update_cluster_membership (@var{V}, @var{X}, @var{m}, @var{k}, @var{n}, @var{sqr_dist})
##
## Compute Mu for each (cluster center, input point) pair.
##
## @seealso{fcm, gustafson_kessel, init_cluster_prototypes, update_cluster_prototypes, compute_cluster_obj_fcn, compute_cluster_convergence}
##
## @end deftypefn
## Authors: Tony Trew, L. Markowsky
## Keywords: fuzzy-logic-toolkit fuzzy partition clustering
## Directory: fuzzy-logic-toolkit/inst/private/
## Filename: update_cluster_membership.m
## Last-Modified: 5 Jun 2024
##----------------------------------------------------------------------
## Note: This function is an implementation of Equation 13.4 in
## Fuzzy Logic: Intelligence, Control and Information, by
## J. Yen and R. Langari, Prentice Hall, 1999, page 380
## (International Edition) and Step 3 of Algorithm 4.1 in
## Fuzzy and Neural Control, by Robert Babuska, November 2009,
## p. 63.
##----------------------------------------------------------------------
function Mu = update_cluster_membership (V, X, m, k, n, sqr_dist)
sqr_dist_zeros = (sqr_dist == 0);
num_zeros = sum (sum (sqr_dist_zeros));
if (num_zeros == 0)
exponent = 1.0 / (m - 1);
summation = (sqr_dist ./ sum(sqr_dist)).^exponent;
if (all (all (summation != 0)))
Mu = 1.0 ./ summation;
Mu ./= sum (Mu);
else
error ("division by 0 in update_cluster_membership'\n");
endif
else
Mu = sqr_dist_zeros / num_zeros;
endif
endfunction
%!test
%! ## Test the vectorized version of this function (above) by comparing its
%! ## output with the output of the previous, nested-for-loop version (below).
%! ##
%! ## The test is run 100 times (but is reported by the Octave interpreter as
%! ## "1 test"). In each of the 100 test runs, the vectorized and loop versions
%! ## of the function are called using randomly generated matrices X, V.
%! ##
%! ## The sizes of X and V, however, aren't random: X has 100 rows, 8 cols,
%! ## and V has 5 rows, 8 cols. That is, the entries in X and V are random
%! ## values in the range [0, 1], but the sizes of X and V are hard-coded.
%! ##
%! ## The test is passed if all entries of the two results differ by less than
%! ## a tolerance of 10e-9 in all 100 test runs.
%!
%! function Mu = update_cluster_membership_using_for_loops (V, X, m, k, n, sqr_dist)
%!
%! Mu = zeros (k, n);
%!
%! if (min (min (sqr_dist)) > 0)
%! exponent = 1.0 / (m - 1);
%! for i = 1 : k
%! for j = 1 : n
%! summation = 0.0;
%! for l = 1 : k
%! summation += (sqr_dist(i, j) / sqr_dist(l, j))^exponent;
%! endfor
%! if (summation != 0)
%! Mu(i, j) = 1.0 / summation;
%! else
%! error ("division by 0 in update_cluster_membership'\n");
%! endif
%! endfor
%! endfor
%!
%! else
%! num_zeros = 0;
%! for i = 1 : k
%! for j = 1 : n
%! if (sqr_dist(i, j) == 0)
%! num_zeros++;
%! Mu(i, j) = 1.0;
%! endif
%! endfor
%! endfor
%! Mu = Mu / num_zeros;
%! endif
%!
%! endfunction
%!
%! ## Fixed array sizes, exponent, and tolerance for the test.
%!
%! n = 100;
%! f = 8;
%! k = 5;
%! m = 2;
%! tolerance = 10e-9;
%!
%! ## Run the test 100 times, in a loop. In the last 5 test runs, make 3 of
%! ## the data points in X identical to cluster centers in V in order to test
%! ## the else case in the function.
%!
%! ## Each test run is successful if the vectorized and nested-for-loop
%! ## version of the function produce results within the hard-coded tolerance.
%!
%! for i = 1 : 100
%! X = rand (n, f);
%! V = rand (k, f);
%!
%! if (i > 95)
%! X(1:3) = V(1:3);
%! endif
%!
%! sqr_dist = square_distance_matrix (X, V);
%! vec_result = update_cluster_membership (V, X, m, k, n, sqr_dist);
%! loop_result = update_cluster_membership_using_for_loops (V, X, m, k, n, sqr_dist);
%! assert (abs (vec_result - loop_result) < tolerance)
%! endfor
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