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[Octave-cvsupdate] SF.net SVN: octave:[10739] trunk/octave-forge/main/fuzzy-logic-toolkit/inst
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From: <lm...@us...> - 2012-07-09 13:17:26
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Revision: 10739
http://octave.svn.sourceforge.net/octave/?rev=10739&view=rev
Author: lmarkov
Date: 2012-07-09 13:17:11 +0000 (Mon, 09 Jul 2012)
Log Message:
-----------
A inst/gustafson_kessel_demo_1.m
A inst/gustafson_kessel_demo_2.m
A inst/partition_coeff.m
A inst/fcm.m
A inst/xie_beni_index.m
A inst/gustafson_kessel.m
A inst/private/square_distance_matrix.m
A inst/private/fcm_init_prototype.m
A inst/private/fcm_update_cluster_centers.m
A inst/private/fcm_compute_convergence_criterion.m
A inst/private/fcm_update_membership_fcn.m
A inst/private/fcm_compute_objective_fcn.m
A inst/fcm_demo_1.m
A inst/partition_entropy.m
A inst/fcm_demo_2.m
Added Paths:
-----------
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_1.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_2.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_1.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_2.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_coeff.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_entropy.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_convergence_criterion.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_objective_fcn.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_init_prototype.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_cluster_centers.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_membership_fcn.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/square_distance_matrix.m
trunk/octave-forge/main/fuzzy-logic-toolkit/inst/xie_beni_index.m
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,204 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{cluster_centers} =} fcm (@var{input_data}, @var{num_clusters})
+## @deftypefnx {Function File} {@var{cluster_centers} =} fcm (@var{input_data}, @var{num_clusters}, @var{options})
+## @deftypefnx {Function File} {@var{cluster_centers} =} fcm (@var{input_data}, @var{num_clusters}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}])
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} fcm (@var{input_data}, @var{num_clusters})
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} fcm (@var{input_data}, @var{num_clusters}, @var{options})
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} fcm (@var{input_data}, @var{num_clusters}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}])
+##
+## Return the soft partition of a set of unlabeled data points.
+## Also, if @var{display_intermediate_results} is true, display intermediate
+## results after each iteration.
+##
+## The required arguments to fcm are:
+## @itemize @w
+## @item
+## @var{input_data} - a matrix of input data points; each row corresponds to one point
+## @item
+## @var{num_clusters} - the number of clusters to form
+## @end itemize
+##
+## The optional arguments to fcm are:
+## @itemize @w
+## @item
+## @var{m} - the parameter (exponent) in the objective function; default = 2.0
+## @item
+## @var{max_iterations} - the maximum number of iterations before stopping; default = 100
+## @item
+## @var{epsilon} - the stopping criteria; default = 1e-5
+## @item
+## @var{display_intermediate_results} - if 1, display results after each iteration, and if 0, do not; default = 1
+## @end itemize
+##
+## The default values are used if any of the optional arguments are missing or
+## evaluate to NaN.
+##
+## The return values are:
+## @itemize @w
+## @item
+## @var{cluster_centers} - a matrix of the cluster centers; each row corresponds to one point
+## @item
+## @var{soft_partition} - a constrained soft partition matrix
+## @item
+## @var{obj_fcn_history} - the values of the objective function after each iteration
+## @end itemize
+##
+## Three important matrices used in the calculation are X (the input points
+## to be clustered), V (the cluster centers), and Mu (the membership of each
+## data point in each cluster). Each row of X and V denotes a single point,
+## and Mu(i, j) denotes the membership degree of input point X(j, :) in the
+## cluster having center V(i, :).
+##
+## X is identical to the required argument @var{input_data}; V is identical
+## to the output @var{cluster_centers}; and Mu is identical to the output
+## @var{soft_partition}.
+##
+## If n denotes the number of input points and k denotes the number of
+## clusters to be formed, then X, V, and Mu have the dimensions:
+##
+## @example
+## @group
+## 1 2 ... #features
+## 1 [ ]
+## X = input_data = 2 [ ]
+## ... [ ]
+## n [ ]
+## @end group
+## @end example
+##
+## @example
+## @group
+## 1 2 ... #features
+## 1 [ ]
+## V = cluster_centers = 2 [ ]
+## ... [ ]
+## k [ ]
+## @end group
+## @end example
+##
+## @example
+## @group
+## 1 2 ... n
+## 1 [ ]
+## Mu = soft_partition = 2 [ ]
+## ... [ ]
+## k [ ]
+## @end group
+## @end example
+##
+## @seealso{fcm_demo_1, fcm_demo_2, gustafson_kessel, gustafson_kessel_demo_1, gustafson_kessel_demo_2, partition_coeff, partition_entropy, xie_beni_index}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: fcm.m
+## Last-Modified: 8 July 2012
+
+function [cluster_centers, soft_partition, obj_fcn_history] = ...
+ fcm (input_data, num_clusters, options = [2.0, 100, 1e-5, 1])
+
+ ## If fcm was called with an incorrect number of arguments, or the
+ ## arguments do not have the correct type, print an error message and halt.
+
+ if ((nargin != 2) && (nargin != 3))
+ puts ("Type 'help fcm' for more information.\n");
+ error ("fcm requires 2 or 3 arguments\n");
+ elseif (!is_real_matrix (input_data))
+ puts ("Type 'help fcm' for more information.\n");
+ error ("fcm's first argument must be matrix of real numbers\n");
+ elseif (!(is_int (num_clusters) && (num_clusters > 1)))
+ puts ("Type 'help fcm' for more information.\n");
+ error ("fcm's second argument must be an integer greater than 1\n");
+ elseif (!(isreal (options) && isvector (options)))
+ puts ("Type 'help fcm' for more information.\n");
+ error ("fcm's third (optional) argument must be a vector of real numbers\n");
+ endif
+
+ ## Assign options to the more readable variable names: m, max_iterations,
+ ## epsilon, and display_intermediate_results. If options are missing or
+ ## NaN (not a number), use the default values.
+
+ default_options = [2.0, 100, 1e-5, 1];
+
+ for i = 1 : 4
+ if ((length (options) < i) || isna (options(i)) || isnan (options(i)))
+ options(i) = default_options(i);
+ endif
+ endfor
+
+ m = options(1);
+ max_iterations = options(2);
+ epsilon = options(3);
+ display_intermediate_results = options(4);
+
+ ## Call a private function to compute the output.
+
+ [cluster_centers, soft_partition, obj_fcn_history] = ...
+ fcm_private (input_data, num_clusters, m, max_iterations, epsilon,
+ display_intermediate_results);
+endfunction
+
+##------------------------------------------------------------------------------
+## Note: This function (fcm_private) is an implementation of Figure 13.4 in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 380 (International Edition)
+## and Algorithm 4.1 in Fuzzy and Neural Control, by Robert Babuska,
+## November 2009, p. 63.
+##------------------------------------------------------------------------------
+
+function [V, Mu, obj_fcn_history] = ...
+ fcm_private (X, k, m, max_iterations, epsilon, display_intermediate_results)
+
+ ## Initialize the prototype and the calculation.
+ V = fcm_init_prototype (X, k);
+ obj_fcn_history = zeros (max_iterations);
+ convergence_criterion = epsilon + 1;
+ iteration = 0;
+
+ ## Calculate a few numbers here to reduce redundant computation.
+ k = rows (V);
+ n = rows (X);
+ sqr_dist = square_distance_matrix (X, V);
+
+ ## Loop until the objective function is within tolerance or the maximum
+ ## number of iterations has been reached.
+ while (convergence_criterion > epsilon && ++iteration <= max_iterations)
+ V_previous = V;
+ Mu = fcm_update_membership_fcn (V, X, m, k, n, sqr_dist);
+ Mu_m = Mu .^ m;
+ V = fcm_update_cluster_centers (Mu_m, X, k);
+ sqr_dist = square_distance_matrix (X, V);
+ obj_fcn_history(iteration) = fcm_compute_objective_fcn (Mu_m, sqr_dist);
+ if (display_intermediate_results)
+ printf ("Iteration count = %d, Objective fcn = %8.6f\n", ...
+ iteration, obj_fcn_history(iteration));
+ endif
+ convergence_criterion = fcm_compute_convergence_criterion (V, V_previous);
+ endwhile
+
+ ## Remove extraneous entries from the tail of the objective function history.
+ if (convergence_criterion <= epsilon)
+ obj_fcn_history = obj_fcn_history(1 : iteration);
+ endif
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_1.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_1.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_1.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,90 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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 {Script File} {} fcm_demo_1
+## Use the Fuzzy C-Means algorithm to classify unlabeled data points and
+## evaluate the quality of the resulting clusters.
+##
+## This demo:
+## @itemize @minus
+## @item
+## classifies a small set of unlabeled data points using the Fuzzy C-Means
+## algorithm into two fuzzy clusters
+## @item
+## calculates and prints (on standard output) three validity measures:
+## the partition coefficient, the partition entropy, and the Xie-Beni
+## validity index
+## @item
+## plots the input points together with the cluster centers
+## @end itemize
+##
+## For a description of the data structures used in the script, see the
+## documentation for fcm.
+##
+## @seealso{fcm, fcm_demo_2, partition_coeff, partition_entropy, xie_beni_index, gustafson_kessel, gustafson_kessel_demo_1, gustafson_kessel_demo_2}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm demo
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: fcm_demo_1.m
+## Last-Modified: 8 July 2012
+
+##------------------------------------------------------------------------------
+## Note: The input_data is taken from Chapter 13, Example 17 in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 381 (International Edition).
+##------------------------------------------------------------------------------
+
+## Use fcm to classify the data in matrix x.
+input_data = [2 12; 4 9; 7 13; 11 5; 12 7; 14 4]
+number_of_clusters = 2
+[cluster_centers, soft_partition, obj_fcn_history] = ...
+ fcm (input_data, number_of_clusters)
+
+## Calculate and print the three validity measures.
+printf ("Partition Coefficient: %f\n", partition_coeff (soft_partition));
+printf ("Partition Entropy (with a = 2): %f\n", partition_entropy (soft_partition, 2));
+printf ("Xie-Beni Index: %f\n\n", xie_beni_index (input_data, cluster_centers, soft_partition));
+
+## Plot the data points as small blue x's.
+figure ('NumberTitle', 'off', 'Name', 'FCM Demo 1');
+for i = 1 : rows (input_data)
+ plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, 'marker', 'x', ...
+ 'color', 'b');
+ hold on;
+endfor
+
+## Plot the cluster centers as larger red *'s.
+for i = 1 : number_of_clusters
+ plot (cluster_centers(i, 1), cluster_centers(i, 2), 'LineWidth', 4, ...
+ 'marker', '*', 'color', 'r');
+ hold on;
+endfor
+
+## Make the figure look a little better:
+## -- scale and label the axes
+## -- show gridlines
+xlim ([0 15]);
+ylim ([0 15]);
+xlabel ('Feature 1');
+ylabel ('Feature 2');
+grid
+hold
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_2.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_2.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/fcm_demo_2.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,121 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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 {Script File} {} fcm_demo_2
+## Use the Fuzzy C-Means algorithm to classify unlabeled data points and
+## evaluate the quality of the resulting clusters.
+##
+## The demo:
+## @itemize @minus
+## @item
+## classifies three-dimensional unlabeled data points using the Fuzzy
+## C-Means algorithm into three fuzzy clusters
+## @item
+## calculates and prints (on standard output) three validity measures:
+## the partition coefficient, the partition entropy, and the Xie-Beni
+## validity index
+## @item
+## plots the input points together with the cluster centers
+## @end itemize
+##
+## For a description of the data structures used in the script, see the
+## documentation for fcm.
+##
+## @seealso{fcm, fcm_demo_1, partition_coeff, partition_entropy, xie_beni_index, gustafson_kessel, gustafson_kessel_demo_1, gustafson_kessel_demo_2}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm demo
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: fcm_demo_2.m
+## Last-Modified: 8 July 2012
+
+##------------------------------------------------------------------------------
+## Note: The input_data was selected to form three areas of different shapes.
+##------------------------------------------------------------------------------
+
+## Use fcm to classify the data in matrix x.
+input_data = [1 11 5; 1 12 6; 1 13 5; 2 11 7; 2 12 6; 2 13 7; 3 11 6; 3 12 5;
+ 3 13 7; 1 1 10; 1 3 9; 2 2 11; 3 1 9; 3 3 10; 3 5 11; 4 4 9;
+ 4 6 8; 5 5 8; 5 7 9; 6 6 10; 9 10 12; 9 12 13; 9 13 14; 10 9 13;
+ 10 13 12; 11 10 14; 11 12 13; 12 6 12; 12 7 15; 12 9 15; 14 6 14;
+ 14 8 13]
+number_of_clusters = 3
+[cluster_centers, soft_partition, obj_fcn_history] = ...
+ fcm (input_data, number_of_clusters, [NaN NaN NaN 0])
+
+## Calculate and print the three validity measures.
+printf ("Partition Coefficient: %f\n", partition_coeff (soft_partition));
+printf ("Partition Entropy (with a = 2): %f\n", partition_entropy (soft_partition, 2));
+printf ("Xie-Beni Index: %f\n\n", xie_beni_index (input_data, cluster_centers, soft_partition));
+
+## Plot the data points in two dimensions (using features 1 and 2)
+## as small blue x's.
+figure ('NumberTitle', 'off', 'Name', 'FCM Demo 2');
+for i = 1 : rows (input_data)
+ plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, 'marker', 'x', ...
+ 'color', 'b');
+ hold on;
+endfor
+
+## Plot the cluster centers in two dimensions (using features 1 and 2)
+## as larger red *'s.
+for i = 1 : number_of_clusters
+ plot (cluster_centers(i, 1), cluster_centers(i, 2), 'LineWidth', 4, ...
+ 'marker', '*', 'color', 'r');
+ hold on;
+endfor
+
+## Make the figure look a little better:
+## -- scale and label the axes
+## -- show gridlines
+xlim ([0 15]);
+ylim ([0 15]);
+xlabel ('Feature 1');
+ylabel ('Feature 2');
+grid
+hold
+
+## Plot the data points in two dimensions (using features 1 and 3)
+## as small blue x's.
+figure ('NumberTitle', 'off', 'Name', 'FCM Demo 2');
+for i = 1 : rows (input_data)
+ plot (input_data(i, 1), input_data(i, 3), 'LineWidth', 2, 'marker', 'x', ...
+ 'color', 'b');
+ hold on;
+endfor
+
+## Plot the cluster centers in two dimensions (using features 1 and 3)
+## as larger red *'s.
+for i = 1 : number_of_clusters
+ plot (cluster_centers(i, 1), cluster_centers(i, 3), 'LineWidth', 4, ...
+ 'marker', '*', 'color', 'r');
+ hold on;
+endfor
+
+## Make the figure look a little better:
+## -- scale and label the axes
+## -- show gridlines
+xlim ([0 15]);
+ylim ([0 15]);
+xlabel ('Feature 1');
+ylabel ('Feature 3');
+grid
+hold
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,272 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters})
+## @deftypefnx {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume})
+## @deftypefnx {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, @var{options})
+## @deftypefnx {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}])
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters})
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume})
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, @var{options})
+## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}])
+##
+## Return the soft partition of a set of unlabeled data points.
+## Also, if @var{display_intermediate_results} is true, display intermediate
+## results after each iteration.
+##
+## The required arguments to gustafson_kessel are:
+## @itemize @w
+## @item
+## @var{input_data} - a matrix of input data points; each row corresponds to one point
+## @item
+## @var{num_clusters} - the number of clusters to form
+## @end itemize
+##
+## The third (optional) argument to gustafson_kessel is a vector of cluster volumes.
+## If omitted, a vector of 1's will be used as the default.
+##
+## The fourth (optional) argument to gustafson_kessel is a vector consisting of:
+## @itemize @w
+## @item
+## @var{m} - the parameter (exponent) in the objective function; default = 2.0
+## @item
+## @var{max_iterations} - the maximum number of iterations before stopping; default = 100
+## @item
+## @var{epsilon} - the stopping criteria; default = 1e-5
+## @item
+## @var{display_intermediate_results} - if 1, display results after each iteration, and if 0, do not; default = 1
+## @end itemize
+##
+## The default values are used if any of the four elements of the vector are missing or
+## evaluate to NaN.
+##
+## The return values are:
+## @itemize @w
+## @item
+## @var{cluster_centers} - a matrix of the cluster centers; each row corresponds to one point
+## @item
+## @var{soft_partition} - a constrained soft partition matrix
+## @item
+## @var{obj_fcn_history} - the values of the objective function after each iteration
+## @end itemize
+##
+## Three important matrices used in the calculation are X (the input points
+## to be clustered), V (the cluster centers), and Mu (the membership of each
+## data point in each cluster). Each row of X and V denotes a single point,
+## and Mu(i, j) denotes the membership degree of input point X(j, :) in the
+## cluster having center V(i, :).
+##
+## X is identical to the required argument @var{input_data}; V is identical
+## to the output @var{cluster_centers}; and Mu is identical to the output
+## @var{soft_partition}.
+##
+## If n denotes the number of input points and k denotes the number of
+## clusters to be formed, then X, V, and Mu have the dimensions:
+##
+## @example
+## @group
+## 1 2 ... #features
+## 1 [ ]
+## X = input_data = 2 [ ]
+## ... [ ]
+## n [ ]
+## @end group
+## @end example
+##
+## @example
+## @group
+## 1 2 ... #features
+## 1 [ ]
+## V = cluster_centers = 2 [ ]
+## ... [ ]
+## k [ ]
+## @end group
+## @end example
+##
+## @example
+## @group
+## 1 2 ... n
+## 1 [ ]
+## Mu = soft_partition = 2 [ ]
+## ... [ ]
+## k [ ]
+## @end group
+## @end example
+##
+## @seealso{fcm, fcm_demo_1, fcm_demo_2, gustafson_kessel_demo_1, gustafson_kessel_demo_2, partition_coeff, partition_entropy, xie_beni_index}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering gustafson_kessel
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: gustafson_kessel.m
+## Last-Modified: 8 July 2012
+
+function [cluster_centers, soft_partition, obj_fcn_history] = ...
+ gustafson_kessel (input_data, num_clusters, cluster_volume = [], options = [2.0, 100, 1e-5, 1])
+
+ ## If gustafson_kessel was called with an incorrect number of arguments, or the
+ ## arguments do not have the correct type, print an error message and halt.
+
+ if ((nargin < 2) || (nargin > 4))
+ puts ("Type 'help gustafson_kessel' for more information.\n");
+ error ("gustafson_kessel requires 2, 3, or 4 arguments\n");
+ elseif (!is_real_matrix (input_data))
+ puts ("Type 'help gustafson_kessel' for more information.\n");
+ error ("gustafson_kessel's first argument must be matrix of real numbers\n");
+ elseif (!(is_int (num_clusters) && (num_clusters > 1)))
+ puts ("Type 'help gustafson_kessel' for more information.\n");
+ error ("gustafson_kessel's second argument must be an integer greater than 1\n");
+ elseif (!(isequal (cluster_volume, []) || ...
+ (isreal (cluster_volume) && isvector (cluster_volume))))
+ puts ("Type 'help gustafson_kessel' for more information.\n");
+ error ("gustafson_kessel's third (optional) argument must be a vector of real numbers\n");
+ elseif (!(isreal (options) && isvector (options)))
+ puts ("Type 'help gustafson_kessel' for more information.\n");
+ error ("gustafson_kessel's fourth (optional) argument must be a vector of real numbers\n");
+ endif
+
+ ## If the cluster volume matrix was not entered, create a default value
+ ## (a vector of 1's).
+
+ if (isequal (cluster_volume, []))
+ cluster_volume = ones (1, num_clusters);
+ endif
+
+ ## Assign options to the more readable variable names: m, max_iterations,
+ ## epsilon, and display_intermediate_results. If options are missing or
+ ## NaN (not a number), use the default values.
+
+ default_options = [2.0, 100, 1e-5, 1];
+
+ for i = 1 : 4
+ if ((length (options) < i) || isna (options(i)) || isnan (options(i)))
+ options(i) = default_options(i);
+ endif
+ endfor
+
+ m = options(1);
+ max_iterations = options(2);
+ epsilon = options(3);
+ display_intermediate_results = options(4);
+
+ ## Call a private function to compute the output.
+
+ [cluster_centers, soft_partition, obj_fcn_history] = ...
+ gustafson_kessel_private (input_data, num_clusters, cluster_volume, m, ...
+ max_iterations, epsilon, display_intermediate_results);
+endfunction
+
+##------------------------------------------------------------------------------
+## Function: gustafson_kessel_private
+## Purpose: Classify unlabeled data points using the Gustafson-Kessel
+## algorithm.
+## Note: This function (gustafson_kessel_private) is an implementation of
+## Algorithm 4.2 in Fuzzy and Neural Control, by Robert Babuska,
+## November 2009, p. 69.
+##------------------------------------------------------------------------------
+
+function [V, Mu, obj_fcn_history] = ...
+ gustafson_kessel_private (X, k, cluster_volume, m, max_iterations, epsilon, display_intermediate_results)
+
+ ## Initialize the prototype and the calculation.
+ V = fcm_init_prototype (X, k);
+ obj_fcn_history = zeros (max_iterations);
+ convergence_criterion = epsilon + 1;
+ iteration = 0;
+
+ ## Calculate a few numbers here to reduce redundant computation.
+ k = rows (V);
+ n = rows (X);
+ sqr_dist = square_distance_matrix (X, V);
+
+ ## Loop until the objective function is within tolerance or the maximum
+ ## number of iterations has been reached.
+ while (convergence_criterion > epsilon && ++iteration <= max_iterations)
+ V_previous = V;
+ Mu = fcm_update_membership_fcn (V, X, m, k, n, sqr_dist);
+ Mu_m = Mu .^ m;
+ V = fcm_update_cluster_centers (Mu_m, X, k);
+ sqr_dist = gk_square_distance_matrix (X, V, Mu_m, cluster_volume);
+ obj_fcn_history(iteration) = fcm_compute_objective_fcn (Mu_m, sqr_dist);
+ if (display_intermediate_results)
+ printf ("Iteration count = %d, Objective fcn = %8.6f\n", ...
+ iteration, obj_fcn_history(iteration));
+ endif
+ convergence_criterion = fcm_compute_convergence_criterion (V, V_previous);
+ endwhile
+
+ ## Remove extraneous entries from the tail of the objective function history.
+ if (convergence_criterion <= epsilon)
+ obj_fcn_history = obj_fcn_history(1 : iteration);
+ endif
+
+endfunction
+
+##------------------------------------------------------------------------------
+## Function: gk_square_distance_matrix
+##------------------------------------------------------------------------------
+
+function sqr_dist = gk_square_distance_matrix (X, V, Mu_m, cluster_volume)
+
+ k = rows (V);
+ n = rows (X);
+ num_features = columns (X);
+ sqr_dist = zeros (k, n);
+
+ for i = 1 : k
+ Vi = V(i, :);
+ covariance_matrix = compute_covariance_matrix (X, V, Mu_m, i);
+
+ for j = 1 : n
+ Vi_to_Xj = X(j, :) - Vi;
+ A = cluster_volume(i) * ...
+ det (covariance_matrix) ^ (1.0 / num_features) * ...
+ inv (covariance_matrix);
+ sqr_dist(i, j) = sum (Vi_to_Xj .* (A * Vi_to_Xj')');
+
+ endfor
+
+ endfor
+
+endfunction
+
+##------------------------------------------------------------------------------
+## Function: compute_covariance_matrix
+##------------------------------------------------------------------------------
+
+function covariance_matrix = compute_covariance_matrix (X, V, Mu_m, i)
+
+ num_features = columns (V);
+ n = rows (X);
+ num = zeros (num_features);
+ denom = 0.0;
+ Vi = V(i, :);
+
+ for j = 1 : n
+ Vi_to_Xj = X(j, :) - Vi;
+ num += Mu_m(i, j) * Vi_to_Xj' * Vi_to_Xj;
+ denom += Mu_m(i, j);
+ endfor
+
+ covariance_matrix = num / denom;
+
+endfunction
+
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_1.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_1.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_1.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,90 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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 {Script File} {} gustafson_kessel_demo_1
+## Use the Gustafson-Kessel algorithm to classify unlabeled data points and
+## evaluate the quality of the resulting clusters.
+##
+## The demo:
+## @itemize @minus
+## @item
+## classifies a small set of unlabeled data points using the Gustafson-Kessel
+## algorithm into two fuzzy clusters
+## @item
+## calculates and prints (on standard output) three validity measures:
+## the partition coefficient, the partition entropy, and the Xie-Beni
+## validity index
+## @item
+## plots the input points together with the cluster centers
+## @end itemize
+##
+## For a description of the data structures used in the script, see the
+## documentation for gustafson_kessel.
+##
+## @seealso{gustafson_kessel, gustafson_kessel_demo_2, partition_coeff, partition_entropy, xie_beni_index, fcm, fcm_demo_1, fcm_demo_2}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering gustafson_kessel demo
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: gustafson_kessel_demo_1.m
+## Last-Modified: 8 July 2012
+
+##------------------------------------------------------------------------------
+## Note: The input_data is taken from Chapter 13, Example 17 in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 381 (International Edition).
+##------------------------------------------------------------------------------
+
+## Use gustafson_kessel to classify the data in matrix x.
+input_data = [2 12; 4 9; 7 13; 11 5; 12 7; 14 4]
+number_of_clusters = 2
+[cluster_centers, soft_partition, obj_fcn_history] = ...
+ gustafson_kessel (input_data, number_of_clusters)
+
+## Calculate and print the three validity measures.
+printf ("Partition Coefficient: %f\n", partition_coeff (soft_partition));
+printf ("Partition Entropy (with a = 2): %f\n", partition_entropy (soft_partition, 2));
+printf ("Xie-Beni Index: %f\n\n", xie_beni_index (input_data, cluster_centers, soft_partition));
+
+## Plot the data points as small blue x's.
+figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 1');
+for i = 1 : rows (input_data)
+ plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, 'marker', 'x', ...
+ 'color', 'b');
+ hold on;
+endfor
+
+## Plot the cluster centers as larger red *'s.
+for i = 1 : number_of_clusters
+ plot (cluster_centers(i, 1), cluster_centers(i, 2), 'LineWidth', 4, ...
+ 'marker', '*', 'color', 'r');
+ hold on;
+endfor
+
+## Make the figure look a little better:
+## -- scale and label the axes
+## -- show gridlines
+xlim ([0 15]);
+ylim ([0 15]);
+xlabel ('Feature 1');
+ylabel ('Feature 2');
+grid
+hold
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_2.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_2.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/gustafson_kessel_demo_2.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,120 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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 {Script File} {} gustafson_kessel_demo_2
+## Use the Gustafson-Kessel algorithm to classify unlabeled data points and
+## evaluate the quality of the resulting clusters.
+##
+## The demo:
+## @itemize @minus
+## @item
+## classifies three-dimensional unlabeled data points using the
+## Gustafson-Kessel algorithm into three fuzzy clusters
+## @item
+## calculates and prints (on standard output) three validity measures:
+## the partition coefficient, the partition entropy, and the Xie-Beni
+## validity index
+## @item
+## plots the input points together with the cluster centers
+## @end itemize
+##
+## For a description of the data structures used in the script, see the
+## documentation for gustafson_kessel.
+##
+## @seealso{gustafson_kessel, gustafson_kessel_demo_1, partition_coeff, partition_entropy, xie_beni_index, fcm, fcm_demo_1, fcm_demo_2}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm demo
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: gustafson_kessel_demo_2.m
+## Last-Modified: 8 July 2012
+
+##------------------------------------------------------------------------------
+## Note: The input_data was selected to form three areas of different shapes.
+##------------------------------------------------------------------------------
+
+## Use gustafson_kessel to classify the data in matrix x.
+input_data = [1 11 5; 1 12 6; 1 13 5; 2 11 7; 2 12 6; 2 13 7; 3 11 6; 3 12 5;
+ 3 13 7; 1 1 10; 1 3 9; 2 2 11; 3 1 9; 3 3 10; 3 5 11; 4 4 9;
+ 4 6 8; 5 5 8; 5 7 9; 6 6 10; 9 10 12; 9 12 13; 9 13 14; 10 9 13;
+ 10 13 12; 11 10 14; 11 12 13; 12 6 12; 12 7 15; 12 9 15; 14 6 14;
+ 14 8 13]
+number_of_clusters = 3
+[cluster_centers, soft_partition, obj_fcn_history] = ...
+ gustafson_kessel (input_data, number_of_clusters, [1 1 1], [NaN NaN NaN 0])
+
+## Calculate and print the three validity measures.
+printf ("Partition Coefficient: %f\n", partition_coeff (soft_partition));
+printf ("Partition Entropy (with a = 2): %f\n", partition_entropy (soft_partition, 2));
+printf ("Xie-Beni Index: %f\n\n", xie_beni_index (input_data, cluster_centers, soft_partition));
+
+## Plot the data points in two dimensions (using features 1 and 2)
+## as small blue x's.
+figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 2');
+for i = 1 : rows (input_data)
+ plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, 'marker', 'x', ...
+ 'color', 'b');
+ hold on;
+endfor
+
+## Plot the cluster centers in two dimensions (using features 1 and 2)
+## as larger red *'s.
+for i = 1 : number_of_clusters
+ plot (cluster_centers(i, 1), cluster_centers(i, 2), 'LineWidth', 4, ...
+ 'marker', '*', 'color', 'r');
+ hold on;
+endfor
+
+## Make the figure look a little better:
+## -- scale and label the axes
+## -- show gridlines
+xlim ([0 15]);
+ylim ([0 15]);
+xlabel ('Feature 1');
+ylabel ('Feature 2');
+grid
+
+## Plot the data points in two dimensions (using features 1 and 3)
+## as small blue x's.
+figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 2');
+for i = 1 : rows (input_data)
+ plot (input_data(i, 1), input_data(i, 3), 'LineWidth', 2, 'marker', 'x', ...
+ 'color', 'b');
+ hold on;
+endfor
+
+## Plot the cluster centers in two dimensions (using features 1 and 3)
+## as larger red *'s.
+for i = 1 : number_of_clusters
+ plot (cluster_centers(i, 1), cluster_centers(i, 3), 'LineWidth', 4, ...
+ 'marker', '*', 'color', 'r');
+ hold on;
+endfor
+
+## Make the figure look a little better:
+## -- scale and label the axes
+## -- show gridlines
+xlim ([0 15]);
+ylim ([0 15]);
+xlabel ('Feature 1');
+ylabel ('Feature 3');
+grid
+hold
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_coeff.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_coeff.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_coeff.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,76 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{vpc} =} partition_coeff (@var{soft_partition})
+##
+## Return the partition coefficient for a given soft partition.
+##
+## The argument to partition_coeff is:
+## @itemize @w
+## @item
+## @var{soft_partition} - the membership degree of each input data point in each cluster
+## @end itemize
+##
+## The return value is:
+## @itemize @w
+## @item
+## @var{vpc} - the partition coefficient for the given soft partition
+## @end itemize
+##
+## For more information about the @var{soft_partition} matrix, please see the
+## documentation for function fcm.
+##
+## @seealso{fcm, fcm_demo_1, fcm_demo_2, gustafson_kessel, gustafson_kessel_demo_1, gustafson_kessel_demo_2, partition_entropy, xie_beni_index}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition coefficient cluster validity
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: partition_coeff.m
+## Last-Modified: 8 July 2012
+
+##------------------------------------------------------------------------------
+## Note: This function is an implementation of Equation 13.9 (corrected -- the
+## equation in the book omits the exponent 2) in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 384 (International Edition).
+##------------------------------------------------------------------------------
+
+function vpc = partition_coeff (soft_partition)
+
+ ## If partition_coeff was called with an incorrect number of arguments, or the
+ ## argument does not have the correct type, print an error message and halt.
+
+ if (nargin != 1)
+ puts ("Type 'help partition_coeff' for more information.\n");
+ error ("partition_coeff requires 1 argument\n");
+ elseif (!(is_real_matrix (soft_partition) &&
+ (min (min (soft_partition)) >= 0) &&
+ (max (max (soft_partition)) <= 1)))
+ puts ("Type 'help partition_coeff' for more information.\n");
+ error ("partition_coeff's argument must be a matrix of real numbers mu, with 0 <= mu <= 1\n");
+ endif
+
+ ## Compute and return the partition coefficient.
+
+ soft_part_sqr = soft_partition .* soft_partition;
+ vpc = (sum (sum (soft_part_sqr))) / columns (soft_partition);
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_entropy.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_entropy.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/partition_entropy.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,82 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{vpe} =} partition_entropy (@var{soft_partition}, @var{a})
+##
+## Return the partition entropy for a given soft partition.
+##
+## The arguments to partition_entropy are:
+## @itemize @w
+## @item
+## @var{soft_partition} - the membership degree of each input data point in each cluster
+## @item
+## @var{a} - the log base to use in the calculation; must be a real number a > 1
+## @end itemize
+##
+## The return value is:
+## @itemize @w
+## @item
+## @var{vpe} - the partition entropy for the given soft partition
+## @end itemize
+##
+## For more information about the @var{soft_partition} matrix, please see the
+## documentation for function fcm.
+##
+## @seealso{fcm, fcm_demo_1, fcm_demo_2, gustafson_kessel, gustafson_kessel_demo_1, gustafson_kessel_demo_2, partition_coeff, xie_beni_index}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition entropy cluster validity
+## Directory: fuzzy-logic-toolkit/inst/
+## Filename: partition_entropy.m
+## Last-Modified: 8 July 2012
+
+##------------------------------------------------------------------------------
+## Note: This function is an implementation of Equation 13.10 in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 384 (International Edition).
+##------------------------------------------------------------------------------
+
+function vpe = partition_entropy (soft_partition, a)
+
+ ## If partition_entropy was called with an incorrect number of arguments, or the
+ ## argument does not have the correct type, print an error message and halt.
+
+ if (nargin != 2)
+ puts ("Type 'help partition_entropy' for more information.\n");
+ error ("partition_entropy requires 2 arguments\n");
+ elseif (!(is_real_matrix (soft_partition) &&
+ (min (min (soft_partition)) >= 0) &&
+ (max (max (soft_partition)) <= 1)))
+ puts ("Type 'help partition_entropy' for more information.\n");
+ error ("partition_entropy's first argument must be a matrix of real numbers mu, with 0 <= mu <= 1\n");
+ elseif (!(is_real (a) && a > 1))
+ puts ("Type 'help partition_entropy' for more information.\n");
+ error ("partition_entropy's second argument argument must be a real number a > 1\n");
+ endif
+
+ ## Compute and return the partition entropy.
+
+ n = columns (soft_partition);
+ Mu = soft_partition;
+ log_a_Mu = log (Mu) / log (a);
+ vpe = -(sum (sum (Mu .* log_a_Mu))) / n;
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_convergence_criterion.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_convergence_criterion.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_convergence_criterion.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,40 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{convergence_criterion} =} fcm_compute_convergence_criterion (@var{V}, @var{V_previous})
+##
+## Compute the sum of the changes in position (using the Euclidean
+## distance) of the cluster centers.
+##
+## @seealso{fcm, fcm_init_prototype, fcm_update_membership_fcn, fcm_update_cluster_centers, fcm_compute_objective_fcn}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm private
+## Directory: fuzzy-logic-toolkit/inst/private/
+## Filename: fcm_compute_convergence_criterion.m
+## Last-Modified: 7 July 2012
+
+function convergence_criterion = fcm_compute_convergence_criterion (V, V_previous)
+
+ V_delta = V - V_previous;
+ convergence_criterion = sum (sqrt (sum (V_delta .* V_delta)'));
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_objective_fcn.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_objective_fcn.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_compute_objective_fcn.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,44 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{obj_fcn} =} fcm_compute_objective_fcn (@var{Mu_m}, @var{sqr_dist})
+##
+## Compute the objective function for the current iteration.
+##
+## @seealso{fcm, fcm_init_prototype, fcm_update_membership_fcn, fcm_update_cluster_centers, fcm_compute_convergence_criterion}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm private
+## Directory: fuzzy-logic-toolkit/inst/private/
+## Filename: fcm_compute_objective_fcn.m
+## Last-Modified: 7 July 2012
+
+##------------------------------------------------------------------------------
+## Note: This function is an implementation of Equation 13.3 in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 379 (International Edition).
+##------------------------------------------------------------------------------
+
+function obj_fcn = fcm_compute_objective_fcn (Mu_m, sqr_dist)
+
+ obj_fcn = sum (sum (Mu_m .* sqr_dist));
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_init_prototype.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_init_prototype.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_init_prototype.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,47 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{V} =} fcm_init_prototype (@var{X}, @var{k})
+##
+## Initialize k cluster centers to random locations in the ranges
+## given by the min/max values of each feature of the dataset.
+##
+## @seealso{fcm, fcm_update_membership_fcn, fcm_update_cluster_centers, fcm_compute_objective_fcn, fcm_compute_convergence_criterion}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm private
+## Directory: fuzzy-logic-toolkit/inst/private/
+## Filename: fcm_init_prototype.m
+## Last-Modified: 7 July 2012
+
+function V = fcm_init_prototype (X, k)
+
+ num_features = columns (X);
+ min_feature_value = min (X);
+ max_feature_value = max (X);
+ V = rand (k, num_features);
+
+ for i = 1 : num_features
+ V(:, i) = (max_feature_value(i) - min_feature_value(i)) * V(:, i) + ...
+ min_feature_value(i);
+ endfor
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_cluster_centers.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_cluster_centers.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_cluster_centers.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,54 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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{V} =} fcm_update_cluster_centers (@var{Mu_m}, @var{X}, @var{k})
+##
+## Update the cluster centers to correspond to the given membership
+## function values.
+##
+## @seealso{fcm, fcm_init_prototype, fcm_update_membership_fcn, fcm_compute_objective_fcn, fcm_compute_convergence_criterion}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm private
+## Directory: fuzzy-logic-toolkit/inst/private/
+## Filename: fcm_update_cluster_centers.m
+## Last-Modified: 7 July 2012
+
+##------------------------------------------------------------------------------
+## Note: This function is an implementation of Equation 13.5 in
+## Fuzzy Logic: Intelligence, Control and Information, by J. Yen and
+## R. Langari, Prentice Hall, 1999, page 380 (International Edition).
+##------------------------------------------------------------------------------
+
+function V = fcm_update_cluster_centers (Mu_m, X, k)
+
+ V = Mu_m * X;
+ sum_Mu_m = sum (Mu_m');
+
+ if (prod (sum_Mu_m) == 0)
+ error ("division by 0 in function fcm_update_cluster_centers\n");
+ endif
+
+ for i = 1 : k
+ V(i, :) /= sum_Mu_m(i);
+ endfor
+
+endfunction
Added: trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_membership_fcn.m
===================================================================
--- trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_membership_fcn.m (rev 0)
+++ trunk/octave-forge/main/fuzzy-logic-toolkit/inst/private/fcm_update_membership_fcn.m 2012-07-09 13:17:11 UTC (rev 10739)
@@ -0,0 +1,75 @@
+## Copyright (C) 2012 L. Markowsky <lm...@us...>
+##
+## 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} =} fcm_update_membership_fcn (@var{V}, @var{X}, @var{m}, @var{k}, @var{n}, @var{sqr_dist})
+##
+## Compute Mu for each (cluster center, input point) pair.
+##
+## @seealso{fcm, fcm_init_prototype, fcm_update_cluster_centers, fcm_compute_objective_fcn, fcm_compute_convergence_criterion}
+##
+## @end deftypefn
+
+## Author: L. Markowsky
+## Keywords: fuzzy-logic-toolkit fuzzy partition clustering fcm private
+## Directory: fuzzy-logic-toolkit/inst/private/
+## Filename: fcm_update_membership_fcn.m
+## Last-Modified: 7 July 2012
+
+##------------------------------------------------------------------------------
+## 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 = fcm_update_membership_fcn (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, ...
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