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Hi Paul,
I am getting this error message when tryout to tun fslnets:
Error: File: linkage.m Line: 1 Column: 1
The input character is not valid in MATLAB statements or expressions.
Thanks, Jasmin
This is the program:
___________________
## Copyright (C) 2008 Francesco Potort� <[log in to unmask]>
##
## 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{y} =} linkage (@var{d})
## @deftypefnx {Function File} {@var{y} =} linkage (@var{d}, @var{method})
## @deftypefnx {Function File} @
## {@var{y} =} linkage (@var{x}, @var{method}, @var{metric})
## @deftypefnx {Function File} @
## {@var{y} =} linkage (@var{x}, @var{method}, @var{arglist})
##
## Produce a hierarchical clustering dendrogram
##
## @var{d} is the dissimilarity matrix relative to n observations,
## formatted as a @math{(n-1)*n/2}x1 vector as produced by @code{pdist}.
## Alternatively, @var{x} contains data formatted for input to
## @code{pdist}, @var{metric} is a metric for @code{pdist} and
## @var{arglist} is a cell array containing arguments that are passed to
## @code{pdist}.
##
## @code{linkage} starts by putting each observation into a singleton
## cluster and numbering those from 1 to n. Then it merges two
## clusters, chosen according to @var{method}, to create a new cluster
## numbered n+1, and so on until all observations are grouped into
## a single cluster numbered 2(n-1). Row k of the
## (m-1)x3 output matrix relates to cluster n+k: the first
## two columns are the numbers of the two component clusters and column
## 3 contains their distance.
##
## @var{method} defines the way the distance between two clusters is
## computed and how they are recomputed when two clusters are merged:
##
## @table @samp
## @item "single" (default)
## Distance between two clusters is the minimum distance between two
## elements belonging each to one cluster. Produces a cluster tree
## known as minimum spanning tree.
##
## @item "complete"
## Furthest distance between two elements belonging each to one cluster.
##
## @item "average"
## Unweighted pair group method with averaging (UPGMA).
## The mean distance between all pair of elements each belonging to one
## cluster.
##
## @item "weighted"
## Weighted pair group method with averaging (WPGMA).
## When two clusters A and B are joined together, the new distance to a
## cluster C is the mean between distances A-C and B-C.
##
## @item "centroid"
## Unweighted Pair-Group Method using Centroids (UPGMC).
## Assumes Euclidean metric. The distance between cluster centroids,
## each centroid being the center of mass of a cluster.
##
## @item "median"
## Weighted pair-group method using centroids (WPGMC).
## Assumes Euclidean metric. Distance between cluster centroids. When
## two clusters are joined together, the new centroid is the midpoint
## between the joined centroids.
##
## @item "ward"
## Ward's sum of squared deviations about the group mean (ESS).
## Also known as minimum variance or inner squared distance.
## Assumes Euclidean metric. How much the moment of inertia of the
## merged cluster exceeds the sum of those of the individual clusters.
## @end table
##
## @strong{Reference}
## Ward, J. H. Hierarchical Grouping to Optimize an Objective Function
## J. Am. Statist. Assoc. 1963, 58, 236-244,
## @url{http://iv.slis.indiana.edu/sw/data/ward.pdf}.
## @end deftypefn
##
## @seealso{pdist,squareform}
## Author: Francesco Potort� <[log in to unmask]>
function dgram = linkage (d, method = "single", distarg)
## check the input
if (nargin < 1) || (nargin > 3)
print_usage ();
endif
if (isempty (d))
error ("linkage: d cannot be empty");
elseif ( nargin < 3 && ~ isvector (d))
error ("linkage: d must be a vector");
endif
methods = struct ...
("name", { "single"; "complete"; "average"; "weighted";
"centroid"; "median"; "ward" },
"distfunc", {(@(x) min(x)) # single
(@(x) max(x)) # complete
(@(x,i,j,w) sum(diag(q=w([i,j]))*x)/sum(q)) # average
(@(x) mean(x)) # weighted
(@massdist) # centroid
(@(x,i) massdist(x,i)) # median
(@inertialdist) # ward
});
mask = strcmp (lower (method), {methods.name});
if (! any (mask))
error ("linkage: %s: unknown method", method);
endif
dist = {methods.distfunc}{mask};
if (nargin == 3)
if (ischar (distarg))
d = pdist (d, distarg);
elseif (iscell (distarg))
d = pdist (d, distarg{:});
else
print_usage ();
endif
endif
d = squareform (d, "tomatrix"); # dissimilarity NxN matrix
n = rows (d); # the number of observations
diagidx = sub2ind ([n,n], 1:n, 1:n); # indices of diagonal elements
d(diagidx) = Inf; # consider a cluster as far from itself
## For equal-distance nodes, the order in which clusters are
## merged is arbitrary. Rotating the initial matrix produces an
## ordering similar to Matlab's.
cname = n:-1:1; # cluster names in d
d = rot90 (d, 2); # exchange low and high cluster numbers
weight = ones (1, n); # cluster weights
dgram = zeros (n-1, 3); # clusters from n+1 to 2*n-1
for cluster = n+1:2*n-1
## Find the two nearest clusters
[m midx] = min (d(:));
[r, c] = ind2sub (size (d), midx);
## Here is the new cluster
dgram(cluster-n, :) = [cname(r) cname(c) d(r, c)];
## Put it in place of the first one and remove the second
cname(r) = cluster;
cname(c) = [];
## Compute the new distances
newd = dist (d([r c], :), r, c, weight);
newd(r) = Inf; # take care of the diagonal element
## Put distances in place of the first ones, remove the second ones
d(r,:) = newd;
d(:,r) = newd';
d(c,:) = [];
d(:,c) = [];
## The new weight is the sum of the components' weights
weight(r) += weight(c);
weight(c) = [];
endfor
## Sort the cluster numbers, as Matlab does
dgram(:,1:2) = sort (dgram(:,1:2), 2);
## Check that distances are monotonically increasing
if (any (diff (dgram(:,3)) < 0))
warning ("clustering",
"linkage: cluster distances do not monotonically increase\n\
you should probably use a method different from \"%s\"", method);
endif
endfunction
## Take two row vectors, which are the Euclidean distances of clusters I
## and J from the others. Column I of second row contains the distance
## between clusters I and J. The centre of gravity of the new cluster
## is on the segment joining the old ones. W are the weights of all
## clusters. Use the law of cosines to find the distances of the new
## cluster from all the others.
function y = massdist (x, i, j, w)
x .^= 2; # squared Euclidean distances
if (nargin == 2) # median distance
qi = 0.5; # equal weights ("weighted")
else # centroid distance
qi = 1 / (1 + w(j) / w(i)); # proportional weights ("unweighted")
endif
y = sqrt (qi*x(1,:) + (1-qi)*(x(2,:) - qi*x(2,i)));
endfunction
## Take two row vectors, which are the inertial distances of clusters I
## and J from the others. Column I of second row contains the inertial
## distance between clusters I and J. The centre of gravity of the new
## cluster K is on the segment joining I and J. W are the weights of
## all clusters. Convert inertial to Euclidean distances, then use the
## law of cosines to find the Euclidean distances of K from all the
## other clusters, convert them back to inertial distances and return
## them.
function y = inertialdist (x, i, j, w)
wi = w(i); wj = w(j); # the cluster weights
s = [wi + w; wj + w]; # sum of weights for all cluster pairs
p = [wi * w; wj * w]; # product of weights for all cluster pairs
x = x.^2 .* s ./ p; # convert inertial dist. to squared Eucl.
sij = wi + wj; # sum of weights of I and J
qi = wi/sij; # normalise the weight of I
## Squared Euclidean distances between all clusters and new cluster K
x = qi*x(1,:) + (1-qi)*(x(2,:) - qi*x(2,i));
y = sqrt (x * sij .* w ./ (sij + w)); # convert Eucl. dist. to inertial
endfunction
%!shared x, t
%! x = reshape(mod(magic(6),5),[],3);
%! t = 1e-6;
%!assert (cond (linkage (pdist (x))), 34.119045,t);
%!assert (cond (linkage (pdist (x), "complete")), 21.793345,t);
%!assert (cond (linkage (pdist (x), "average")), 27.045012,t);
%!assert (cond (linkage (pdist (x), "weighted")), 27.412889,t);
%! lastwarn(); # Clear last warning before the test
%!warning <monotonically> linkage (pdist (x), "centroid");
%!test warning off clustering
%! assert (cond (linkage (pdist (x), "centroid")), 27.457477,t);
%! warning on clustering
%!warning <monotonically> linkage (pdist (x), "median");
%!test warning off clustering
%! assert (cond (linkage (pdist (x), "median")), 27.683325,t);
%! warning on clustering
%!assert (cond (linkage (pdist (x), "ward")), 17.195198,t);
%!assert (cond (linkage(x,"ward","euclidean")), 17.195198,t);
%!assert (cond (linkage(x,"ward",{"euclidean"})), 17.195198,t);
%!assert (cond (linkage(x,"ward",{"minkowski",2})),17.195198,t);
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