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function [h,Coord,Color,height] = som_dendrogram(Z,varargin)
%SOM_DENDROGRAM Visualize a dendrogram.
%
% [h,Coord,Color,height] = som_dendrogram(Z, [[argID,] value, ...])
%
% Z = som_linkage(sM);
% som_dendrogram(Z);
% som_dendrogram(Z,sM);
% som_dendrogram(Z,'coord',co);
%
% Input and output arguments ([]'s are optional):
% h (vector) handle to the arc lines
% Z (matrix) size n-1 x 1, the hierarchical cluster matrix
% returned by functions like LINKAGE and SOM_LINKAGE
% n is the number of original data samples.
% [argID, (string) See below. The values which are unambiguous can
% value] (varies) be given without the preceeding argID.
% Coord (matrix) size 2*n-1 x {1,2}, the coordinates of the
% original data samples and cluster nodes used
% in the visualization
% Color (matrix) size 2*n-1 x 3, the colors of ...
% height (vector) size 2*n-1 x 1, the heights of ...
%
% Here are the valid argument IDs and corresponding values. The values
% which are unambiguous (marked with '*') can be given without the
% preceeding argID.
% 'data' *(struct) map or data struct: many other optional
% arguments require this
% (matrix) data matrix
% 'coord' (matrix) size n x 1 or n x 2, the coordinates of
% the original data samples either in 1D or 2D
% (matrix) size 2*n-1 x {1,2}, the coordinates of both
% original data samples and each cluster
% *(string) 'SOM', 'pca#', 'sammon#', or 'cca#': the coordinates
% are calculated using the given data and the
% required projection algorithm. The '#' at the
% end of projection algorithms refers to the
% desired output dimension and can be either 1 or 2
% (2 by default). In case of 'SOM', the unit
% coordinates (given by SOM_VIS_COORDS) are used.
% 'color' (matrix) size n x 3, the color of the original data samples
% (matrix) size 2*n-1 x 3, the colors of both original
% data samples and each cluster
% (string) color specification, e.g. 'r.', used for each node
% 'height' (vector) size n-1 x 1, the heights used for each cluster
% (vector) size 2*n-1 x 1, the heights used for both original
% data samples and each cluster
% *(string) 'order', the order of combination determines height
% 'depth', the depth at which the combination
% happens determines height
% 'linecolor' (string) color specification for the arc color, 'k' by default
% (vector) size 1 x 3
%
% See also SOM_LINKAGE, DENDROGRAM.
% Copyright (c) 2000 by Juha Vesanto
% Contributed to SOM Toolbox on June 16th, 2000 by Juha Vesanto
% http://www.cis.hut.fi/projects/somtoolbox/
% Version 2.0beta juuso 160600
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% read the arguments
% Z
nd = size(Z,1)+1;
nc = size(Z,1);
% varargin
Coordtype = 'natural'; Coord = []; codim = 1;
Colortype = 'none'; Color = [];
height = [zeros(nd,1); Z(:,3)];
M = [];
linecol = 'k';
i=1;
while i<=length(varargin),
argok = 1;
if ischar(varargin{i}),
switch varargin{i},
case 'data', i = i + 1; M = varargin{i};
case 'coord',
i=i+1;
if isnumeric(varargin{i}), Coord = varargin{i}; Coordtype = 'given';
else
if strcmp(varargin{i},'SOM'), Coordtype = 'SOM';
else Coordtype = 'projection'; Coord = varargin{i};
end
end
case 'color',
i=i+1;
if isempty(varargin{i}), Colortype = 'none';
elseif ischar(varargin{i}), Colortype = 'colorspec'; Color = varargin{i};
else Colortype = 'given'; Color = varargin{i};
end
case 'height', i=i+1; height = varargin{i};
case 'linecolor', i=i+1; linecol = varargin{i};
case 'SOM',
Coordtype = 'SOM';
case {'pca','pca1','pca2','sammon','sammon1','sammon2','cca','cca1','cca2'},
Coordtype = 'projection'; Coord = varargin{i};
case {'order','depth'}, height = varargin{i};
end
elseif isstruct(varargin{i}), M = varargin{i};
else
argok = 0;
end
if ~argok,
disp(['(som_dendrogram) Ignoring invalid argument #' num2str(i+1)]);
end
i = i+1;
end
switch Coordtype,
case 'SOM',
if isempty(M) | ~any(strcmp(M.type,{'som_map','som_topol'})) ,
error('Cannot determine SOM coordinates without a SOM.');
end
if strcmp(M.type,'som_map'), M = M.topol; end
case 'projection',
if isempty(M), error('Cannot do projection without the data.'); end
if isstruct(M),
if strcmp(M.type,'som_data'), M = M.data;
elseif strcmp(M.type,'som_map'), M = M.codebook;
end
end
if size(M,1) ~= nd,
error('Given data must be equal in length to the number of original data samples.')
end
case 'given',
if size(Coord,1) ~= nd & size(Coord,1) ~= nd+nc,
error('Size of given coordinate matrix does not match the cluster hierarchy.');
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% initialization
% Coordinates
switch Coordtype,
case 'natural', o = leavesorder(Z)'; [dummy,Coord] = sort(o); codim = 1;
case 'SOM', Coord = som_vis_coords(M.lattice,M.msize); codim = 2;
case 'projection',
switch Coord,
case {'pca','pca2'}, Coord = pcaproj(M,2); codim = 2;
case 'pca1', Coord = pcaproj(M,1); codim = 1;
case {'cca','cca2'}, Coord = cca(M,2,20); codim = 2;
case 'cca1', Coord = cca(M,1,20); codim = 1;
case {'sammon','sammon2'}, Coord = sammon(M,2,50); codim = 2;
case 'sammon1', Coord = sammon(M,1,50); codim = 1;
end
case 'given', codim = min(size(Coord,2),2); % nill
end
if size(Coord,1) == nd,
Coord = [Coord; zeros(nc,size(Coord,2))];
for i=(nd+1):(nd+nc),
leaves = leafnodes(Z,i,nd);
if any(leaves), Coord(i,:) = mean(Coord(leaves,:),1); else Coord(i,:) = Inf; end
end
end
% Colors
switch Colortype,
case 'colorspec', % nill
case 'none', Color = '';
case 'given',
if size(Color,1) == nd,
Color = [Color; zeros(nc,3)];
for i=(nd+1):(nd+nc),
leaves = leafnodes(Z,i,nd);
if any(leaves), Color(i,:) = mean(Color(leaves,:),1);
else Color(i,:) = 0.8;
end
end
end
end
% height
if ischar(height),
switch height,
case 'order', height = [zeros(nd,1); [1:nc]'];
case 'depth', height = nodedepth(Z); height = max(height) - height;
end
else
if length(height)==nc, height = [zeros(nd,1); height]; end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% draw
% the arcs
lfrom = []; lto = [];
for i=1:nd+nc,
if i<=nd, ch = [];
elseif ~isfinite(Z(i-nd,3)), ch = [];
else ch = Z(i-nd,1:2)';
end
if any(ch),
lfrom = [lfrom; i*ones(length(ch),1)];
lto = [lto; ch];
end
end
% the coordinates of the arcs
if codim == 1,
Lx = [Coord(lfrom), Coord(lto), Coord(lto)];
Ly = [height(lfrom), height(lfrom), height(lto)];
Lz = [];
else
Lx = [Coord(lfrom,1), Coord(lto,1), Coord(lto,1)];
Ly = [Coord(lfrom,2), Coord(lto,2), Coord(lto,2)];
Lz = [height(lfrom), height(lfrom), height(lto)];
end
washold = ishold;
if ~washold, cla; end
% plot the lines
if isempty(Lz),
h = line(Lx',Ly','color',linecol);
else
h = line(Lx',Ly',Lz','color',linecol);
if ~washold, view(3); end
rotate3d on
end
% plot the nodes
hold on
switch Colortype,
case 'none', % nill
case 'colorspec',
if codim == 1, plot(Coord,height,Color);
else plot3(Coord(:,1), Coord(:,2), height, Color);
end
case 'given',
som_grid('rect',[nd+nc 1],'line','none','Coord',[Coord, height],...
'Markersize',10,'Markercolor',Color);
end
if ~washold, hold off, end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% subfunctions
function depth = nodedepth(Z)
nd = size(Z,1)+1;
nc = size(Z,1);
depth = zeros(nd+nc,1);
ch = nc+nd-1;
while any(ch),
c = ch(1); ch = ch(2:end);
if c>nd & isfinite(Z(c-nd,3)),
chc = Z(c-nd,1:2);
depth(chc) = depth(c) + 1;
ch = [ch, chc];
end
end
return;
function inds = leafnodes(Z,i,nd)
inds = [];
ch = i;
while any(ch),
c = ch(1); ch = ch(2:end);
if c>nd & isfinite(Z(c-nd,3)), ch = [ch, Z(c-nd,1:2)]; end
if c<=nd, inds(end+1) = c; end
end
return;
function order = leavesorder(Z)
nd = size(Z,1)+1;
order = 2*nd-1;
nonleaves = 1;
while any(nonleaves),
j = nonleaves(1);
ch = Z(order(j)-nd,1:2);
if j==1, oleft = []; else oleft = order(1:(j-1)); end
if j==length(order), oright = []; else oright = order((j+1):length(order)); end
order = [oleft, ch, oright];
nonleaves = find(order>nd);
end
return;