function [S,m,l,t,s]=som_grid(varargin) %SOM_GRID Visualization of a SOM grid % % [sGrid,m,l,t,s]=som_grid(sGrid, ['argID', value, ...]) % [sGrid,m,l,t,s]=som_grid(topol, ['argID', value, ...]) % [sGrid,m,l,t,s]=som_grid(lattice, msize, ['argID', value, ...]) % % Input and output arguments ([]'s are optional) % sGrid (struct) som_grid struct (see output arguments) % topol (struct) map or topol struct for giving the topology % (cell array) of form {'lattice', msize, ['shape']}. % Default value for 'shape' is 'sheet'. % lattice (string) 'hexa', 'rect' % (matrix) size M x M, defines topological connections % msize (vector) 1x2 vector defines the grid size, M=msize(1)*msize(2) % ['argID',(string) Other arguments can be given as 'argID', value % value] (varies) pairs. See list below for valid values. % % sGrid (struct) with fields S.msize, S.shape, S.lattice, S.coord, S.marker, % S.markersize, S.markercolor, S.line, S.linewidth, S.linecolor, % S.surf, S.label, S.labelsize, S.labelcolor % m (matrix) handels to LINE objects (unit markers) % l (matrix) handles to LINE objects (lines connecting the units) % t (matrix) handles to TEXT objects (labels) % s (scalar) handle to SURF object (surface between units) % % Here are the valid argument IDs (case insensitive) and % associated values: % 'Coord' Mx2 or Mx3 matrix of coordinates % (default: according to lattice as in som_cplane) % 'Marker' string 'o','+','x','*','v','^','<','>','h','s','d','p','.', % 'none' or Mx1 cell or char array of these strings % Default: 'o'. % 'MarkerSize' scalar or Mx1 matrix of double. Default: 6. % 'MarkerColor' ColorSpec or Mx3 matrix of RGB triples. Default: 'k'. % 'Line' string '-',':','--' or '-.' or 'none'. Default: '-'. % 'Surf' [], Mx1 or Mx3 matrix of RGB triples % to define surface values. Default: [] = no surf. % Note: shading is turned to 'interp'. % 'LineWidth' scalar or MxM matrix, default: 0.5 % 'LineColor' ColorSepc, MxMx3 matrix of RGB triples or a cell array % of form {r g b} where r,g, and b are MxM % (sparse) matrices of R,G, and B values % 'Label' Mx1 char array, cell array of strings size MxL % or [] to indicate no labels, default: [] = no labels. % 'LabelSize' scalar % 'LabelColor' ColorSpec or string 'none', default: 'g'. % % For more help, try 'type som_grid' or check out online documentation. % See also SOM_CONNECTION, SOM_SHOW, SOM_CPLANE, SOM_SET, SCATTER, SCATTER3. %%%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % som_grid % % PURPOSE % % To visualize the SOM grid in various ways % % SYNTAX % % [sGrid,m,l,t,s]=som_grid(sGrid) % [sGrid,m,l,t,s]=som_grid(sTopol) % [sGrid,m,l,t,s]=som_grid(sMap) % [sGrid,m,l,t,s]=som_grid({lattice, msize, [shape]}) % [sGrid,m,l,t,s]=som_grid(lattice, msize) % [sGrid,m,l,t,s]=som_grid(..., ['argID', value, ...]) % % DESCRIPTION % % The SOM can be defined as a set of units (neurons) and their % topological relations. This function is used to visualize these in % various ways. The units may be drawn using different markers and % colors, in different sizes and in different locations in 2D or % 3D. However the topological neighborhood is limited to be % 2-dimensional. The connections between these units may be drawn using % lines having different thicknesses and colors. Labeling text may be % plotted on the units. It is possible also to draw a surface between % the units. The surface coloring is either indexed (one value per % unit) or fixed RGB (a 1x3 RGB triple per unit). % % REQUIRED INPUT ARGUMENTS % % Note: M is the number of map units. % % The first (or first two) argument may have various different types of values % % 1. sGrid (struct) som_grid struct (the output of this function) % % The struct initiates the visualization. The argID-value -pairs % are used to alter the initiation. % % Following argument types may be used to give the topology for the grid % % 2. sTopol (struct) som_topol struct % 3. sMap (struct) som_map struct (only topology matters) % 4. {lattice, msize} or {lattice, msize, sheet} (cell array) % - lattice must be 'hexa' or 'rect' % - msize must be a 1x2 vector % - shape (if specified) must be string 'sheet', 'cyl' or 'toroid' % If shape is not given it is 'sheet' by default. % 5. lattice (string or matrix) AND msize (1x2 vector) as two separate arguments % - lattice may be string 'rect' or 'hexa' or a connection matrix % (see SOM_CONNECTION) to define a free topology. This connection % matrix is of size MxM and its element i,j (i','h','s','d', 'p','.', or 'none' % give the same marker for each unit. % (cell array) of size Mx1 of previous strings gives individual % markers for each unit. % % 'MarkerSize' Size (pt) of unit markers, default is 6 (pt). % (scalar) gives the same size for every unit. % (matrix) Mx1 gives an individual size for each unit marker. % % 'MarkerColor' Unit marker colors, default is 'k' % (ColorSpec) gives the same color each unit. % (matrix) Mx3 of RGB triples gives individual color for each unit % Note that indexed coloring - like in SOM_CPLANE - is % not possible. If indexed coloring is needed, you can % use SOM_NORMCOLOR to calculate RGB colors that % emulate indexed coloring. However, the colors for the % units are fixed, so changing colormap will not % change the colors. % % 'Line' Line type, default is '-'. % (string) '-',':','--' or '-.' or 'none'. Only one linetype in % grid is allowed. % % 'LineWidth' Width of the topological connection lines (edges) % (scalar) gives the same width for each line. Default is 0.5. % (matrix) MxM sparse (or full) matrix gives individual width for % each connection. The element (i,j), i= i are ignored in % order to avoid ambiguous situations if the matrix would be % non-symmetric. The "connections to oneself" is not drawn. % % Line width zero is valid and causes the line to disappear. % % 'LineColor' Color of connection lines, default is [0.9 0.9 0.9]. % (ColorSpec) gives the same color for each line % (matrix) MxMx3 matrix of RGB triples gives individual width for % each connection. The element (i,j,:), i= i are ignored in order to avoid ambiguous situations % if the matrix was non-symmetric. The "connections to oneself" % is not drawn. % % % 'Label' Labels for units, default is []. % (empty) [] means no labels. % (char array) of size Mx1. Element (i,:) has the label for unit i. % (cell array) of size MxL consisting of sets of labels. Element {i,:} % contains the labeling for unit i. % In case of multiple labels, the labels for one unit are shown % in one column centered at that unit. % % 'LabelSize' Text size of labels (points), default is 10. % (scalar) Default is 10. % % 'LabelColor' Color of labels, default is 'c' (cyan). % (ColorSpec) gives the same color for each label string 'xor' % sets the colors automatically so that they differ % from the background (using Matlab's built-in xor-color feature.) % % 'Surf' Surface between nodes, default is []. % (empty) [] gives no surface % (vector) Mx1 gives an indexed interpolated color surface between % units using the actual colormap. % (matrix) Mx3 matrix of RGB triples gives a interpolated color surface % between units using fixed RGB colors. % % Note that the interpolation is done using Matlab's built-in % color interpolation for SURF objects. % % OUTPUT ARGUMENTS % % sGrid (struct) with fields S.msize, S.shape, S.lattice, S.coord, S.marker, % S.markersize, S.markercolor, S.line, S.linewidth, S.linecolor, % S.surf, S.label, S.labelsize, S.labelcolor % % m (matrix) handels to LINE objects (unit markers) % % l (matrix) handles to LINE objects (lines connecting the units) % % t (matrix) handles to TEXT objects (labels) % % s (scalar) handle to SURF object (surface between units) % % EXAMPLES % % % Make map of size 15x10 on random data: % % map=som_make(rand(1000,4),'msize',[15 10], 'lattice', 'hexa'); % % % Draw the grid using two frist varable values as coordinates % % and store the sGrid struct in varable S: % % S=som_grid(map, 'coord', map.codebook(:,[1 2])) % % %Define some things: % % % % Create a cell array of size 150x1 that divides map in to two label classes % % 'circles' and 'squares' % % L(1:75,1)='o'; L(76:150,1)='s'; L = cellstr(L); % % % Create a coloring according to the 3rd variable according to current % % colormap: % % C = som_normcolor(map.codebook(:,3)); % % % Change the visualization: use black lines, unit markers in M and unit % % color in C, and set unit size to 10: % % S=som_grid(S, 'linecolor', 'k', 'marker', L, 'MarkerColor',C, ... % 'MarkerSize', 10); % % % Do a new visualization, use indexed color surface calcualted from the % % first variable, coordinates according to the lattice (default) but % % no markers nor lines: % % S=som_grid(map,'line','none','marker','none','surf',map.codebook(:,1)); % % % Set coordinates according to three last varables % % som_grid(S,'coord',map.codebook(:,2:4)); % % % Create a random connection matrix R1 and the usual hexagonal % % neighborhood connection matrix R2: % % R1=sparse(rand(150,150)>0.9); % R2=som_connection(map); % % % Show these connections. Note that coordinates _must_ now be given % % explicitly: we form default topological coordinates using % % som_unit_coords. % % som_grid(R1,map.topol.msize,'coord',som_unit_coords(map)); % som_grid(R2,map.topol.msize,'coord',som_unit_coords(map)); % % % Show connections (R1 AND R2) % som_grid(R2.*R2,map.topol.msize,'coord',som_unit_coords(map)); % % OBJECT TAGS % % No tags are set. % % SEE ALSO % % som_show The basic map visualization routine % som_cplane The basic component plane visualization % som_connection The basic topological connections % scatter Scatter plots % scatter3 3-dimensional scatter plots % Copyright (c) 1999-2000 by the SOM toolbox programming team. % http://www.cis.hut.fi/projects/somtoolbox/ % Version 2.0beta Johan 061099 juuso 151199 310300 %% Init %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% True=1; False=0; % const. m=[]; l=[]; t=[]; s=[]; % default values for outputs Ref=som_set('som_grid'); % reference struct num_of_args=length(varargin); % numb. of varargins if num_of_args==0, S=som_set('som_grid'); return; end switch class(varargin{1}) case 'struct' S=varargin{1}; first_identifier=2; if ~isfield(S,'type'), error('Input struct is invalid: field ''type'' is missing.'); end switch S.type case 'som_grid' S=varargin{1}; first_identifier=2; case 'som_map' Ref.lattice=S.topol.lattice; Ref.msize=S.topol.msize; Ref.shape=S.topol.shape; S=Ref; first_identifier=2; case 'som_topol' Ref.lattice=S.lattice; Ref.msize=S.msize; Ref.shape=S.shape; S=Ref; first_identifier=2; otherwise error('Input struct has to be of type som_grid, som_map or som_topol.'); end case 'cell' S=varargin{1}; first_identifier=2; if vis_valuetype(S,{'topol_cell_no_shape'}), Ref.lattice=S{1}; Ref.msize=S{2}; elseif vis_valuetype(S,{'topol_cell'}), Ref.lattice=S{1}; Ref.msize=S{2}; Ref.shape=S{3}; else error(['The cell value for 1st argument has to be {lattice, msize}' ... 'or {lattice, msize, shape}.']); end S=Ref; case{'double','sparse','char'} % Set defaults S=Ref; first_identifier=3; if num_of_args<2, error('Not enough input arguments.'); end S.lattice=varargin{1}; S.msize=varargin{2}; otherwise error('Invalid input arguments!'); end %% Check input args %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=first_identifier:2:num_of_args, if ischar(varargin{i}) & isfield(Ref,lower(varargin{i})), if i+1>num_of_args, error('Invalid identifier-value pairs or wrong argument order.'); else S=setfield(S,lower(varargin{i}),varargin{i+1}); end elseif ischar(varargin{i}), error(['Identifier ''' varargin{i} ''' is unknown.']); else error('Invalid identifier-value pairs or wrong argument order.'); end end % msize if ~vis_valuetype(S.msize,{'1x2'}), error('msize has to be a 1x2 vector.'); end munits=prod(S.msize); % Default coordinates according to negihborhood if isempty(S.coord), if ischar(S.lattice), switch S.lattice, case{'hexa','rect'} S.coord=som_vis_coords(S.lattice,S.msize); otherwise error('String value for lattice must be ''hexa'' or ''rect''.'); end else error('Lattice is not ''hexa'' or ''rect'': coordinates must be given.'); end end % connections type=class(S.lattice); switch type case {'sparse','double'} % free topology fixedline=False; case 'char' % default topologies (hexa,char) switch S.lattice case 'hexa' hexa=True; case 'rect' hexa=False; otherwise error('Unknown lattice or neighborhood.'); end % If topology is hexa/rect but linetype, color etc. is % not constant, the topology is set to free if size(S.linewidth,1)>1 | size(S.linecolor,1)>1 | ... iscell(S.linecolor) % matrix or cell = not constant fixedline=False; S.lattice=som_connection({S.lattice,S.msize,S.shape}); else fixedline=True; end end % Check coordinate matrix size and set dummy zeros to z-axis % if 2D coordinates (always 3D plots!) if ~vis_valuetype(S.coord,{[munits 2],[munits 3]}), error('Coordinate matrix has wrong size.'); elseif size(S.coord,2)==2, S.coord(:,3)=0; end % Fixed marker size, color, type? if size(S.markersize,1)>1 | size(S.markercolor,1)>1 | size(S.marker,1)>1 fixedmarker=False; else fixedmarker=True; end % Check labels if ~vis_valuetype(S.label,{'chararray','2Dcellarray_of_char'}) ... & ~isempty(S.label), error('Labels should be in a char array or cell array of strings.'); elseif ischar(S.label) S.label=cellstr(S.label); end if size(S.label,1) ~= munits & ~isempty(S.label), error('Number of labels and map size do not match.'); end % Check line width, marker size, marker color, % label size label color and surf sizes&types: if ~vis_valuetype(S.linewidth,{[munits munits] [1 1]}), error('LineWidth matrix value has wrong size or dimension.'); elseif any(S.linewidth(:)<0), error('All elements of LineWidth must be non-negative.'); elseif ~vis_valuetype(S.markersize,{[munits 1] [1 1]}), error('MarkerSize matrix value has wrong size or dimension.'); elseif any(S.markersize(:)<0), error('All elements of MarkerSize must be non-negative.'); elseif ~vis_valuetype(S.markercolor,{'1x3rgb','colorstyle'}) & ... ~vis_valuetype(S.markercolor,{[munits 3],'nx3rgb'},'all'), error('MarkerColor should be a ColorSpec or Mx3 matrix of RGB triples.'); elseif ~vis_valuetype(S.labelcolor,{'1x3rgb','colorstyle','xor'}), error('LabelColor shoud be a ColorSpec or ''xor'' or ''none''.') elseif ~vis_valuetype(S.labelsize,{'1x1'}) error('LabelSize should be a scalar.'); elseif ~isempty(S.surf) & ~vis_valuetype(S.surf,{[munits 1] [munits 3]}); error('Surf matrix value has wrong size or dimension.'); end % Check marker type & size if vis_valuetype(S.marker,{'cellcolumn_of_char'}) % Don't bother to check the mareker strings in this case % let the plot3 handle them; it returns quite understandable % error messages, anyway if ~size(S.marker) == [munits 1], error(['Marker should be one of Matlab''s valid marker type,' ... ' string ''none'' or a Mx1 cell array of these.']); end elseif ~vis_valuetype(S.marker,{'markerstyle','none'}), error(['Marker should be one of Matlab''s valid marker type,' ... ' string ''none'' or a Mx1 cell array of these.']); end % Check line type & size: only one line style allowed if ~vis_valuetype(S.line,{'linestyle','none'}) error(['Line should be a valid Matlab''s line style string or' ... ' string ''none''.']); end % Check line color if iscell(S.linecolor), if ndims(S.linecolor) ~= 2 | any(size(S.linecolor) ~= [1 3]), error('Cell input for LineColor should be of form {r,g,b}.') elseif ~vis_valuetype(S.linecolor{1},{[munits munits],'nxn[0,1]'},'all')| ... ~vis_valuetype(S.linecolor{2},{[munits munits],'nxn[0,1]'},'all')| ... ~vis_valuetype(S.linecolor{3},{[munits munits],'nxn[0,1]'},'all'), error(['In cell input {r,g,b} some matrix r,g or b is invalid: ' ... 'Size must be MxM and values in interval [0,1].']); end elseif ~vis_valuetype(S.linecolor,{'colorstyle','1x3rgb'}) & ... ~vis_valuetype(S.linecolor,{'nxnx3rgb', [munits munits 3]},'all'), error('Invalid LineColor: see help text for valid values.'), elseif vis_valuetype(S.linecolor, {'none'}), error('LineColor ''none'' not allowed: set Line to ''none'' instead.'); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Action memhold=ishold; % take hold state if ~memhold cla; end hold on; % Set surf if it exist if ~isempty(S.surf), for i=1:3, s(:,:,i)=reshape(S.coord(:,i),S.msize); end s(:,:,4:3+size(S.surf,2))=reshape(S.surf,[S.msize size(S.surf,2)]); s=surf(s(:,:,1),s(:,:,2),s(:,:,3),s(:,:,4:end)); set(s,'EdgeColor','none','Marker','none','FaceColor','interp'); end if fixedline, % Line properties are fixed: draw fast, but % if line is set to 'none' set empty handle ans skip if strcmp(S.line,'none') l={}; else p1=reshape(S.coord, [S.msize 3]); p2=zeros(size(p1)-[0 1 0]); p2(1:2:end,:,:)=p1(1:2:end,2:end,:); p2(2:2:end,:,:)=p1(2:2:end,1:end-1,:); l{1}=plot3(p1(:,:,1), p1(:,:,2), p1(:,:,3), ... 'Color', S.linecolor(1,:), ... 'LineWidth', S.linewidth(1), ... 'LineStyle', S.line); l{2}=plot3(p1(:,:,1)', p1(:,:,2)', p1(:,:,3)', ... 'Color', S.linecolor(1,:), ... 'LineWidth', S.linewidth(1), ... 'LineStyle', S.line); if hexa, l{3}=plot3(p2(:,:,1), p2(:,:,2), p2(:,:,3), ... 'Color', S.linecolor(1,:), ... 'LineWidth', S.linewidth(1), ... 'LineStyle', S.line); end end l=cat(1,l{:}); else % Variable properties: draw connection by connection [I,J,lw]=find(S.lattice); x=[S.coord(I,1)'; S.coord(J,1)']; y=[S.coord(I,2)'; S.coord(J,2)']; z=[S.coord(I,3)'; S.coord(J,3)']; if S.linewidth(1)==0, linewidth=0.5; else linewidth=S.linewidth(1); end if ndims(S.linecolor) ~= 3 if isstr(S.linecolor) l=plot3(x, y, z, ... 'Color', S.linecolor, ... 'LineWidth', linewidth, ... 'LineStyle',S.line); else if iscell(S.linecolor) lcolor=[S.linecolor{1}(1,1) S.linecolor{2}(1,1) S.linecolor{3}(1,1)]; l=plot3(x, y, z, ... 'Color', lcolor, ... 'LineWidth', linewidth, ... 'LineStyle',S.line); else l=plot3(x, y, z, ... 'Color', S.linecolor(1,:), ... 'LineWidth', linewidth, ... 'LineStyle',S.line); end end else l=plot3(x, y, z, ... 'Color', S.linecolor(1,1,:), ... 'LineWidth', linewidth, ... 'LineStyle',S.line); end end if fixedmarker, % If marker is set to 'none' skip and set empty handle if strcmp(S.marker,'none') m=[]; else % Fixed markers: draw all in one command m=plot3(S.coord(:,1), S.coord(:,2), S.coord(:,3), ... 'LineStyle', 'none', ... 'Marker', S.marker, ... 'MarkerSize', S.markersize(1), ... 'MarkerFaceColor', S.markercolor(1,:), ... 'MarkerEdgeColor', S.markercolor(1,:)); end else % Variable marker properties: draw marker by marker x=[S.coord(:,1)'; S.coord(:,1)']; y=[S.coord(:,2)'; S.coord(:,2)']; z=[S.coord(:,3)'; S.coord(:,3)']; if iscell(S.marker) marker=S.marker{1}; else marker=S.marker(1); end sz=max(S.markersize(1),0.1); m=plot3(x, y, z, ... 'LineStyle', 'none', ... 'Marker', marker, ... 'MarkerSize', sz, ... 'MarkerFaceColor', S.markercolor(1,:), ... 'MarkerEdgeColor', S.markercolor(1,:)); end L=length(l); n=munits; %%% Set variable properties %%% % Line width if length(S.linewidth)>1 lwidth=diag(S.linewidth(I,J)); % Handle zero width iszero=(lwidth == 0);lwidth(iszero)=0.5; for i=1:length(l), set(l(i),'LineWidth', lwidth(i)); end if ~isempty(iszero), % zero width set(l(iszero),'Visible','off'); end end % Line color if size(S.linecolor,1)>1 | iscell(S.linecolor) if length(size(S.linecolor)) == 3 | iscell(S.linecolor) if ~iscell(S.linecolor) for i=1:L set(l(i),'Color',S.linecolor(I(i),J(i),:)); end else for i=1:L lcolor=[S.linecolor{1}(I(i),J(i)),... S.linecolor{2}(I(i),J(i)),... S.linecolor{3}(I(i),J(i))]; set(l(i),'Color',lcolor); end end else for i=1:L, set(l(i),'Color', S.linecolor(I(i),:)); end end end % Marker size if length(S.markersize)>1 % handle zero size iszero=find(~S.markersize); S.markersize(iszero)=1; for i=1:n, set(m(i),'MarkerSize', S.markersize(i)); end if ~isempty(iszero), % zero size set(m(iszero),'Visible','off'); end end % Marker type if size(S.marker,1)>1 S.marker=char(S.marker); for i=1:n, set(m(i),'Marker', S.marker(i)); end end % Marker color if size(S.markercolor,1)>1 for i=1:n, set(m(i),'MarkerFaceColor', S.markercolor(i,:), ... 'MarkerEdgeColor', S.markercolor(i,:)); end end % Set labels if they exist if ~isempty(S.label) if vis_valuetype(S.labelcolor,{'xor'}), S.labelcolor='g'; XOR=1; else XOR=0; end if vis_valuetype(S.labelcolor,{'none'}), S.labelcolor='g'; VIS = 1; else VIS = 0; end for i=1:size(S.label,1), L=cat(1,S.label(i,:)); for j=length(L):-1:1, if isempty(L{j}), L=L(1:end-1); end end if isempty(L), L=''; end t(i)=text(S.coord(i,1), S.coord(i,2), S.coord(i,3), L,... 'FontSize', S.labelsize, 'Color',S.labelcolor, ... 'HorizontalAlignment', 'center'); end if XOR set(t,'EraseMode','xor'); end if VIS set(t,'Visible','off'); end else t=[]; end %% Set hold state if ~memhold, hold off; end if nargout==0, clear S m l t s; end