som_demo3.m

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%SOM_DEMO3 Self-organizing map visualization.

% Contributed to SOM Toolbox 2.0, February 11th, 2000 by Juha Vesanto
% http://www.cis.hut.fi/projects/somtoolbox/

% Version 1.0beta juuso 071197 
% Version 2.0beta juuso 080200 070600

clf reset;
figure(gcf)
echo on




clc
%    ==========================================================
%    SOM_DEMO3 - VISUALIZATION
%    ==========================================================

%    som_show           - Visualize map.
%    som_grid           - Visualization with free coordinates.
%
%    som_show_add       - Add markers on som_show visualization.
%    som_show_clear     - Remove markers from som_show visualization.
%    som_recolorbar     - Refresh and rescale colorbars in som_show 
%                         visualization.
%
%    som_cplane         - Visualize component/color/U-matrix plane.
%    som_pieplane       - Visualize prototype vectors as pie charts.
%    som_barplane       - Visualize prototype vectors as bar charts.
%    som_plotplane      - Visualize prototype vectors as line graphs.
%
%    pcaproj            - Projection to principal component space.
%    cca                - Projection with Curvilinear Component Analysis.
%    sammon             - Projection with Sammon's mapping.
%    som_umat           - Calculate U-matrix.
%    som_colorcode      - Color coding for the map.
%    som_normcolor      - RGB values of indexed colors.
%    som_hits           - Hit histograms for the map.

%    The basic functions for SOM visualization are SOM_SHOW and
%    SOM_GRID. The SOM_SHOW has three auxiliary functions:
%    SOM_SHOW_ADD, SOM_SHOW_CLEAR and SOM_RECOLORBAR which are used 
%    to add and remove markers and to control the colorbars.
%    SOM_SHOW actually uses SOM_CPLANE to make the visualizations.
%    Also SOM_{PIE,BAR,PLOT}PLANE can be used to visualize SOMs.

%    The other functions listed above do not themselves visualize
%    anything, but their results are used in the visualizations.
    
%    There's an important limitation that visualization functions have:
%    while the SOM Toolbox otherwise supports N-dimensional map grids, 
%    visualization only works for 1- and 2-dimensional map grids!!!

pause % Strike any key to create demo data and map...





clc
%    DEMO DATA AND MAP
%    =================

%    The data set contructed for this demo consists of random vectors
%    in three gaussian kernels the centers of which are at [0, 0, 0],
%    [3 3 3] and [9 0 0]. The map is trained using default parameters.

D1 = randn(100,3);
D2 = randn(100,3) + 3;
D3 = randn(100,3); D3(:,1) = D3(:,1) + 9;

sD = som_data_struct([D1; D2; D3],'name','Demo3 data',...
		     'comp_names',{'X-coord','Y-coord','Z-coord'});
sM = som_make(sD);

%    Since the data (and thus the prototypes of the map) are
%    3-dimensional, they can be directly plotted using PLOT3.
%    Below, the data is plotted using red 'o's and the map
%    prototype vectors with black '+'s.

plot3(sD.data(:,1),sD.data(:,2),sD.data(:,3),'ro',...
      sM.codebook(:,1),sM.codebook(:,2),sM.codebook(:,3),'k+')
rotate3d on

%    From the visualization it is pretty easy to see what the data is
%    like, and how the prototypes have been positioned. One can see
%    that there are three clusters, and that there are some prototype
%    vectors between the clusters, although there is actually no
%    data there. The map units corresponding to these prototypes
%    are called 'dead' or 'interpolative' map units.

pause % Strike any key to continue...



clc
%    VISUALIZATION OF MULTIDIMENSIONAL DATA
%    ======================================

%    Usually visualization of data sets is not this straightforward,
%    since the dimensionality is much higher than three. In principle,
%    one can embed additional information to the visualization by
%    using properties other than position, for example color, size or
%    shape.

%    Here the data set and map prototypes are plotted again, but
%    information of the cluster is shown using color: red for the
%    first cluster, green for the second and blue for the last.

plot3(sD.data(1:100,1),sD.data(1:100,2),sD.data(1:100,3),'ro',...
      sD.data(101:200,1),sD.data(101:200,2),sD.data(101:200,3),'go',...
      sD.data(201:300,1),sD.data(201:300,2),sD.data(201:300,3),'bo',...
      sM.codebook(:,1),sM.codebook(:,2),sM.codebook(:,3),'k+')
rotate3d on

%    However, this works only for relatively small dimensionality, say
%    less than 10. When the information is added this way, the
%    visualization becomes harder and harder to understand. Also, not
%    all properties are equal: the human visual system perceives
%    colors differently from position, not to mention the complex
%    rules governing perception of shape. 

pause % Strike any key to learn about linking...





clc
%    LINKING MULTIPLE VISUALIZATIONS
%    ===============================

%    The other option is to use *multiple visualizations*, so called
%    small multiples, instead of only one. The problem is then how to
%    link these visualizations together: one should be able to idetify
%    the same object from the different visualizations.

%    This could be done using, for example, color: each object has
%    the same color in each visualization. Another option is to use 
%    similar position: each object has the same position in each
%    small multiple.

%    For example, here are four subplots, one for each component and
%    one for cluster information, where color denotes the value and
%    position is used for linking. The 2D-position is derived by
%    projecting the data into the space spanned by its two greatest
%    eigenvectors.

[Pd,V,me] = pcaproj(sD.data,2);        % project the data
Pm        = pcaproj(sM.codebook,V,me); % project the prototypes
colormap(hot);                         % colormap used for values

echo off
for c=1:3, 
  subplot(2,2,c), cla, hold on
  som_grid('rect',[300 1],'coord',Pd,'Line','none',...
	   'MarkerColor',som_normcolor(sD.data(:,c)));
  som_grid(sM,'Coord',Pm,'Line','none','marker','+');
  hold off, title(sD.comp_names{c}), xlabel('PC 1'), ylabel('PC 2');
end

subplot(2,2,4), cla
plot(Pd(1:100,1),Pd(1:100,2),'ro',...
     Pd(101:200,1),Pd(101:200,2),'go',...
     Pd(201:300,1),Pd(201:300,2),'bo',...
     Pm(:,1),Pm(:,2),'k+')
title('Cluster')
echo on

pause % Strike any key to use color for linking...

%    Here is another example, where color is used for linking. On the
%    top right triangle are the scatter plots of each variable without
%    color coding, and on the bottom left triangle with the color
%    coding. In the colored figures, each data sample can be
%    identified by a unique color. Well, almost identified: there are
%    quite a lot of samples with almost the same color. Color is not as
%    precise linking method as position.

echo off 
Col = som_normcolor([1:300]',jet(300));
k=1;
for i=1:3, 
  for j=1:3, 
    if i<j, i1=i; i2=j; else i1=j; i2=i; end
    if i<j,
      subplot(3,3,k); cla
      plot(sD.data(:,i1),sD.data(:,i2),'ko')
      xlabel(sD.comp_names{i1}), ylabel(sD.comp_names{i2})
    elseif i>j,
      subplot(3,3,k); cla
      som_grid('rect',[300 1],'coord',sD.data(:,[i1 i2]),...
	       'Line','none','MarkerColor',Col);
      xlabel(sD.comp_names{i1}), ylabel(sD.comp_names{i2})
    end
    k=k+1;
  end
end
echo on

pause % Strike any key to learn about data visualization using SOM...


clc
%    DATA VISUALIZATION USING SOM
%    ============================

%    The basic visualization functions and their usage have already
%    been introduced in SOM_DEMO2. In this demo, a more structured
%    presentation is given. 

%    Data visualization techniques using the SOM can be divided to
%    three categories based on their goal:

%     1. visualization of clusters and shape of the data:
%        projections, U-matrices and other distance matrices
%
%     2. visualization of components / variables: 
%        component planes, scatter plots
%
%     3. visualization of data projections: 
%        hit histograms, response surfaces

pause % Strike any key to visualize clusters with distance matrices...



clf
clc
%    1. VISUALIZATION OF CLUSTERS: DISTANCE MATRICES
%    ===============================================

%    Distance matrices are typically used to show the cluster
%    structure of the SOM. They show distances between neighboring
%    units, and are thus closely related to single linkage clustering
%    techniques. The most widely used distance matrix technique is
%    the U-matrix. 

%    Here, the U-matrix of the map is shown (using all three
%    components in the distance calculation):

colormap(1-gray)
som_show(sM,'umat','all');

pause % Strike any key to see more examples of distance matrices...

%    The function SOM_UMAT can be used to calculate U-matrix.  The
%    resulting matrix holds distances between neighboring map units,
%    as well as the median distance from each map unit to its
%    neighbors. These median distances corresponding to each map unit
%    can be easily extracted. The result is a distance matrix using
%    median distance.

U = som_umat(sM);
Um = U(1:2:size(U,1),1:2:size(U,2));

%    A related technique is to assign colors to the map units such
%    that similar map units get similar colors.

%    Here, four clustering figures are shown: 
%     - U-matrix
%     - median distance matrix (with grayscale)
%     - median distance matrix (with map unit size)
%     - similarity coloring, made by spreading a colormap
%       on top of the principal component projection of the
%       prototype vectors

subplot(2,2,1)
h=som_cplane([sM.topol.lattice,'U'],sM.topol.msize, U(:)); 
set(h,'Edgecolor','none'); title('U-matrix')

subplot(2,2,2)
h=som_cplane(sM, Um(:));
set(h,'Edgecolor','none'); title('D-matrix (grayscale)')

subplot(2,2,3)
som_cplane(sM,'none',1-Um(:)/max(Um(:)))
title('D-matrix (marker size)')

subplot(2,2,4)
C = som_colorcode(Pm);  % Pm is the PC-projection calculated earlier
som_cplane(sM,C)
title('Similarity coloring')

pause % Strike any key to visualize shape and clusters with projections...



clf
clc
%    1. VISUALIZATION OF CLUSTERS AND SHAPE: PROJECTIONS
%    ===================================================

%    In vector projection, a set of high-dimensional data samples is
%    projected to a lower dimensional such that the distances between
%    data sample pairs are preserved as well as possible. Depending 
%    on the technique, the projection may be either linear or
%    non-linear, and it may place special emphasis on preserving
%    local distances. 

%    For example SOM is a projection technique, since the prototypes
%    have well-defined positions on the 2-dimensional map grid. SOM as
%    a projection is however a very crude one. Other projection
%    techniques include the principal component projection used
%    earlier, Sammon's mapping and Curvilinear Component Analysis
%    (to name a few). These have been implemented in functions
%    PCAPROJ, SAMMON and CCA. 

%    Projecting the map prototype vectors and joining neighboring map
%    units with lines gives the SOM its characteristic net-like look.
%    The projection figures can be linked to the map planes using
%    color coding.

%    Here is the distance matrix, color coding, a projection without
%    coloring and a projection with one. In the last projection,
%    the size of interpolating map units has been set to zero.

subplot(2,2,1)
som_cplane(sM,Um(:));
title('Distance matrix')

subplot(2,2,2)
C = som_colorcode(sM,'rgb4');
som_cplane(sM,C);
title('Color code')

subplot(2,2,3)
som_grid(sM,'Coord',Pm,'Linecolor','k');
title('PC-projection')

subplot(2,2,4)
h = som_hits(sM,sD); s=6*(h>0);
som_grid(sM,'Coord',Pm,'MarkerColor',C,'Linecolor','k','MarkerSize',s);
title('Colored PC-projection')

pause % Strike any key to visualize component planes...


clf
clc
%    2. VISUALIZATION OF COMPONENTS: COMPONENT PLANES
%    ================================================

%    The component planes visualizations shows what kind of values the
%    prototype vectors of the map units have for different vector
%    components.

%    Here is the U-matrix and the three component planes of the map.

som_show(sM)