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%SOM_DEMO2 Basic usage of the SOM Toolbox.
% 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 070200
clf reset;
figure(gcf)
echo on
clc
% ==========================================================
% SOM_DEMO2 - BASIC USAGE OF SOM TOOLBOX
% ==========================================================
% som_data_struct - Create a data struct.
% som_read_data - Read data from file.
%
% som_normalize - Normalize data.
% som_denormalize - Denormalize data.
%
% som_make - Initialize and train the map.
%
% som_show - Visualize map.
% som_show_add - Add markers on som_show visualization.
% som_grid - Visualization with free coordinates.
%
% som_autolabel - Give labels to map.
% som_hits - Calculate hit histogram for the map.
% BASIC USAGE OF THE SOM TOOLBOX
% The basic usage of the SOM Toolbox proceeds like this:
% 1. construct data set
% 2. normalize it
% 3. train the map
% 4. visualize map
% 5. analyse results
% The four first items are - if default options are used - very
% simple operations, each executable with a single command. For
% the last, several different kinds of functions are provided in
% the Toolbox, but as the needs of analysis vary, a general default
% function or procedure does not exist.
pause % Strike any key to construct data...
clc
% STEP 1: CONSTRUCT DATA
% ======================
% The SOM Toolbox has a special struct, called data struct, which
% is used to group information regarding the data set in one
% place.
% Here, a data struct is created using function SOM_DATA_STRUCT.
% First argument is the data matrix itself, then is the name
% given to the data set, and the names of the components
% (variables) in the data matrix.
D = rand(1000,3); % 1000 samples from unit cube
sData = som_data_struct(D,'name','unit cube','comp_names',{'x','y','z'});
% Another option is to read the data directly from an ASCII file.
% Here, the IRIS data set is loaded from a file (please make sure
% the file can be found from the current path):
try,
sDiris = som_read_data('iris.data');
catch
echo off
warning('File ''iris.data'' not found. Using simulated data instead.')
D = randn(50,4);
D(:,1) = D(:,1)+5; D(:,2) = D(:,2)+3.5;
D(:,3) = D(:,3)/2+1.5; D(:,4) = D(:,4)/2+0.3;
D(find(D(:)<=0)) = 0.01;
D2 = randn(100,4); D2(:,2) = sort(D2(:,2));
D2(:,1) = D2(:,1)+6.5; D2(:,2) = D2(:,2)+2.8;
D2(:,3) = D2(:,3)+5; D2(:,4) = D2(:,4)/2+1.5;
D2(find(D2(:)<=0)) = 0.01;
sDiris = som_data_struct([D; D2],'name','iris (simulated)',...
'comp_names',{'SepalL','SepalW','PetalL','PetalW'});
sDiris = som_label(sDiris,'add',[1:50]','Setosa');
sDiris = som_label(sDiris,'add',[51:100]','Versicolor');
sDiris = som_label(sDiris,'add',[101:150]','Virginica');
echo on
end
% Here are the histograms and scatter plots of the four variables.
echo off
k=1;
for i=1:4,
for j=1:4,
if i==j,
subplot(4,4,k);
hist(sDiris.data(:,i)); title(sDiris.comp_names{i})
elseif i<j,
subplot(4,4,k);
plot(sDiris.data(:,i),sDiris.data(:,j),'k.')
xlabel(sDiris.comp_names{i})
ylabel(sDiris.comp_names{j})
end
k=k+1;
end
end
echo on
% Actually, as you saw in SOM_DEMO1, most SOM Toolbox functions
% can also handle plain data matrices, but then one is without the
% convenience offered by component names, labels and
% denormalization operations.
pause % Strike any key to normalize the data...
clc
% STEP 2: DATA NORMALIZATION
% ==========================
% Since SOM algorithm is based on Euclidian distances, the scale of
% the variables is very important in determining what the map will
% be like. If the range of values of some variable is much bigger
% than of the other variables, that variable will probably dominate
% the map organization completely.
% For this reason, the components of the data set are usually
% normalized, for example so that each component has unit
% variance. This can be done with function SOM_NORMALIZE:
sDiris = som_normalize(sDiris,'var');
% The function has also other normalization methods.
% However, interpreting the values may be harder when they have
% been normalized. Therefore, the normalization operations can be
% reversed with function SOM_DENORMALIZE:
x = sDiris.data(1,:)
orig_x = som_denormalize(x,sDiris)
pause % Strike any key to to train the map...
clc
% STEP 3: MAP TRAINING
% ====================
% The function SOM_MAKE is used to train the SOM. By default, it
% first determines the map size, then initializes the map using
% linear initialization, and finally uses batch algorithm to train
% the map. Function SOM_DEMO1 has a more detailed description of
% the training process.
sMap = som_make(sDiris);
pause % Strike any key to continues...
% The IRIS data set also has labels associated with the data
% samples. Actually, the data set consists of 50 samples of three
% species of Iris-flowers (a total of 150 samples) such that the
% measurements are width and height of sepal and petal leaves. The
% label associated with each sample is the species information:
% 'Setosa', 'Versicolor' or 'Virginica'.
% Now, the map can be labelled with these labels. The best
% matching unit of each sample is found from the map, and the
% species label is given to the map unit. Function SOM_AUTOLABEL
% can be used to do this:
sMap = som_autolabel(sMap,sDiris,'vote');
pause % Strike any key to visualize the map...
clc
% STEP 4: VISUALIZING THE SELF-ORGANIZING MAP: SOM_SHOW
% =====================================================
% The basic visualization of the SOM is done with function SOM_SHOW.
colormap(1-gray)
som_show(sMap,'norm','d')
% Notice that the names of the components are included as the
% titles of the subplots. Notice also that the variable values
% have been denormalized to the original range and scale.
% The component planes ('PetalL', 'PetalW', 'SepalL' and 'SepalW')
% show what kind of values the prototype vectors of the map units
% have. The value is indicated with color, and the colorbar on the
% right shows what the colors mean.
% The 'U-matrix' shows distances between neighboring units and thus
% visualizes the cluster structure of the map. Note that the
% U-matrix visualization has much more hexagons that the
% component planes. This is because distances *between* map units
% are shown, and not only the distance values *at* the map units.
% High values on the U-matrix mean large distance between
% neighboring map units, and thus indicate cluster
% borders. Clusters are typically uniform areas of low
% values. Refer to colorbar to see which colors mean high
% values. In the IRIS map, there appear to be two clusters.
pause % Strike any key to continue...
% The subplots are linked together through similar position. In
% each axis, a particular map unit is always in the same place. For
% example:
h=zeros(sMap.topol.msize); h(1,2) = 1;
som_show_add('hit',h(:),'markercolor','r','markersize',0.5,'subplot','all')
% the red marker is on top of the same unit on each axis.
pause % Strike any key to continue...
clf
clc
% STEP 4: VISUALIZING THE SELF-ORGANIZING MAP: SOM_SHOW_ADD
% =========================================================
% The SOM_SHOW_ADD function can be used to add markers, labels and
% trajectories on top of SOM_SHOW created figures. The function
% SOM_SHOW_CLEAR can be used to clear them away.
% Here, the U-matrix is shown on the left, and an empty grid
% named 'Labels' is shown on the right.
som_show(sMap,'umat','all','empty','Labels')
pause % Strike any key to add labels...
% Here, the labels added to the map with SOM_AUTOLABEL function
% are shown on the empty grid.
som_show_add('label',sMap,'Textsize',8,'TextColor','r','Subplot',2)
pause % Strike any key to add hits...
% An important tool in data analysis using SOM are so called hit
% histograms. They are formed by taking a data set, finding the BMU
% of each data sample from the map, and increasing a counter in a
% map unit each time it is the BMU. The hit histogram shows the
% distribution of the data set on the map.
% Here, the hit histogram for the whole data set is calculated
% and visualized on the U-matrix.
h = som_hits(sMap,sDiris);
som_show_add('hit',h,'MarkerColor','w','Subplot',1)
pause % Strike any key to continue...
% Multiple hit histograms can be shown simultaniously. Here, three
% hit histograms corresponding to the three species of Iris
% flowers is calculated and shown.
% First, the old hit histogram is removed.
som_show_clear('hit',1)
% Then, the histograms are calculated. The first 50 samples in
% the data set are of the 'Setosa' species, the next 50 samples
% of the 'Versicolor' species and the last 50 samples of the
% 'Virginica' species.
h1 = som_hits(sMap,sDiris.data(1:50,:));
h2 = som_hits(sMap,sDiris.data(51:100,:));
h3 = som_hits(sMap,sDiris.data(101:150,:));
som_show_add('hit',[h1, h2, h3],'MarkerColor',[1 0 0; 0 1 0; 0 0 1],'Subplot',1)
% Red color is for 'Setosa', green for 'Versicolor' and blue for
% 'Virginica'. One can see that the three species are pretty well
% separated, although 'Versicolor' and 'Virginica' are slightly
% mixed up.
pause % Strike any key to continue...
clf
clc
% STEP 4: VISUALIZING THE SELF-ORGANIZING MAP: SOM_GRID
% =====================================================
% There's also another visualization function: SOM_GRID. This
% allows visualization of the SOM in freely specified coordinates,
% for example the input space (of course, only upto 3D space). This
% function has quite a lot of options, and is pretty flexible.
% Basically, the SOM_GRID visualizes the SOM network: each unit is
% shown with a marker and connected to its neighbors with lines.
% The user has control over:
% - the coordinate of each unit (2D or 3D)
% - the marker type, color and size of each unit
% - the linetype, color and width of the connecting lines
% There are also some other options.
pause % Strike any key to see some visualizations...
% Here are four visualizations made with SOM_GRID:
% - The map grid in the output space.
subplot(2,2,1)
som_grid(sMap,'Linecolor','k')
view(0,-90), title('Map grid')
% - A surface plot of distance matrix: both color and
% z-coordinate indicate average distance to neighboring
% map units. This is closely related to the U-matrix.
subplot(2,2,2)
Co=som_unit_coords(sMap); U=som_umat(sMap); U=U(1:2:size(U,1),1:2:size(U,2));
som_grid(sMap,'Coord',[Co, U(:)],'Surf',U(:),'Marker','none');
view(-80,45), axis tight, title('Distance matrix')
% - The map grid in the output space. Three first components
% determine the 3D-coordinates of the map unit, and the size
% of the marker is determined by the fourth component.
% Note that the values have been denormalized.
subplot(2,2,3)
M = som_denormalize(sMap.codebook,sMap);
som_grid(sMap,'Coord',M(:,1:3),'MarkerSize',M(:,4)*2)
view(-80,45), axis tight, title('Prototypes')
% - Map grid as above, but the original data has been plotted
% also: coordinates show the values of three first components
% and color indicates the species of each sample. Fourth
% component is not shown.
subplot(2,2,4)
som_grid(sMap,'Coord',M(:,1:3),'MarkerSize',M(:,4)*2)
hold on
D = som_denormalize(sDiris.data,sDiris);
plot3(D(1:50,1),D(1:50,2),D(1:50,3),'r.',...
D(51:100,1),D(51:100,2),D(51:100,3),'g.',...
D(101:150,1),D(101:150,2),D(101:150,3),'b.')
view(-72,64), axis tight, title('Prototypes and data')
pause % Strike any key to continue...
% STEP 5: ANALYSIS OF RESULTS
% ===========================
% The purpose of this step highly depends on the purpose of the
% whole data analysis: is it segmentation, modeling, novelty
% detection, classification, or something else? For this reason,
% there is not a single general-purpose analysis function, but
% a number of individual functions which may, or may not, prove
% useful in any specific case.
% Visualization is of course part of the analysis of
% results. Examination of labels and hit histograms is another
% part. Yet another is validation of the quality of the SOM (see
% the use of SOM_QUALITY in SOM_DEMO1).
[qe,te] = som_quality(sMap,sDiris)
% People have contributed a number of functions to the Toolbox
% which can be used for the analysis. These include functions for
% vector projection, clustering, pdf-estimation, modeling,
% classification, etc. However, ultimately the use of these
% tools is up to you.
% More about visualization is presented in SOM_DEMO3.
% More about data analysis is presented in SOM_DEMO4.
echo off
warning on