wolffd@0: 
wolffd@0: %SOM_DEMO2 Basic usage of the SOM Toolbox.
wolffd@0: 
wolffd@0: % Contributed to SOM Toolbox 2.0, February 11th, 2000 by Juha Vesanto
wolffd@0: % http://www.cis.hut.fi/projects/somtoolbox/
wolffd@0: 
wolffd@0: % Version 1.0beta juuso 071197 
wolffd@0: % Version 2.0beta juuso 070200
wolffd@0: 
wolffd@0: clf reset;
wolffd@0: figure(gcf)
wolffd@0: echo on
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clc
wolffd@0: %    ==========================================================
wolffd@0: %    SOM_DEMO2 - BASIC USAGE OF SOM TOOLBOX
wolffd@0: %    ==========================================================
wolffd@0: 
wolffd@0: %    som_data_struct    - Create a data struct.
wolffd@0: %    som_read_data      - Read data from file.
wolffd@0: %
wolffd@0: %    som_normalize      - Normalize data.
wolffd@0: %    som_denormalize    - Denormalize data.
wolffd@0: %
wolffd@0: %    som_make           - Initialize and train the map. 
wolffd@0: %
wolffd@0: %    som_show           - Visualize map.
wolffd@0: %    som_show_add       - Add markers on som_show visualization.
wolffd@0: %    som_grid           - Visualization with free coordinates.
wolffd@0: %
wolffd@0: %    som_autolabel      - Give labels to map.
wolffd@0: %    som_hits           - Calculate hit histogram for the map.
wolffd@0: 
wolffd@0: %    BASIC USAGE OF THE SOM TOOLBOX
wolffd@0: 
wolffd@0: %    The basic usage of the SOM Toolbox proceeds like this: 
wolffd@0: %      1. construct data set
wolffd@0: %      2. normalize it
wolffd@0: %      3. train the map
wolffd@0: %      4. visualize map
wolffd@0: %      5. analyse results
wolffd@0: 
wolffd@0: %    The four first items are - if default options are used - very
wolffd@0: %    simple operations, each executable with a single command.  For
wolffd@0: %    the last, several different kinds of functions are provided in
wolffd@0: %    the Toolbox, but as the needs of analysis vary, a general default
wolffd@0: %    function or procedure does not exist. 
wolffd@0: 
wolffd@0: pause % Strike any key to construct data...
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clc
wolffd@0: %    STEP 1: CONSTRUCT DATA
wolffd@0: %    ======================
wolffd@0: 
wolffd@0: %    The SOM Toolbox has a special struct, called data struct, which
wolffd@0: %    is used to group information regarding the data set in one
wolffd@0: %    place.
wolffd@0: 
wolffd@0: %    Here, a data struct is created using function SOM_DATA_STRUCT.
wolffd@0: %    First argument is the data matrix itself, then is the name 
wolffd@0: %    given to the data set, and the names of the components
wolffd@0: %    (variables) in the data matrix.
wolffd@0: 
wolffd@0: D = rand(1000,3); % 1000 samples from unit cube
wolffd@0: sData = som_data_struct(D,'name','unit cube','comp_names',{'x','y','z'});
wolffd@0: 			
wolffd@0: %    Another option is to read the data directly from an ASCII file.
wolffd@0: %    Here, the IRIS data set is loaded from a file (please make sure
wolffd@0: %    the file can be found from the current path):
wolffd@0: 
wolffd@0: try, 
wolffd@0:   sDiris = som_read_data('iris.data');
wolffd@0: catch
wolffd@0:   echo off
wolffd@0: 
wolffd@0:   warning('File ''iris.data'' not found. Using simulated data instead.')
wolffd@0:   
wolffd@0:   D = randn(50,4); 
wolffd@0:   D(:,1) = D(:,1)+5;     D(:,2) = D(:,2)+3.5; 
wolffd@0:   D(:,3) = D(:,3)/2+1.5; D(:,4) = D(:,4)/2+0.3;
wolffd@0:   D(find(D(:)<=0)) = 0.01; 
wolffd@0:   
wolffd@0:   D2 = randn(100,4); D2(:,2) = sort(D2(:,2));
wolffd@0:   D2(:,1) = D2(:,1)+6.5; D2(:,2) = D2(:,2)+2.8; 
wolffd@0:   D2(:,3) = D2(:,3)+5;   D2(:,4) = D2(:,4)/2+1.5;
wolffd@0:   D2(find(D2(:)<=0)) = 0.01; 
wolffd@0:   
wolffd@0:   sDiris = som_data_struct([D; D2],'name','iris (simulated)',...
wolffd@0: 			  'comp_names',{'SepalL','SepalW','PetalL','PetalW'});
wolffd@0:   sDiris = som_label(sDiris,'add',[1:50]','Setosa');
wolffd@0:   sDiris = som_label(sDiris,'add',[51:100]','Versicolor');
wolffd@0:   sDiris = som_label(sDiris,'add',[101:150]','Virginica');
wolffd@0:   
wolffd@0:   echo on
wolffd@0: end
wolffd@0: 
wolffd@0: %     Here are the histograms and scatter plots of the four variables.
wolffd@0: 
wolffd@0: echo off 
wolffd@0: k=1;
wolffd@0: for i=1:4, 
wolffd@0:   for j=1:4, 
wolffd@0:     if i==j, 
wolffd@0:       subplot(4,4,k); 
wolffd@0:       hist(sDiris.data(:,i)); title(sDiris.comp_names{i})
wolffd@0:     elseif i<j, 
wolffd@0:       subplot(4,4,k); 
wolffd@0:       plot(sDiris.data(:,i),sDiris.data(:,j),'k.')
wolffd@0:       xlabel(sDiris.comp_names{i})
wolffd@0:       ylabel(sDiris.comp_names{j})
wolffd@0:     end
wolffd@0:     k=k+1;
wolffd@0:   end
wolffd@0: end
wolffd@0: echo on
wolffd@0: 
wolffd@0: %     Actually, as you saw in SOM_DEMO1, most SOM Toolbox functions
wolffd@0: %     can also handle plain data matrices, but then one is without the
wolffd@0: %     convenience offered by component names, labels and
wolffd@0: %     denormalization operations.
wolffd@0: 
wolffd@0: 
wolffd@0: pause % Strike any key to normalize the data...
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clc
wolffd@0: %    STEP 2: DATA NORMALIZATION
wolffd@0: %    ==========================
wolffd@0: 
wolffd@0: %    Since SOM algorithm is based on Euclidian distances, the scale of
wolffd@0: %    the variables is very important in determining what the map will
wolffd@0: %    be like. If the range of values of some variable is much bigger
wolffd@0: %    than of the other variables, that variable will probably dominate
wolffd@0: %    the map organization completely. 
wolffd@0: 
wolffd@0: %    For this reason, the components of the data set are usually
wolffd@0: %    normalized, for example so that each component has unit
wolffd@0: %    variance. This can be done with function SOM_NORMALIZE:
wolffd@0: 
wolffd@0: sDiris = som_normalize(sDiris,'var');
wolffd@0: 
wolffd@0: %    The function has also other normalization methods.
wolffd@0: 
wolffd@0: %    However, interpreting the values may be harder when they have
wolffd@0: %    been normalized. Therefore, the normalization operations can be
wolffd@0: %    reversed with function SOM_DENORMALIZE:
wolffd@0: 
wolffd@0: x = sDiris.data(1,:)
wolffd@0: 
wolffd@0: orig_x = som_denormalize(x,sDiris)
wolffd@0: 
wolffd@0: pause % Strike any key to to train the map...
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clc
wolffd@0: %    STEP 3: MAP TRAINING
wolffd@0: %    ====================
wolffd@0: 
wolffd@0: %    The function SOM_MAKE is used to train the SOM. By default, it
wolffd@0: %    first determines the map size, then initializes the map using
wolffd@0: %    linear initialization, and finally uses batch algorithm to train
wolffd@0: %    the map.  Function SOM_DEMO1 has a more detailed description of
wolffd@0: %    the training process.
wolffd@0: 
wolffd@0: sMap = som_make(sDiris);
wolffd@0: 
wolffd@0: 
wolffd@0: pause % Strike any key to continues...
wolffd@0: 
wolffd@0: %    The IRIS data set also has labels associated with the data
wolffd@0: %    samples. Actually, the data set consists of 50 samples of three
wolffd@0: %    species of Iris-flowers (a total of 150 samples) such that the
wolffd@0: %    measurements are width and height of sepal and petal leaves. The
wolffd@0: %    label associated with each sample is the species information:
wolffd@0: %    'Setosa', 'Versicolor' or 'Virginica'.
wolffd@0: 
wolffd@0: %    Now, the map can be labelled with these labels. The best
wolffd@0: %    matching unit of each sample is found from the map, and the
wolffd@0: %    species label is given to the map unit. Function SOM_AUTOLABEL 
wolffd@0: %    can be used to do this: 
wolffd@0: 
wolffd@0: sMap = som_autolabel(sMap,sDiris,'vote');
wolffd@0: 
wolffd@0: pause % Strike any key to visualize the map...
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clc
wolffd@0: %    STEP 4: VISUALIZING THE SELF-ORGANIZING MAP: SOM_SHOW
wolffd@0: %    =====================================================
wolffd@0: 
wolffd@0: %    The basic visualization of the SOM is done with function SOM_SHOW.
wolffd@0: 
wolffd@0: colormap(1-gray)
wolffd@0: som_show(sMap,'norm','d')
wolffd@0: 
wolffd@0: %    Notice that the names of the components are included as the
wolffd@0: %    titles of the subplots. Notice also that the variable values
wolffd@0: %    have been denormalized to the original range and scale.
wolffd@0: 
wolffd@0: %    The component planes ('PetalL', 'PetalW', 'SepalL' and 'SepalW')
wolffd@0: %    show what kind of values the prototype vectors of the map units
wolffd@0: %    have. The value is indicated with color, and the colorbar on the
wolffd@0: %    right shows what the colors mean.
wolffd@0: 
wolffd@0: %    The 'U-matrix' shows distances between neighboring units and thus
wolffd@0: %    visualizes the cluster structure of the map. Note that the
wolffd@0: %    U-matrix visualization has much more hexagons that the
wolffd@0: %    component planes. This is because distances *between* map units
wolffd@0: %    are shown, and not only the distance values *at* the map units. 
wolffd@0: 
wolffd@0: %    High values on the U-matrix mean large distance between
wolffd@0: %    neighboring map units, and thus indicate cluster
wolffd@0: %    borders. Clusters are typically uniform areas of low
wolffd@0: %    values. Refer to colorbar to see which colors mean high
wolffd@0: %    values. In the IRIS map, there appear to be two clusters.
wolffd@0: 
wolffd@0: pause % Strike any key to continue...
wolffd@0: 
wolffd@0: %    The subplots are linked together through similar position. In
wolffd@0: %    each axis, a particular map unit is always in the same place. For
wolffd@0: %    example:
wolffd@0: 
wolffd@0: h=zeros(sMap.topol.msize); h(1,2) = 1;
wolffd@0: som_show_add('hit',h(:),'markercolor','r','markersize',0.5,'subplot','all')
wolffd@0: 
wolffd@0: %    the red marker is on top of the same unit on each axis. 
wolffd@0: 
wolffd@0: pause % Strike any key to continue...
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clf
wolffd@0: 
wolffd@0: clc
wolffd@0: 
wolffd@0: %    STEP 4: VISUALIZING THE SELF-ORGANIZING MAP: SOM_SHOW_ADD
wolffd@0: %    =========================================================
wolffd@0: 
wolffd@0: %    The SOM_SHOW_ADD function can be used to add markers, labels and
wolffd@0: %    trajectories on top of SOM_SHOW created figures. The function
wolffd@0: %    SOM_SHOW_CLEAR can be used to clear them away.
wolffd@0: 
wolffd@0: %    Here, the U-matrix is shown on the left, and an empty grid
wolffd@0: %    named 'Labels' is shown on the right.
wolffd@0: 
wolffd@0: som_show(sMap,'umat','all','empty','Labels')
wolffd@0: 
wolffd@0: pause % Strike any key to add labels...
wolffd@0: 
wolffd@0: %    Here, the labels added to the map with SOM_AUTOLABEL function
wolffd@0: %    are shown on the empty grid.
wolffd@0: 
wolffd@0: som_show_add('label',sMap,'Textsize',8,'TextColor','r','Subplot',2)
wolffd@0: 
wolffd@0: pause % Strike any key to add hits...
wolffd@0: 
wolffd@0: %    An important tool in data analysis using SOM are so called hit
wolffd@0: %    histograms. They are formed by taking a data set, finding the BMU
wolffd@0: %    of each data sample from the map, and increasing a counter in a
wolffd@0: %    map unit each time it is the BMU. The hit histogram shows the
wolffd@0: %    distribution of the data set on the map.
wolffd@0: 
wolffd@0: %    Here, the hit histogram for the whole data set is calculated
wolffd@0: %    and visualized on the U-matrix.
wolffd@0: 
wolffd@0: h = som_hits(sMap,sDiris);
wolffd@0: som_show_add('hit',h,'MarkerColor','w','Subplot',1)
wolffd@0: 
wolffd@0: pause % Strike any key to continue...
wolffd@0: 
wolffd@0: %    Multiple hit histograms can be shown simultaniously. Here, three
wolffd@0: %    hit histograms corresponding to the three species of Iris
wolffd@0: %    flowers is calculated and shown. 
wolffd@0: 
wolffd@0: %    First, the old hit histogram is removed.
wolffd@0: 
wolffd@0: som_show_clear('hit',1)
wolffd@0: 
wolffd@0: %    Then, the histograms are calculated. The first 50 samples in
wolffd@0: %    the data set are of the 'Setosa' species, the next 50 samples
wolffd@0: %    of the 'Versicolor' species and the last 50 samples of the
wolffd@0: %    'Virginica' species. 
wolffd@0: 
wolffd@0: h1 = som_hits(sMap,sDiris.data(1:50,:));
wolffd@0: h2 = som_hits(sMap,sDiris.data(51:100,:));
wolffd@0: h3 = som_hits(sMap,sDiris.data(101:150,:));
wolffd@0: 
wolffd@0: som_show_add('hit',[h1, h2, h3],'MarkerColor',[1 0 0; 0 1 0; 0 0 1],'Subplot',1)
wolffd@0: 
wolffd@0: %    Red color is for 'Setosa', green for 'Versicolor' and blue for
wolffd@0: %    'Virginica'. One can see that the three species are pretty well
wolffd@0: %    separated, although 'Versicolor' and 'Virginica' are slightly
wolffd@0: %    mixed up.
wolffd@0: 
wolffd@0: pause % Strike any key to continue...
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: clf
wolffd@0: clc
wolffd@0: 
wolffd@0: %    STEP 4: VISUALIZING THE SELF-ORGANIZING MAP: SOM_GRID
wolffd@0: %    =====================================================
wolffd@0: 
wolffd@0: %    There's also another visualization function: SOM_GRID.  This
wolffd@0: %    allows visualization of the SOM in freely specified coordinates,
wolffd@0: %    for example the input space (of course, only upto 3D space). This
wolffd@0: %    function has quite a lot of options, and is pretty flexible.
wolffd@0: 
wolffd@0: %    Basically, the SOM_GRID visualizes the SOM network: each unit is
wolffd@0: %    shown with a marker and connected to its neighbors with lines.
wolffd@0: %    The user has control over: 
wolffd@0: %     - the coordinate of each unit (2D or 3D)
wolffd@0: %     - the marker type, color and size of each unit
wolffd@0: %     - the linetype, color and width of the connecting lines
wolffd@0: %    There are also some other options.
wolffd@0: 
wolffd@0: pause % Strike any key to see some visualizations...
wolffd@0: 
wolffd@0: %    Here are four visualizations made with SOM_GRID: 
wolffd@0: %     - The map grid in the output space.
wolffd@0: 
wolffd@0: subplot(2,2,1)
wolffd@0: som_grid(sMap,'Linecolor','k')
wolffd@0: view(0,-90), title('Map grid')
wolffd@0: 
wolffd@0: %     - A surface plot of distance matrix: both color and 
wolffd@0: %       z-coordinate indicate average distance to neighboring 
wolffd@0: %       map units. This is closely related to the U-matrix.
wolffd@0: 
wolffd@0: subplot(2,2,2)
wolffd@0: Co=som_unit_coords(sMap); U=som_umat(sMap); U=U(1:2:size(U,1),1:2:size(U,2));
wolffd@0: som_grid(sMap,'Coord',[Co, U(:)],'Surf',U(:),'Marker','none');
wolffd@0: view(-80,45), axis tight, title('Distance matrix')
wolffd@0: 
wolffd@0: %     - The map grid in the output space. Three first components
wolffd@0: %       determine the 3D-coordinates of the map unit, and the size
wolffd@0: %       of the marker is determined by the fourth component.
wolffd@0: %       Note that the values have been denormalized.
wolffd@0: 
wolffd@0: subplot(2,2,3)
wolffd@0: M = som_denormalize(sMap.codebook,sMap);
wolffd@0: som_grid(sMap,'Coord',M(:,1:3),'MarkerSize',M(:,4)*2)
wolffd@0: view(-80,45), axis tight, title('Prototypes')
wolffd@0: 
wolffd@0: %     - Map grid as above, but the original data has been plotted
wolffd@0: %       also: coordinates show the values of three first components
wolffd@0: %       and color indicates the species of each sample.  Fourth
wolffd@0: %       component is not shown.
wolffd@0: 
wolffd@0: subplot(2,2,4)
wolffd@0: som_grid(sMap,'Coord',M(:,1:3),'MarkerSize',M(:,4)*2)
wolffd@0: hold on
wolffd@0: D = som_denormalize(sDiris.data,sDiris); 
wolffd@0: plot3(D(1:50,1),D(1:50,2),D(1:50,3),'r.',...
wolffd@0:       D(51:100,1),D(51:100,2),D(51:100,3),'g.',...
wolffd@0:       D(101:150,1),D(101:150,2),D(101:150,3),'b.')
wolffd@0: view(-72,64), axis tight, title('Prototypes and data')
wolffd@0: 
wolffd@0: pause % Strike any key to continue...
wolffd@0: 
wolffd@0: %    STEP 5: ANALYSIS OF RESULTS
wolffd@0: %    ===========================
wolffd@0: 
wolffd@0: %    The purpose of this step highly depends on the purpose of the
wolffd@0: %    whole data analysis: is it segmentation, modeling, novelty
wolffd@0: %    detection, classification, or something else? For this reason, 
wolffd@0: %    there is not a single general-purpose analysis function, but 
wolffd@0: %    a number of individual functions which may, or may not, prove 
wolffd@0: %    useful in any specific case.
wolffd@0: 
wolffd@0: %    Visualization is of course part of the analysis of
wolffd@0: %    results. Examination of labels and hit histograms is another
wolffd@0: %    part. Yet another is validation of the quality of the SOM (see
wolffd@0: %    the use of SOM_QUALITY in SOM_DEMO1).
wolffd@0: 
wolffd@0: [qe,te] = som_quality(sMap,sDiris)
wolffd@0: 
wolffd@0: %    People have contributed a number of functions to the Toolbox
wolffd@0: %    which can be used for the analysis. These include functions for 
wolffd@0: %    vector projection, clustering, pdf-estimation, modeling,
wolffd@0: %    classification, etc. However, ultimately the use of these
wolffd@0: %    tools is up to you.
wolffd@0: 
wolffd@0: %    More about visualization is presented in SOM_DEMO3.
wolffd@0: %    More about data analysis is presented in SOM_DEMO4.
wolffd@0: 
wolffd@0: echo off
wolffd@0: warning on
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: