%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 070600clf reset;figure(gcf)echo onclc%    ==========================================================%    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 dataPm        = pcaproj(sM.codebook,V,me); % project the prototypescolormap(hot);                         % colormap used for valuesecho offfor 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');endsubplot(2,2,4), claplot(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 onpause % 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;  endendecho onpause % 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 surfacespause % Strike any key to visualize clusters with distance matrices...clfclc%    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 vectorssubplot(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 earliersom_cplane(sM,C)title('Similarity coloring')pause % Strike any key to visualize shape and clusters with projections...clfclc%    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...clfclc%    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)