pause % Strike any key to continue...%    Besides SOM_SHOW and SOM_CPLANE, there are three other%    functions specifically designed for showing the values of the %    component planes: SOM_PIEPLANE, SOM_BARPLANE, SOM_PLOTPLANE. %    SOM_PIEPLANE shows a single pie chart for each map unit.  Each%    pie shows the relative proportion of each component of the sum of%    all components in that map unit. The component values must be%    positive. %    SOM_BARPLANE shows a barchart in each map unit. The scaling of %    bars can be made unit-wise or variable-wise. By default it is%    determined variable-wise.%    SOM_PLOTPLANE shows a linegraph in each map unit. M = som_normalize(sM.codebook,'range'); subplot(1,3,1)som_pieplane(sM, M);title('som\_pieplane')subplot(1,3,2)som_barplane(sM, M, '', 'unitwise');title('som\_barplane')subplot(1,3,3)som_plotplane(sM, M, 'b');title('som\_plotplane')pause % Strike any key to visualize cluster properties...clfclc%    2. VISUALIZATION OF COMPONENTS: CLUSTERS%    ========================================%    An interesting question is of course how do the values of the%    variables relate to the clusters: what are the values of the%    components in the clusters, and which components are the ones%    which *make* the clusters.som_show(sM)%    From the U-matrix and component planes, one can easily see%    what the typical values are in each cluster. pause % Strike any key to continue...%    The significance of the components with respect to the clustering%    is harder to visualize. One indication of importance is that on%    the borders of the clusters, values of important variables change%    very rabidly.%    Here, the distance matrix is calculated with respect to each%    variable. u1 = som_umat(sM,'mask',[1 0 0]'); u1=u1(1:2:size(u1,1),1:2:size(u1,2));u2 = som_umat(sM,'mask',[0 1 0]'); u2=u2(1:2:size(u2,1),1:2:size(u2,2));u3 = som_umat(sM,'mask',[0 0 1]'); u3=u3(1:2:size(u3,1),1:2:size(u3,2));%    Here, the distance matrices are shown, as well as a piechart%    indicating the relative importance of each variable in each%    map unit. The size of piecharts has been scaled by the%    distance matrix calculated from all components.subplot(2,2,1)som_cplane(sM,u1(:));title(sM.comp_names{1})subplot(2,2,2)som_cplane(sM,u2(:));title(sM.comp_names{2})subplot(2,2,3)som_cplane(sM,u3(:));title(sM.comp_names{3})subplot(2,2,4)som_pieplane(sM, [u1(:), u2(:), u3(:)], hsv(3), Um(:)/max(Um(:)));title('Relative importance')%    From the last subplot, one can see that in the area where the%    bigger cluster border is, the 'X-coord' component (red color)%    has biggest effect, and thus is the main factor in separating%    that cluster from the rest.pause % Strike any key to learn about correlation hunting...clfclc%    2. VISUALIZATION OF COMPONENTS: CORRELATION HUNTING%    ===================================================%    Finally, the component planes are often used for correlation%    hunting. When the number of variables is high, the component%    plane visualization offers a convenient way to visualize all%    components at once and hunt for correlations (as opposed to%    N*(N-1)/2 scatterplots).%    Hunting correlations this way is not very accurate. However, it%    is easy to select interesting combinations for further%    investigation.%    Here, the first and third components are shown with scatter%    plot. As with projections, a color coding is used to link the%    visualization to the map plane. In the color coding, size shows%    the distance matrix information.C = som_colorcode(sM);subplot(1,2,1)som_cplane(sM,C,1-Um(:)/max(Um(:)));title('Color coding + distance matrix')subplot(1,2,2)som_grid(sM,'Coord',sM.codebook(:,[1 3]),'MarkerColor',C);title('Scatter plot'); xlabel(sM.comp_names{1}); ylabel(sM.comp_names{3})axis equalpause % Strike any key to visualize data responses...clfclc%    3. DATA ON MAP%    ==============%    The SOM is a map of the data manifold. An interesting question%    then is where on the map a specific data sample is located, and%    how accurate is that localization? One is interested in the%    response of the map to the data sample. %    The simplest answer is to find the BMU of the data sample.%    However, this gives no indication of the accuracy of the%    match. Is the data sample close to the BMU, or is it actually%    equally close to the neighboring map units (or even approximately%    as close to all map units)? Sometimes accuracy doesn't really%    matter, but if it does, it should be visualized somehow.%    Here are different kinds of response visualizations for two%    vectors: [0 0 0] and [99 99 99]. %     - BMUs indicated with labels       %     - BMUs indicated with markers, relative quantization errors%       (in this case, proportion between distances to BMU and %       Worst-MU) with vertical lines%     - quantization error between the samples and all map units %     - fuzzy response (a non-linear function of quantization%       error) of all map unitsecho off[bm,qe] = som_bmus(sM,[0 0 0; 99 99 99],'all'); % distance to all map units[dummy,ind] = sort(bm(1,:)); d0 = qe(1,ind)'; [dummy,ind] = sort(bm(2,:)); d9 = qe(2,ind)'; bmu0 = bm(1,1); bmu9 = bm(2,1); % bmush0 = zeros(prod(sM.topol.msize),1); h0(bmu0) = 1; % crisp hitsh9 = zeros(prod(sM.topol.msize),1); h9(bmu9) = 1; lab = cell(prod(sM.topol.msize),1); lab{bmu0} = '[0,0,0]'; lab{bmu9} = '[99,99,99]';hf0 = som_hits(sM,[0 0 0],'fuzzy'); % fuzzy responsehf9 = som_hits(sM,[99 99 99],'fuzzy'); som_show(sM,'umat',{'all','BMU'},...	 'color',{d0,'Qerror 0'},'color',{hf0,'Fuzzy response 0'},...	 'empty','BMU+qerror',...	 'color',{d9,'Qerror 99'},'color',{hf9,'Fuzzy response 99'});	 som_show_add('label',lab,'Subplot',1,'Textcolor','r');som_show_add('hit',[h0, h9],'Subplot',4,'MarkerColor','r');hold onCo = som_vis_coords(sM.topol.lattice,sM.topol.msize);plot3(Co(bmu0,[1 1]),Co(bmu0,[2 2]),[0 10*qe(1,1)/qe(1,end)],'r-')plot3(Co(bmu9,[1 1]),Co(bmu9,[2 2]),[0 10*qe(2,1)/qe(2,end)],'r-')view(3), axis equalecho on%    Here are the distances to BMU, 2-BMU and WMU:qe(1,[1,2,end]) % [0 0 0]qe(2,[1,2,end]) % [99 99 99]%    One can see that for [0 0 0] the accuracy is pretty good as the%    quantization error of the BMU is much lower than that of the%    WMU. On the other hand [99 99 99] is very far from the map:%    distance to BMU is almost equal to distance to WMU.pause % Strike any key to visualize responses of multiple samples...clcclf%    3. DATA ON MAP: HIT HISTOGRAMS%    ==============================%    One can also investigate whole data sets using the map. When the%    BMUs of multiple data samples are aggregated, a hit histogram%    results. Instead of BMUs, one can also aggregate for example%    fuzzy responses.%    The hit histograms (or aggregated responses) can then be compared%    with each other. %    Here are hit histograms of three data sets: one with 50 first%    vectors of the data set, one with 150 samples from the data%    set, and one with 50 randomly selected samples. In the last%    subplot, the fuzzy response of the first data set.dlen = size(sD.data,1);Dsample1 = sD.data(1:50,:); h1 = som_hits(sM,Dsample1); Dsample2 = sD.data(1:150,:); h2 = som_hits(sM,Dsample2); Dsample3 = sD.data(ceil(rand(50,1)*dlen),:); h3 = som_hits(sM,Dsample3); hf = som_hits(sM,Dsample1,'fuzzy');som_show(sM,'umat','all','umat','all','umat','all','color',{hf,'Fuzzy'})som_show_add('hit',h1,'Subplot',1,'Markercolor','r')som_show_add('hit',h2,'Subplot',2,'Markercolor','r')som_show_add('hit',h3,'Subplot',3,'Markercolor','r')pause % Strike any key to visualize trajectories...clcclf%    3. DATA ON MAP: TRAJECTORIES%    ============================%    A special data mapping technique is trajectory. If the samples%    are ordered, forming a time-series for example, their response on%    the map can be tracked. The function SOM_SHOW_ADD can be used to%    show the trajectories in two different modes: 'traj' and 'comet'.%    Here, a series of data points is formed which go from [8,0,0]%    to [2,2,2]. The trajectory is plotted using the two modes.Dtraj = [linspace(9,2,20); linspace(0,2,20); linspace(0,2,20)]';T = som_bmus(sM,Dtraj);som_show(sM,'comp',[1 1]);som_show_add('traj',T,'Markercolor','r','TrajColor','r','subplot',1);som_show_add('comet',T,'MarkerColor','r','subplot',2);%    There's also a function SOM_TRAJECTORY which lauches a GUI%    specifically designed for displaying trajectories (in 'comet'%    mode).pause % Strike any key to learn about color handling...clcclf%    COLOR HANDLING%    ==============%    Matlab offers flexibility in the colormaps. Using the COLORMAP%    function, the colormap may be changed. There are several useful%    colormaps readily available, for example 'hot' and 'jet'. The%    default number of colors in the colormaps is 64. However, it is%    often advantageous to use less colors in the colormap. This way%    the components planes visualization become easier to interpret.%    Here the three component planes are visualized using the 'hot'%    colormap and only three colors.som_show(sM,'comp',[1 2 3])colormap(hot(3));som_recolorbar pause % Press any key to change the colorbar labels...%     The function SOM_RECOLORBAR can be used to reconfigure%     the labels beside the colorbar. %     Here the colorbar of the first subplot is labeled using labels%     'small', 'medium' and 'big' at values 0, 1 and 2.  For the%     colorbar of the second subplot, values are calculated for the%     borders between colors.som_recolorbar(1,{[0 4 9]},'',{{'small','medium','big'}});som_recolorbar(2,'border','');pause % Press any key to learn about SOM_NORMCOLOR...%     Some SOM Toolbox functions do not use indexed colors if the%     underlying Matlab function (e.g. PLOT) do not use indexed%     colors. SOM_NORMCOLOR is a convenient function to simulate%     indexed colors: it calculates fixed RGB colors that%     are similar to indexed colors with the specified colormap. %     Here, two SOM_GRID visualizations are created. One uses the%     'surf' mode to show the component colors in indexed color%     mode, and the other uses SOM_NORMALIZE to do the same. clfcolormap(jet(64))subplot(1,2,1)som_grid(sM,'Surf',sM.codebook(:,3));title('Surf mode')subplot(1,2,2)som_grid(sM,'Markercolor',som_normcolor(sM.codebook(:,3)));title('som\_normcolor')pause % Press any key to visualize different map shapes...clcclf%    DIFFERENT MAP SHAPES%    ====================%    There's no direct way to visualize cylinder or toroid maps. When%    visualized, they are treated exactly as if they were sheet%    shaped. However, if function SOM_UNIT_COORDS is used to provide%    unit coordinates, then SOM_GRID can be used to visualize these%    alternative map shapes.%    Here the grids of the three possible map shapes (sheet, cylinder%    and toroid) are visualized. The last subplot shows a component %    plane visualization of the toroid map.Cor = som_unit_coords(sM.topol.msize,'hexa','sheet');Coc = som_unit_coords(sM.topol.msize,'hexa','cyl');Cot = som_unit_coords(sM.topol.msize,'hexa','toroid');subplot(2,2,1)som_grid(sM,'Coord',Cor,'Markersize',3,'Linecolor','k');title('sheet'), view(0,-90), axis tight, axis equalsubplot(2,2,2)som_grid(sM,'Coord',Coc,'Markersize',3,'Linecolor','k');title('cylinder'), view(5,1), axis tight, axis equalsubplot(2,2,3)som_grid(sM,'Coord',Cot,'Markersize',3,'Linecolor','k');title('toroid'), view(-100,0), axis tight, axis equalsubplot(2,2,4)som_grid(sM,'Coord',Cot,'Surf',sM.codebook(:,3));colormap(jet), colorbartitle('toroid'), view(-100,0), axis tight, axis equalecho off