comparison toolboxes/MIRtoolbox1.3.2/somtoolbox/som_demo3.m @ 0:e9a9cd732c1e tip

first hg version after svn

+
+%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)
+
+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...
+
+
+
+clf
+clc
+%    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...
+
+
+clf
+clc
+%    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 equal
+
+pause % Strike any key to visualize data responses...
+
+
+clf
+clc
+%    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 units
+
+echo 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); % bmus
+
+h0 = zeros(prod(sM.topol.msize),1); h0(bmu0) = 1; % crisp hits
+h9 = 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 response
+hf9 = 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 on
+Co = 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 equal
+echo 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...
+
+
+
+clc
+clf
+%    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...
+
+
+
+clc
+clf
+%    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...
+
+
+
+
+clc
+clf
+%    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. 
+
+clf
+colormap(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...
+
+
+
+clc
+clf
+%    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 equal
+
+subplot(2,2,2)
+som_grid(sM,'Coord',Coc,'Markersize',3,'Linecolor','k');
+title('cylinder'), view(5,1), axis tight, axis equal
+
+subplot(2,2,3)
+som_grid(sM,'Coord',Cot,'Markersize',3,'Linecolor','k');
+title('toroid'), view(-100,0), axis tight, axis equal
+
+subplot(2,2,4)
+som_grid(sM,'Coord',Cot,'Surf',sM.codebook(:,3));
+colormap(jet), colorbar
+title('toroid'), view(-100,0), axis tight, axis equal
+
+echo off