%SOM_DEMO4 Data analysis using the SOM.% 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 090200 070600clf reset;f0 = gcf;echo onclc%    ==========================================================%    SOM_DEMO4 - DATA ANALYSIS USING THE SOM%    ==========================================================%    In this demo, the IRIS data set is analysed using SOM. First, the%    data is read from ascii file (please make sure they can be found%    from the current path), normalized, and a map is%    trained. Since the data also had labels, the map is labelled.try,   sD = 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;  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;    sD = som_data_struct([D; D2],'name','iris (simulated)',...		       'comp_names',{'SepalL','SepalW','PetalL','PetalW'});  sD = som_label(sD,'add',[1:50]','Setosa');  sD = som_label(sD,'add',[51:100]','Versicolor');  sD = som_label(sD,'add',[101:150]','Virginica');    echo onendsD = som_normalize(sD,'var');sM = som_make(sD);sM = som_autolabel(sM,sD,'vote');pause % Strike any key to visualize the map...clc %    VISUAL INSPECTION OF THE MAP%    ============================%    The first step in the analysis of the map is visual inspection.%    Here is the U-matrix, component planes and labels (you may%    need to enlarge the figure in order to make out the labels).som_show(sM,'umat','all','comp',[1:4],'empty','Labels','norm','d');som_show_add('label',sM.labels,'textsize',8,'textcolor','r','subplot',6);%    From this first visualization, one can see that:%     - there are essentially two clusters%     - PetalL and PetalW are highly correlated%     - SepalL is somewhat correlated to PetalL and PetalW%     - one cluster corresponds to the Setosa species and exhibits%       small petals and short but wide sepals%     - the other cluster corresponds to Virginica and Versicolor%       such that Versicolor has smaller leaves (both sepal and%       petal) than Virginica%     - inside both clusters, SepalL and SepalW are highly correlatedpause % Strike any key to continue...%    Next, the projection of the data set is investigated. A%    principle component projection is made for the data, and applied%    to the map. The colormap is done by spreading a colormap on the%    projection. Distance matrix information is extracted from the%    U-matrix, and it is modified by knowledge of zero-hits%    (interpolative) units. Finally, three visualizations are shown:%    the color code, with clustering information and the number of%    hits in each unit, the projection and the labels.echo offf1=figure;[Pd,V,me,l] = pcaproj(sD,2); Pm = pcaproj(sM,V,me); % PC-projectionCode = som_colorcode(Pm); % color codinghits = som_hits(sM,sD);  % hitsU = som_umat(sM); % U-matrixDm = U(1:2:size(U,1),1:2:size(U,2)); % distance matrixDm = 1-Dm(:)/max(Dm(:)); Dm(find(hits==0)) = 0; % clustering infosubplot(1,3,1)som_cplane(sM,Code,Dm);hold onsom_grid(sM,'Label',cellstr(int2str(hits)),...	 'Line','none','Marker','none','Labelcolor','k');hold off title('Color code')subplot(1,3,2)som_grid(sM,'Coord',Pm,'MarkerColor',Code,'Linecolor','k');hold on, plot(Pd(:,1),Pd(:,2),'k+'), hold off, axis tight, axis equaltitle('PC projection')subplot(1,3,3)som_cplane(sM,'none')hold onsom_grid(sM,'Label',sM.labels,'Labelsize',8,...	 'Line','none','Marker','none','Labelcolor','r');hold offtitle('Labels')echo on%    From these figures one can see that: %     - the projection confirms the existence of two different clusters%     - interpolative units seem to divide the Virginica%       flowers into two classes, the difference being in the size of%       sepal leaves    pause % Strike any key to continue...%    Finally, perhaps the most informative figure of all: simple%    scatter plots and histograms of all variables. The species%    information is coded as a fifth variable: 1 for Setosa, 2 for%    Versicolor and 3 for Virginica. Original data points are in the%    upper triangle, map prototype values on the lower triangle, and%    histograms on the diagonal: black for the data set and red for%    the map prototype values. The color coding of the data samples%    has been copied from the map (from the BMU of each sample). Note%    that the variable values have been denormalized.echo off% denormalize and add species informationnames = sD.comp_names; names{end+1} = 'species';D = som_denormalize(sD.data,sD); dlen = size(D,1);s = zeros(dlen,1)+NaN; s(strcmp(sD.labels,'Setosa'))=1;s(strcmp(sD.labels,'Versicolor'))=2; s(strcmp(sD.labels,'Virginica'))=3;D = [D, s];M = som_denormalize(sM.codebook,sM); munits = size(M,1);s = zeros(munits,1)+NaN; s(strcmp(sM.labels,'Setosa'))=1;s(strcmp(sM.labels,'Versicolor'))=2; s(strcmp(sM.labels,'Virginica'))=3;M = [M, s];f2=figure;% color coding copied from the mapbmus = som_bmus(sM,sD); Code_data = Code(bmus,:); k=1; for i=1:5, for j=1:5,     if i<j, i1=i; i2=j; else i1=j; i2=i; end    subplot(5,5,k); cla    if i<j,      som_grid('rect',[dlen 1],'coord',D(:,[i1 i2]),...	       'Line','none','MarkerColor',Code_data,'Markersize',2);      title(sprintf('%s vs. %s',names{i1},names{i2}))    elseif i>j,      som_grid(sM,'coord',M(:,[i1 i2]),...	       'markersize',2,'MarkerColor',Code);      title(sprintf('%s vs. %s',names{i1},names{i2}))    else      if i1<5, b = 10; else b = 3; end      [nd,x] = hist(D(:,i1),b); nd=nd/sum(nd);       nm = hist(M(:,i1),x); nm = nm/sum(nm);      h=bar(x,nd,0.8); set(h,'EdgeColor','none','FaceColor','k');       hold on       h=bar(x,nm,0.3); set(h,'EdgeColor','none','FaceColor','r');       hold off      title(names{i1})    end    k=k+1;  endendecho on%    This visualization shows quite a lot of information:%    distributions of single and pairs of variables both in the data%    and in the map. If the number of variables was even slightly%    more, it would require a really big display to be convenient to%    use.%    From this visualization we can conform many of the earlier%    conclusions, for example: %     - there are two clusters: 'Setosa' (blue, dark green) and %       'Virginica'/'Versicolor' (light green, yellow, reds)%       (see almost any of the subplots)%     - PetalL and PetalW have a high linear correlation (see%       subplots 4,3 and 3,4)%     - SepalL is correlated (at least in the bigger cluster) with%       PetalL and PetalW (in subplots 1,3 1,4 3,1 and 4,1)%     - SepalL and SepalW have a clear linear correlation, but it%       is slightly different for the two main clusters (in%       subplots 2,1 and 1,2)       pause % Strike any key to cluster the map...close(f1), close(f2), figure(f0), clfclc %    CLUSTERING OF THE MAP%    =====================%    Visual inspection already hinted that there are at least two%    clusters in the data, and that the properties of the clusters are%    different from each other (esp. relation of SepalL and%    SepalW). For further investigation, the map needs to be%    partitioned.%    Here, the KMEANS_CLUSTERS function is used to find an initial%    partitioning. The plot shows the Davies-Boulding clustering%    index, which is minimized with best clustering.subplot(1,3,1)[c,p,err,ind] = kmeans_clusters(sM, 7); % find at most 7 clustersplot(1:length(ind),ind,'x-')[dummy,i] = min(ind)cl = p{i};%    The Davies-Boulding index seems to indicate that there are%    two clusters on the map. Here is the clustering info%    calculated previously and the partitioning result: subplot(1,3,2)som_cplane(sM,Code,Dm)subplot(1,3,3)som_cplane(sM,cl)%    You could use also function SOM_SELECT to manually make or modify%    the partitioning.%    After this, the analysis would proceed with summarization of the%    results, and analysis of each cluster one at a time.%    Unfortunately, you have to do that yourself. The SOM Toolbox does%    not, yet, have functions for those purposes.pause % Strike any key to continue...clfclc %    MODELING%    ========%    One can also build models on top of the SOM. Typically, these%    models are simple local or nearest-neighbor models. %    Here, SOM is used for probability density estimation. Each map %    prototype is the center of a gaussian kernel, the parameters%    of which are estimated from the data. The gaussian mixture%    model is estimated with function SOM_ESTIMATE_GMM and the%    probabilities can be calculated with SOM_PROBABILITY_GMM.[K,P] = som_estimate_gmm(sM,sD);[pd,Pdm,pmd] = som_probability_gmm(sD,sM,K,P);%    Here is the probability density function value for the first data%    sample (x=sD.data(:,1)) in terms of each map unit (m):som_cplane(sM,Pdm(:,1))colorbartitle('p(x|m)')pause % Strike any key to continue...%    Here, SOM is used for classification. Although the SOM can be%    used for classification as such, one has to remember that it does%    not utilize class information at all, and thus its results are%    inherently suboptimal. However, with small modifications, the%    network can take the class into account. The function%    SOM_SUPERVISED does this.%    Learning vector quantization (LVQ) is an algorithm that is very%    similar to the SOM in many aspects. However, it is specifically%    designed for classification. In the SOM Toolbox, there are%    functions LVQ1 and LVQ3 that implement two versions of this%    algorithm.%    Here, the function SOM_SUPERVISED is used to create a classifier%    for IRIS data set:sM = som_supervised(sD,'small');som_show(sM,'umat','all');som_show_add('label',sM.labels,'TextSize',8,'TextColor','r')sD2 = som_label(sD,'clear','all'); sD2 = som_autolabel(sD2,sM);       % classificationok = strcmp(sD2.labels,sD.labels); % errors100*(1-sum(ok)/length(ok))         % error percentage (%)echo off