comparison toolboxes/MIRtoolbox1.3.2/somtoolbox/som_demo4.m @ 0:e9a9cd732c1e tip

first hg version after svn

+
+%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 070600
+
+clf reset;
+f0 = gcf;
+echo on
+
+
+
+
+clc
+%    ==========================================================
+%    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 on
+end
+
+sD = 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 correlated
+
+pause % 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 off
+
+f1=figure;
+[Pd,V,me,l] = pcaproj(sD,2); Pm = pcaproj(sM,V,me); % PC-projection
+Code = som_colorcode(Pm); % color coding
+hits = som_hits(sM,sD);  % hits
+U = som_umat(sM); % U-matrix
+Dm = U(1:2:size(U,1),1:2:size(U,2)); % distance matrix
+Dm = 1-Dm(:)/max(Dm(:)); Dm(find(hits==0)) = 0; % clustering info
+
+subplot(1,3,1)
+som_cplane(sM,Code,Dm);
+hold on
+som_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 equal
+title('PC projection')
+
+subplot(1,3,3)
+som_cplane(sM,'none')
+hold on
+som_grid(sM,'Label',sM.labels,'Labelsize',8,...
+	 'Line','none','Marker','none','Labelcolor','r');
+hold off
+title('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 information
+names = 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 map
+bmus = 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;
+  end
+end
+
+echo 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), clf
+
+clc 
+%    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 clusters
+plot(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...
+
+
+clf
+clc 
+%    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))
+colorbar
+title('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);       % classification
+ok = strcmp(sD2.labels,sD.labels); % errors
+100*(1-sum(ok)/length(ok))         % error percentage (%)
+
+echo off
+
+
+
+
+
+
+