%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

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