关于使用Simulink训练自组织图(SOM)中数据点移动的可视化

本文介绍了关于使用Simulink训练自组织图(SOM)中数据点移动的可视化的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 问题描述

我已经在MATLAB中实现了自组织映射(SOM)算法.假设每个数据点都在二维空间中表示.问题是我想在训练阶段中可视化每个数据点的移动，即我想看看在每个固定持续时间内算法进行时，这些点如何移动并最终形成集群.我相信可以通过MATLAB中的Simulation来完成，但是我不知道如何将我的MATLAB代码用于可视化?

I have implemented the Self-Organizing Map(SOM) algorithm in MATLAB. Suppose each of the data points are represented in 2-dimensional space. The problem is that I want to visualize the movement of each of the data points in the training phase i.e. I want to see how the points are moving and eventually forming clusters as the algorithm is in progress say at every fix duration. I believe that this can be done through Simulation in MATLAB,but I don't know how to incorporate my MATLAB code for visualization?

推荐答案

我开发了一个代码示例，使用所有可能的二维数据投影来可视化具有多个维度的聚类数据.可能不是可视化的最佳主意(有一些为此开发的技术，因为SOM本身可用于此需求)，特别是对于较大尺寸的数字，但是当可能的投影数(n-1)!不太高时，是一个很好的可视化工具.

I developed a code example to visualize clustering data with multiple dimensions using all possible data projection in 2-D. It may not be the best idea for visualization (there are techniques developed for this, as SOM itself may be used for this need), specially for a higher dimension numbers, but when the number of possible projections (n-1)! is not that high it is a quite good visualizer.

由于我需要访问代码，以便可以保存每次迭代的聚类平均值和聚类标签，因此我使用了使用快速kmeans算法"进行聚类" rel ="nofollow noreferrer"> > Mo Chen ，但我必须对其进行调整，这样我才能获得此访问权限.修改后的代码如下:

Since I needed access to the code so that I could save the cluster means and cluster labels for each iteration, I used a fast kmeans algorithm available at FEX by Mo Chen, but I had to adapt it so I could have this access. The adapted code is the following:

function [label,m] = litekmeans(X, k) % Perform k-means clustering. % X: d x n data matrix % k: number of seeds % Written by Michael Chen (sth4nth@gmail). n = size(X,2); last = 0; iter = 1; label{iter} = ceil(k*rand(1,n)); % random initialization checkLabel = label{iter}; m = {}; while any(checkLabel ~= last) [u,~,checkLabel] = unique(checkLabel); % remove empty clusters k = length(u); E = sparse(1:n,checkLabel,1,n,k,n); % transform label into indicator matrix curM = X*(E*spdiags(1./sum(E,1)',0,k,k)); % compute m of each cluster m{iter} = curM; last = checkLabel'; [~,checkLabel] = max(bsxfun(@minus,curM'*X,dot(curM,curM,1)'/2),[],1); % assign samples to the nearest centers iter = iter + 1; label{iter} = checkLabel; end % Get last clusters centers m{iter} = curM; % If to remove empty clusters: %for k=1:iter % [~,~,label{k}] = unique(label{k}); %end

Gif创建

我还使用了 @Amro的Matlab视频教程来创建gif.

Gif Creation

I also used @Amro's Matlab video tutorial for the gif creation.

我使用了很棒的FEX 通过 Tim Holy 来使群集颜色更易于区分.

I used this great FEX by Tim Holy for making the cluster colors easier to distinguish.

我得到的代码如下.我遇到了一些问题，因为每次迭代的簇数都会改变，这将导致散点图更新删除所有簇中心而不会出现任何错误.由于我没有注意到，所以我尝试使用可以找到网络的任何晦涩方法解决散点函数(顺便说一句，我发现了一个非常不错的散点图替代方法此处)，但幸运的是，我得到了今天发生的一切.这是我为此编写的代码，您可以随意使用，修改它，但是如果使用它，请保留我的参考.

My resulting code is as follows. I had some issues because the number of clusters would change for each iteration which would cause scatter plot update to delete all cluster centers without giving any errors. Since I didn't noticed that, I was trying to workaround the scatter function with any obscure method that I could find the web (btw, I found a really nice scatter plot alternative here), but fortunately I got what was happening going back to this today. Here is the code I did for it, you may feel free to use it, adapt it, but please keep my reference if you use it.

function varargout=kmeans_test(data,nClusters,plotOpts,dimLabels,... bigXDim,bigYDim,gifName) % % [label,m,figH,handles]=kmeans_test(data,nClusters,plotOpts,... % dimLabels,bigXDim,bigYDim,gifName) % Demonstrate kmeans algorithm iterative progress. Inputs are: % % -> data (rand(5,100)): the data to use. % % -> nClusters (7): number of clusters to use. % % -> plotOpts: struct holding the following fields: % % o leftBase: the percentage distance from the left % % o rightBase: the percentage distance from the right % % o bottomBase: the percentage distance from the bottom % % o topBase: the percentage distance from the top % % o FontSize: FontSize for axes labels. % % o widthUsableArea: Total width occupied by axes % % o heigthUsableArea: Total heigth occupied by axes % % -> bigXDim (1): the big subplot x dimension % % -> bigYDim (2): the big subplot y dimension % % -> dimLabels: If you want to specify dimensions labels % % -> gifName: gif file name to save % % Outputs are: % % -> label: Sample cluster center number for each iteration % % -> m: cluster center mean for each iteration % % -> figH: figure handle % % -> handles: axes handles % % % - Creation Date: Fri, 13 Sep 2013 % - Last Modified: Mon, 16 Sep 2013 % - Author(s): % - W.S.Freund <wsfreund_at_gmail_dot_com> % % TODO List (?): % % - Use input parser % - Adapt it to be able to cluster any algorithm function. % - Use arrows indicating cluster centers movement before moving them. % - Drag and drop small axes to big axes. % % Pre-start if nargin < 7 gifName = 'kmeansClusterization.gif'; if nargin < 6 bigYDim = 2; if nargin < 5 bigXDim = 1; if nargin < 4 nDim = size(data,1); maxDigits = numel(num2str(nDim)); dimLabels = mat2cell(sprintf(['Dim %0' num2str(maxDigits) 'd'],... 1:nDim),1,zeros(1,nDim)+4+maxDigits); if nargin < 3 plotOpts = struct('leftBase',.05,'rightBase',.02,... 'bottomBase',.05,'topBase',.02,'FontSize',10,... 'widthUsableArea',.87,'heigthUsableArea',.87); if nargin < 2 nClusters = 7; if nargin < 1 center1 = [1; 0; 0; 0; 0]; center2 = [0; 1; 0; 0; 0]; center3 = [0; 0; 1; 0; 0]; center4 = [0; 0; 0; 1; 0]; center5 = [0; 0; 0; 0; 1]; center6 = [0; 0; 0; 0; 1.5]; center7 = [0; 0; 0; 1.5; 1]; data = [... bsxfun(@plus,center1,.5*rand(5,20)) ... bsxfun(@plus,center2,.5*rand(5,20)) ... bsxfun(@plus,center3,.5*rand(5,20)) ... bsxfun(@plus,center4,.5*rand(5,20)) ... bsxfun(@plus,center5,.5*rand(5,20)) ... bsxfun(@plus,center6,.2*rand(5,20)) ... bsxfun(@plus,center7,.2*rand(5,20)) ... ]; end end end end end end end % NOTE of advice: It seems that Matlab does not test while on % refreshdata if the dimension of the inputs are equivalent for the % XData, YData and CData while using scatter. Because of this I wasted % a lot of time trying to debug what was the problem, trying many % workaround since my cluster centers would disappear for no reason. % Draw axes: nDim = size(data,1); figH = figure; set(figH,'Units', 'normalized', 'Position',... [0, 0, 1, 1],'Color','w','Name',... 'k-means example','NumberTitle','Off',... 'MenuBar','none','Toolbar','figure',... 'Renderer','zbuffer'); % Create dintinguishable colors matrix: colorMatrix = distinguishable_colors(nClusters); % Create axes, deploy them on handles matrix more or less how they % will be positioned: [handles,horSpace,vertSpace] = ... createAxesGrid(5,5,plotOpts,dimLabels); % Add main axes bigSubSize = ceil(nDim/2); bigSubVec(bigSubSize^2) = 0; for k = 0:nDim-bigSubSize bigSubVec(k*bigSubSize+1:(k+1)*bigSubSize) = ... ... %(nDim-bigSubSize+k)*nDim+1:(nDim-bigSubSize+k)*nDim+(nDim-bigSubSize+1); bigSubSize+nDim*k:nDim*(k+1); end handles(bigSubSize,bigSubSize) = subplot(nDim,nDim,bigSubVec,... 'FontSize',plotOpts.FontSize,'box','on'); bigSubplotH = handles(bigSubSize,bigSubSize); horSpace(bigSubSize,bigSubSize) = bigSubSize; vertSpace(bigSubSize,bigSubSize) = bigSubSize; set(bigSubplotH,'NextPlot','add',... 'FontSize',plotOpts.FontSize,'box','on',... 'XAxisLocation','top','YAxisLocation','right'); % Squeeze axes through space to optimize space usage and improve % visualization capability: [leftPos,botPos,subplotWidth,subplotHeight]=setCustomPlotArea(... handles,plotOpts,horSpace,vertSpace); pColorAxes = axes('Position',[leftPos(end) botPos(end) ... subplotWidth subplotHeight],'Parent',figH); pcolor([1:nClusters+1;1:nClusters+1]) % image(reshape(colorMatrix,[1 size(colorMatrix)])); % Used image to % check if the upcoming buggy behaviour would be fixed. I was not % lucky, though... colormap(pColorAxes,colorMatrix); % Change XTick positions to its center: set(pColorAxes,'XTick',.5:1:nClusters+.5); set(pColorAxes,'YTick',[]); % Change its label to cluster number: set(pColorAxes,'XTickLabel',[nClusters 1:nClusters-1]); % FIXME At % least on my matlab I have to use this buggy way to set XTickLabel. % Am I doing something wrong? Since I dunno why this is caused, I just % change the code so that it looks the way it should look, but this is % quite strange... xlabel(pColorAxes,'Clusters Colors','FontSize',plotOpts.FontSize); % Now iterate throw data and get cluster information: [label,m]=litekmeans(data,nClusters); nIters = numel(m)-1; scatterColors = colorMatrix(label{1},:); annH = annotation('textbox',[leftPos(1),botPos(1) subplotWidth ... subplotHeight],'String',sprintf('Start Conditions'),'EdgeColor',... 'none','FontSize',18); % Creates dimData_%d variables for first iteration: for curDim=1:nDim curDimVarName = genvarname(sprintf('dimData_%d',curDim)); eval([curDimVarName,'= m{1}(curDim,:);']); end % clusterColors will hold the colors for the total number of clusters % on each iteration: clusterColors = colorMatrix; % Draw cluster information for first iteration: for curColumn=1:nDim for curLine=curColumn+1:nDim % Big subplot data: if curColumn == bigXDim && curLine == bigYDim curAxes = handles(bigSubSize,bigSubSize); curScatter = scatter(curAxes,data(curColumn,:),... data(curLine,:),16,'filled'); set(curScatter,'CDataSource','scatterColors'); % Draw cluster centers curColumnVarName = genvarname(sprintf('dimData_%d',curColumn)); curLineVarName = genvarname(sprintf('dimData_%d',curLine)); eval(['curScatter=scatter(curAxes,' curColumnVarName ',' ... curLineVarName ',100,colorMatrix,''^'',''filled'');']); set(curScatter,'XDataSource',curColumnVarName,'YDataSource',... curLineVarName,'CDataSource','clusterColors') end % Small subplots data: curAxes = handles(curLine,curColumn); % Draw data: curScatter = scatter(curAxes,data(curColumn,:),... data(curLine,:),16,'filled'); set(curScatter,'CDataSource','scatterColors'); % Draw cluster centers curColumnVarName = genvarname(sprintf('dimData_%d',curColumn)); curLineVarName = genvarname(sprintf('dimData_%d',curLine)); eval(['curScatter=scatter(curAxes,' curColumnVarName ',' ... curLineVarName ',100,colorMatrix,''^'',''filled'');']); set(curScatter,'XDataSource',curColumnVarName,'YDataSource',... curLineVarName,'CDataSource','clusterColors'); if curLine==nDim xlabel(curAxes,dimLabels{curColumn}); set(curAxes,'XTick',xlim(curAxes)); end if curColumn==1 ylabel(curAxes,dimLabels{curLine}); set(curAxes,'YTick',ylim(curAxes)); end end end refreshdata(figH,'caller'); % Preallocate gif frame. From Amro's tutorial here: % stackoverflow/a/11054155/1162884 f = getframe(figH); [f,map] = rgb2ind(f.cdata, 256, 'nodither'); mov = repmat(f, [1 1 1 nIters+4]); % Add one frame at start conditions: curFrame = 1; % Add three frames without movement at start conditions f = getframe(figH); mov(:,:,1,curFrame) = rgb2ind(f.cdata, map, 'nodither'); for curIter = 1:nIters curFrame = curFrame+1; % Change label text set(annH,'String',sprintf('Iteration %d',curIter)); % Update cluster point colors scatterColors = colorMatrix(label{curIter+1},:); % Update cluster centers: for curDim=1:nDim curDimVarName = genvarname(sprintf('dimData_%d',curDim)); eval([curDimVarName,'= m{curIter+1}(curDim,:);']); end % Update cluster colors: nClusterIter = size(m{curIter+1},2); clusterColors = colorMatrix(1:nClusterIter,:); % Update graphics: refreshdata(figH,'caller'); % Update cluster colors: if nClusterIter~=size(m{curIter},2) % If number of cluster % of current iteration differs from previous iteration (or start % conditions in case we are at first iteration) we redraw colors: pcolor([1:nClusterIter+1;1:nClusterIter+1]) % image(reshape(colorMatrix,[1 size(colorMatrix)])); % Used image to % check if the upcomming buggy behaviour would be fixed. I was not % lucky, though... colormap(pColorAxes,clusterColors); % Change XTick positions to its center: set(pColorAxes,'XTick',.5:1:nClusterIter+.5); set(pColorAxes,'YTick',[]); % Change its label to cluster number: set(pColorAxes,'XTickLabel',[nClusterIter 1:nClusterIter-1]); xlabel(pColorAxes,'Clusters Colors','FontSize',plotOpts.FontSize); end f = getframe(figH); mov(:,:,1,curFrame) = rgb2ind(f.cdata, map, 'nodither'); end set(annH,'String','Convergence Conditions'); for curFrame = nIters+1:nIters+3 % Add three frames without movement at start conditions f = getframe(figH); mov(:,:,1,curFrame) = rgb2ind(f.cdata, map, 'nodither'); end imwrite(mov, map, gifName, 'DelayTime',.5, 'LoopCount',inf) varargout = cell(1,nargout); if nargout > 0 varargout{1} = label; if nargout > 1 varargout{2} = m; if nargout > 2 varargout{3} = figH; if nargout > 3 varargout{4} = handles; end end end end end function [leftPos,botPos,subplotWidth,subplotHeight] = ... setCustomPlotArea(handles,plotOpts,horSpace,vertSpace) % % -> handles: axes handles % % -> plotOpts: struct holding the following fields: % % o leftBase: the percentage distance from the left % % o rightBase: the percentage distance from the right % % o bottomBase: the percentage distance from the bottom % % o topBase: the percentage distance from the top % % o widthUsableArea: Total width occupied by axes % % o heigthUsableArea: Total heigth occupied by axes % % -> horSpace: the axes units size (integers only) that current axes % should occupy in the horizontal (considering that other occupied % axes handles are empty) % % -> vertSpace: the axes units size (integers only) that current axes % should occupy in the vertical (considering that other occupied % axes handles are empty) % nHorSubPlot = size(handles,1); nVertSubPlot = size(handles,2); if nargin < 4 horSpace(nHorSubPlot,nVertSubPlot) = 0; horSpace = horSpace+1; if nargin < 3 vertSpace(nHorSubPlot,nVertSubPlot) = 0; vertSpace = vertSpace+1; end end subplotWidth = plotOpts.widthUsableArea/nHorSubPlot; subplotHeight = plotOpts.heigthUsableArea/nVertSubPlot; totalWidth = (1-plotOpts.rightBase) - plotOpts.leftBase; totalHeight = (1-plotOpts.topBase) - plotOpts.bottomBase; gapHeigthSpace = (totalHeight - ... plotOpts.heigthUsableArea)/(nVertSubPlot); gapWidthSpace = (totalWidth - ... plotOpts.widthUsableArea)/(nHorSubPlot); botPos(nVertSubPlot) = plotOpts.bottomBase + gapWidthSpace/2; leftPos(1) = plotOpts.leftBase + gapHeigthSpace/2; botPos(nVertSubPlot-1:-1:1) = botPos(nVertSubPlot) + (subplotHeight +... gapHeigthSpace)*(1:nVertSubPlot-1); leftPos(2:nHorSubPlot) = leftPos(1) + (subplotWidth +... gapWidthSpace)*(1:nHorSubPlot-1); for curLine=1:nHorSubPlot for curColumn=1:nVertSubPlot if handles(curLine,curColumn) set(handles(curLine,curColumn),'Position',[leftPos(curColumn)... botPos(curLine) horSpace(curLine,curColumn)*subplotWidth ... vertSpace(curLine,curColumn)*subplotHeight]); end end end end function [handles,horSpace,vertSpace] = ... createAxesGrid(nLines,nColumns,plotOpts,dimLabels) handles = zeros(nLines,nColumns); % Those hold the axes size units: horSpace(nLines,nColumns) = 0; vertSpace(nLines,nColumns) = 0; for curColumn=1:nColumns for curLine=curColumn+1:nLines handles(curLine,curColumn) = subplot(nLines,... nColumns,curColumn+(curLine-1)*nColumns); horSpace(curLine,curColumn) = 1; vertSpace(curLine,curColumn) = 1; curAxes = handles(curLine,curColumn); if feature('UseHG2') colormap(handle(curAxes),colorMatrix); end set(curAxes,'NextPlot','add',... 'FontSize',plotOpts.FontSize,'box','on'); if curLine==nLines xlabel(curAxes,dimLabels{curColumn}); else set(curAxes,'XTick',[]); end if curColumn==1 ylabel(curAxes,dimLabels{curLine}); else set(curAxes,'YTick',[]); end end end end

示例

以下是使用5个维度的示例，并使用代码:

Here is an example using 5 dimensions, using the code:

center1 = [1; 0; 0; 0; 0]; center2 = [0; 1; 0; 0; 0]; center3 = [0; 0; 1; 0; 0]; center4 = [0; 0; 0; 1; 0]; center5 = [0; 0; 0; 0; 1]; center6 = [0; 0; 0; 0; 1.5]; center7 = [0; 0; 0; 1.5; 1]; data = [... bsxfun(@plus,center1,.5*rand(5,20)) ... bsxfun(@plus,center2,.5*rand(5,20)) ... bsxfun(@plus,center3,.5*rand(5,20)) ... bsxfun(@plus,center4,.5*rand(5,20)) ... bsxfun(@plus,center5,.5*rand(5,20)) ... bsxfun(@plus,center6,.2*rand(5,20)) ... bsxfun(@plus,center7,.2*rand(5,20)) ... ]; [label,m,figH,handles]=kmeans_test(data,20);