demosimilaritygraphs.m

一个Matlab写的关于图理论以及其在机器学习中应用的教学用GUI软件

drawnow




%disp('start DrawData 1')

% draw data set and plot it: 


switch GD_Global.CurrentDataSet;
  
 case 1 % Two Moons with balanced classes [0.5,0.5]
  density = 2;
  [pointstrans,labelstrans] =GD_GenerateData(density,...
                                                   GD_Global.CurrentNumPoints,...
                                                   GD_Global.CurrentDataDim , ...
                                                   [0.5,0.5],...
                                                   GD_Global.CurrentVarNoise);
  
 case 2 % Two Moons with unbalanced classes [0.2,0.8]
  density=2;  
  [pointstrans,labelstrans] =GD_GenerateData(density,...
                                                   GD_Global.CurrentNumPoints,...
                                                   GD_Global.CurrentDataDim , ...
                                                   [0.2,0.8],...
                                                   GD_Global.CurrentVarNoise);
  
  
  
 case 3 % Two isotropic Gaussians balanced classes [0.5,0.5]
  density=3;
  [pointstrans,labelstrans] =GD_GenerateData(density,...
                                                   GD_Global.CurrentNumPoints,...
                                                   GD_Global.CurrentDataDim , ...
                                                   [0.5,0.5,0],...
                                                   GD_Global.CurrentVarNoise);
  
 case 4 % Two isotropic Gaussians unbalanced classe [0.2,0.8]
  density=3;
  [pointstrans,labelstrans] =GD_GenerateData(density,...
                                                   GD_Global.CurrentNumPoints,...
                                                   GD_Global.CurrentDataDim , ...
                                                   [0.2,0.8,0],...
                                                   GD_Global.CurrentVarNoise);

 case 5 % Two isotropic Gaussians with different variance and balanced classes [0.2,0.8]
  density=4;
    [pointstrans,labelstrans] =GD_GenerateData(density,...
                                                   GD_Global.CurrentNumPoints,...
                                                   GD_Global.CurrentDataDim , ...
                                                   [0.2,0.8,0],...
                                                   GD_Global.CurrentVarNoise);
  
 case 6 % Three isotropic Gaussians almost balanced [0.3,0.3,0.4]
  density=3;
  
    [pointstrans,labelstrans] =GD_GenerateData(density,...
                                                   GD_Global.CurrentNumPoints,...
                                                   GD_Global.CurrentDataDim , ...
                                                   [0.3,0.3,0.4],...
                                                   GD_Global.CurrentVarNoise);

  
end

GD_Global.points = pointstrans';




% set current axis to plot in: 
set(gcf, 'CurrentAxes',handles.axes_data_left); 


% now plot it: 
GD_PlotLabels(GD_Global.points(:,1:2), ones(size(GD_Global.points(:,1))), 'Data set (relvant dimensions)');
axis equal



% ------------------------------------------------------------
function ComputeSimilarityAndPlot(handles)
% ------------------------------------------------------------
global GD_Global; 
%disp('start compute sim')

% compute similarity matrix: 
GD_Global.D = DistEuclideanPiotrDollar( GD_Global.points, GD_Global.points ); % GD_ComputeDistanceMatrix(GD_Global.points,2);
GD_Global.S = exp(- GD_Global.D / (2 * GD_Global.CurrentSigma^2)); 
%compute_gaussian_kernel_matrix(GD_Global.points,GD_Global.points,GD_Global.CurrentSigma);


% plot similarity heat map: 
set(gcf, 'CurrentAxes',handles.axes_data_middle); cla
imagesc(GD_Global.S)
title('Heat map of similarity values')
colorbar('Xtick',[1,60], 'XtickLabels',[0,1], 'FontSize', 10)


% plot similarity histogram
set(gcf, 'CurrentAxes',handles.axes_data_right); cla
hist(GD_Global.S(:))
title('Histogram of the similarity values')


% set max epsilon to max distance: 
GD_Global.MaxEps = max(max(GD_Global.D)); 



% if one of the current graphs is an eps graph, assign good para to it: 
if (GD_Global.CurrentGraph1 == 1 || GD_Global.CurrentGraph1 == 4)
  GD_Global.CurrentGraphPara1 = SelectGoodEps(handles);
end
if (GD_Global.CurrentGraph2 == 1 || GD_Global.CurrentGraph2 == 4)  
  GD_Global.CurrentGraphPara2 = SelectGoodEps(handles);
end
% need to initialize sliders again afterwards: 
InitializeSliders(handles);




% ------------------------------------------------------------
function ComputeGraphAndPlot(handles, whichone)
% ------------------------------------------------------------
global GD_Global; 

%disp('start comptue graph')
if (whichone==1)
  type = GD_Global.CurrentGraph1;
  currentPara = GD_Global.CurrentGraphPara1;
  cla(handles.axes_graph1_left)
  cla(handles.axes_graph1_middle)
  cla(handles.axes_graph1_right)
  cla(handles.axes_graph1_rr)
  drawnow
  
else
  type = GD_Global.CurrentGraph2;
  currentPara = GD_Global.CurrentGraphPara2;
  cla(handles.axes_graph2_left)
  cla(handles.axes_graph2_middle)
  cla(handles.axes_graph2_right)
  cla(handles.axes_graph2_rr)
  drawnow

end

% compute adjacency matrix of graph: 
switch type; 
 case 1 %weighted eps graph
%  W = build_epsilon_graph(GD_Global.S, currentPara,'sim');
  Wunweighted = GD_BuildEpsilonGraph(GD_Global.D, currentPara, 'dist'); 
  W = Wunweighted .* GD_Global.S; 
 case 2 %symm knn 
  W = GD_BuildSymmetricKnnGraph(GD_Global.S, ceil(currentPara),'sim');
 case 3 % mut knn
  W = GD_BuildMutualKnnGraph(GD_Global.S, ceil(currentPara),'sim');
 case 4 % unweithed eps graph
  W = GD_BuildEpsilonGraph(GD_Global.D, currentPara, 'dist'); 
end

if (whichone ==1 )
  GD_Global.W1 = W;
  
else
  GD_Global.W2 = W;
end



% plot it graph itself: 
if (whichone==1)
  set(gcf, 'CurrentAxes',handles.axes_graph1_left); cla 
else
  set(gcf, 'CurrentAxes',handles.axes_graph2_left); cla 
end
cla

GD_PlotGraph(GD_Global.points(:,1:2), W, 'Connectivity')
axis equal





% plot the degrees of the graph nodes: 
if (whichone==1)
  set(gcf, 'CurrentAxes',handles.axes_graph1_middle); cla 
else
  set(gcf, 'CurrentAxes',handles.axes_graph2_middle); cla 
end
cla

d = sum(W,2); 
GD_PlotFunction(gca, GD_Global.points(:,1:2),d,'Degrees of the vertices')
%colorbar('Location','EastOutside')
axis equal



% % plot the degrees statitics: 
% if (whichone==1)
%   set(gcf, 'CurrentAxes',handles.axes_graph1_right); cla 
% else
%   set(gcf, 'CurrentAxes',handles.axes_graph2_right); cla 
% end
% cla
% hist(d); 
% title('Histogram of degrees')

% plot the adjacency heat map: 
if (whichone==1)
  set(gcf, 'CurrentAxes',handles.axes_graph1_right); cla
imagesc(GD_Global.W1); 

else
  set(gcf, 'CurrentAxes',handles.axes_graph2_right); cla 
  imagesc(GD_Global.W2); 
end
title('Adjacency matrix')



% plot statistics on connected components: 
%[num_components, index_components] = connected_components_ule(W); 
index_components = GD_GetComps(W); 
num_components = max(index_components);

size_components = zeros(max([num_components,5]),1);
for it=1:num_components
  size_components(it) = length(find(index_components==it));
end

size_components = sort(size_components,'descend');

if (whichone==1)
  set(gcf, 'CurrentAxes',handles.axes_graph1_rr); cla 
else
  set(gcf, 'CurrentAxes',handles.axes_graph2_rr); cla 
end
cla

bar(size_components)
title('Points per conn. comp.')
%ylabel('Points per component')
%xlabel('Index of the component')



% ------------------------------------------------------------
function goodeps = SelectGoodEps(handles)
% ------------------------------------------------------------
% set current value of current eps to something useful in the beginning:

global GD_Global; 


if (isempty(GD_Global.S))
  goodeps = GD_Global.DefaultEps; 
else 
  
  % try to select reasonable eps according to bold rule of thumb
  % mean of distance of k-th nearest neighbor: 
  
  k = 7; 
  Ssorted = sort(GD_Global.S,2,'descend');
  Sk = Ssorted(:,k+1); %attention, start to count at second col, first is always 1
  epsilon = mean(Sk); 

  Dsorted = sort(GD_Global.D,2,'ascend');
  Dk = Dsorted(:,k+1); %attention, start to count at second col, first is always 1
  epsilon = mean(Dk); 


  % but need to make sure it is ine the correct range: 
  if (GD_Global.MinEps <= epsilon && GD_Global.MaxEps >= epsilon)
    goodeps = epsilon; 
  else
    disp(sprintf('goodeps would be %f, which is not in the range',epsilon))
  goodeps = GD_Global.DefaultEps; 
  end
end


% ------------------------------------------------------------
function goodeps = SelectGoodSigma(handles)
% ------------------------------------------------------------
% set current value of current eps to something useful in the beginning:

global GD_Global; 


if (isempty(GD_Global.D))
  goodsigma = GD_Global.DefaultSigma; 
else 
  
  % try to select reasonable eps according to bold rule of thumb
  % mean of similarity of k-th nearest neighbor: 
  
  k = 7; 
  Dsorted = sort(GD_Global.D,2,'ascend');
  Dk = Dsorted(:,k+1); %attention, start to count at second col, first is always 1
  sigma = mean(Dk); 

  % but need to make sure it is ine the correct range: 
  if (GD_Global.MinSigma <= sigma && GD_Global.MaxSigma >= sigma)
    goodsigma = sigma; 
  else
    disp(sprintf('goodsigma would be %f, which is not in the range',sigma))
    goodsigma = GD_Global.DefaultSigma; 
  end
end