处理输入为非对角阵的Clustering by fast search and find of density peak代码

Clustering by fast search and find of density peak. Alex Rodriguez, Alessandro Laio

是发表在Science上的一篇很好的阐述一种新聚类算法的paper，其自带代码

http://www.sciencemag.org/content/suppl/2014/06/25/344.6191.1492.DC1/1242072DataS1.zip

展示了该代码的实现过程和使用结果。

不过，该测试代码要求输入为一个格式特殊的三角矩阵，为了使用方便，这里我把源代码做少量修改，

增加预处理部分，使得可以直接处理标准的距离矩阵格式数据

clear all
close all
% disp('The only input needed is a distance matrix file')
% disp('The format of this file should be: ')
% disp('Column 1: id of element i')
% disp('Column 2: id of element j')
% disp('Column 3: dist(i,j)')
% mdist=input('name of the distance matrix file (with single quotes)?\n');
% disp('Reading input distance matrix')
% xx=load(mdist);
% xx = load('D:\example_distances.dat')
%x = load('C:\UseTraceOfAllUsers.txt');
x = load('D:\Courses\Cloud Computing\Clustering\dataWaitingForClustering4.2.txt');
minX = min(x);
maxX = max(x);
ran = maxX - minX;
nx(:,1) = (x(:,1) - minX(1,1)) / ran(1,1);
nx(:,2) = (x(:,2) - minX(1,2)) / ran(1,2);
dist = pdist2(nx, nx);
N = size(dist,1);
xx = zeros((N-1)*N/2, 3);
idx = 1;
for i=1:N
    for j=i+1:N
        xx(idx, 1) = i;
        xx(idx, 2) = j;
        xx(idx, 3) = dist(i, j);
        idx = idx + 1;
    end
end
N = size(xx, 1);
ND=max(xx(:,2));
NL=max(xx(:,1));
if (NL>ND)
  ND=NL;
end
% N=size(xx,1);
% for i=1:ND
%   for j=1:ND
%     dist(i,j)=0;
%   end
% end
% for i=1:N
%   ii=xx(i,1);
%   jj=xx(i,2);
%   dist(ii,jj)=xx(i,3);
%   dist(jj,ii)=xx(i,3);
% end
% percent=2;
% fprintf('average percentage of neighbours (hard coded): %5.6f\n', percent);
%
% position=round(N*percent/100);
% sda=sort(xx(:,3));
% dc=sda(position);
dc = 0.15;

fprintf('Computing Rho with gaussian kernel of radius: %12.6f\n', dc);

for i=1:ND
  rho(i)=0.;
end
%
% Gaussian kernel
%
for i=1:ND-1
  for j=i+1:ND
     rho(i)=rho(i)+exp(-(dist(i,j)/dc)*(dist(i,j)/dc));
     rho(j)=rho(j)+exp(-(dist(i,j)/dc)*(dist(i,j)/dc));
  end
end
%
% "Cut off" kernel
%
% for i=1:ND-1
%  for j=i+1:ND
%    if (dist(i,j)<dc)S
%       rho(i)=rho(i)+1.;
%       rho(j)=rho(j)+1.;
%    end
%  end
% end

maxd=max(max(dist));

[rho_sorted,ordrho]=sort(rho,'descend');
delta(ordrho(1))=-1.;
nneigh(ordrho(1))=0;

for ii=2:ND
   delta(ordrho(ii))=maxd;
   for jj=1:ii-1
     if(dist(ordrho(ii),ordrho(jj))<delta(ordrho(ii)))
        delta(ordrho(ii))=dist(ordrho(ii),ordrho(jj));
        nneigh(ordrho(ii))=ordrho(jj);
     end
   end
end
delta(ordrho(1))=max(delta(:));
disp('Generated file:DECISION GRAPH')
disp('column 1:Density')
disp('column 2:Delta')

fid = fopen('DECISION_GRAPH', 'w');
for i=1:ND
   fprintf(fid, '%6.2f %6.2f\n', rho(i),delta(i));
end

disp('Select a rectangle enclosing cluster centers')
scrsz = get(0,'ScreenSize');
figure('Position',[6 72 scrsz(3)/4. scrsz(4)/1.3]);
for i=1:ND
  ind(i)=i;
  gamma(i)=rho(i)*delta(i);
end
subplot(2,1,1)
tt=plot(rho(:),delta(:),'o','MarkerSize',5,'MarkerFaceColor','k','MarkerEdgeColor','k');
title ('Decision Graph','FontSize',15.0)
xlabel ('\rho')
ylabel ('\delta')

subplot(2,1,1)
rect = getrect(1);
rhomin=rect(1);
deltamin=rect(4);
NCLUST=0;
for i=1:ND
  cl(i)=-1;
end
for i=1:ND
  if ( (rho(i)>rhomin) && (delta(i)>deltamin))
     NCLUST=NCLUST+1;
     cl(i)=NCLUST;
     icl(NCLUST)=i;
  end
end
fprintf('NUMBER OF CLUSTERS: %i \n', NCLUST);
disp('Performing assignation')

%assignation
for i=1:ND
  if (cl(ordrho(i))==-1)
    cl(ordrho(i))=cl(nneigh(ordrho(i)));
  end
end
%halo
for i=1:ND
  halo(i)=cl(i);
end
if (NCLUST>1)
  for i=1:NCLUST
    bord_rho(i)=0.;
  end
  for i=1:ND-1
    for j=i+1:ND
      if ((cl(i)~=cl(j))&& (dist(i,j)<=dc))
        rho_aver=(rho(i)+rho(j))/2.;
        if (rho_aver>bord_rho(cl(i)))
          bord_rho(cl(i))=rho_aver;
        end
        if (rho_aver>bord_rho(cl(j)))
          bord_rho(cl(j))=rho_aver;
        end
      end
    end
  end
  for i=1:ND
    if (rho(i)<bord_rho(cl(i)))
      halo(i)=0;
    end
  end
end
for i=1:NCLUST
  nc=0;
  nh=0;
  for j=1:ND
    if (cl(j)==i)
      nc=nc+1;
    end
    if (halo(j)==i)
      nh=nh+1;
    end
  end
  fprintf('CLUSTER: %i CENTER: %i ELEMENTS: %i CORE: %i HALO: %i \n', i,icl(i),nc,nh,nc-nh);
end

cmap=colormap;
for i=1:NCLUST
   ic=int8((i*64.)/(NCLUST*1.));
   subplot(2,1,1)
   hold on
   plot(rho(icl(i)),delta(icl(i)),'o','MarkerSize',8,'MarkerFaceColor',cmap(ic,:),'MarkerEdgeColor',cmap(ic,:));
end
subplot(2,1,2)
disp('Performing 2D nonclassical multidimensional scaling')
Y1 = mdscale(dist, 2, 'criterion','metricstress');
plot(Y1(:,1),Y1(:,2),'o','MarkerSize',2,'MarkerFaceColor','k','MarkerEdgeColor','k');
title ('2D Nonclassical multidimensional scaling','FontSize',15.0)
xlabel ('X')
ylabel ('Y')
for i=1:ND
 A(i,1)=0.;
 A(i,2)=0.;
end
for i=1:NCLUST
  nn=0;
  ic=int8((i*64.)/(NCLUST*1.));
  for j=1:ND
    if (halo(j)==i)
      nn=nn+1;
      A(nn,1)=Y1(j,1);
      A(nn,2)=Y1(j,2);
    end
  end
  hold on
  plot(A(1:nn,1),A(1:nn,2),'o','MarkerSize',2,'MarkerFaceColor',cmap(ic,:),'MarkerEdgeColor',cmap(ic,:));
end

%for i=1:ND
%   if (halo(i)>0)
%      ic=int8((halo(i)*64.)/(NCLUST*1.));
%      hold on
%      plot(Y1(i,1),Y1(i,2),'o','MarkerSize',2,'MarkerFaceColor',cmap(ic,:),'MarkerEdgeColor',cmap(ic,:));
%   end
%end
faa = fopen('CLUSTER_ASSIGNATION', 'w');
disp('Generated file:CLUSTER_ASSIGNATION')
disp('column 1:element id')
disp('column 2:cluster assignation without halo control')
disp('column 3:cluster assignation with halo control')
for i=1:ND
   fprintf(faa, '%i %i %i\n',i,cl(i),halo(i));
end