A new clustering algorithm published in science

    This June, Alex Rodriguez and Alessandro Laio published an article in science entitled Clustering by Fast search and find density peaks, for the clustering algorithm Design provides a new way of thinking. Although the article came out after many readers questioned, but overall, the basic idea of the new clustering algorithm is very novel, and simple and lively, it is worth learning. The core idea of this new clustering algorithm lies in the characterization of the clustering center, the principle of the algorithm is introduced in detail, and some details are discussed.

Finally, attach the Matlab sample program (with appropriate code comments) provided by the author in the supplemental material.

[Plain]  View Plain  copy   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)      %%  reading data from a file    mdist=input (' name of  the distance matrix file  (with single quotes) \ n ');   disp (' Reading  input distance matrix ')    xx=load (mdist);   Nd=max (XX (:, 2));   NL= Max (XX (:, 1));   if  (nl>nd)      ND=NL;  %%  ensure  DN  Taken as the largest of the 12th column and as the total number of data points    end      n=size (xx,1); %% xx  the length of the first dimension, Equivalent to FileNumber of rows (that is, the total number of distances)      %%  initialized to 0    for i=1:nd     for j =1:nd       dist (i,j) =0;     end   end     %%  use  xx  to assign a value to the  dist  array, note that the input only has  0.5*DN (DN-1)   values, which is filled with the full matrix    %%  here does not consider diagonal elements    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     %%  OK  dc      percent=2.0;   fprintf (' average percentage of neighbours  (hard coded):  %5.6f\n ',  percent);       Position=round (n*percent/100); %% round  is a rounding function    Sda=sort (XX (:, 3) ); %%  all distance values in ascending order    DC=SDA (position);     %%  compute local density  rho (using  Gaussian  Core)       fprintf (' computing rho with gaussian  Kernel of radius: %12.6f\n ',  DC);     %%  The  rho  of each data point Values are initialized to 0    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