how can i compute those variables using matlab?

I'm very new to Matlab and I applied the density peak algorithm to my data using the Matlab code but I need to calculate sigma and rho. how can I start

the code is

mdist="ex.dat"
    disp('Reading input distance matrix')
    xx=load(mdist);
    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=2.0;
    fprintf('average percentage of neighbours (hard coded): %5.6f\n', percent);    
    position=round(N*percent/100);
    sda=sort(xx(:,3));
    dc=sda(position);        
    fprintf('Computing Rho with gaussian kernel of radius: %12.6f\n', dc);
    for i=1:ND
      rho(i)=0.;
    end
    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  

    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

the variables that i need to compute is

    rho(i) = sum(X(dij-dc))

and

    sigma(i) = min(dij)

Answer 1

[Anurag]

Hi Sam,

I understand that you want to compute the variables “Rho” and “Sigma” based on the explanation and the code that you have provided.

• For computing “Rho” for each data point “(i") you need to calculate the sum of Gaussian-weighted distances between point “i” and all other data points. Which translates to the following in code –

 rho(i) = rho(i) + exp(-(dist(i, j) / dc) * (dist(i, j) / dc));

• To compute “sigma” for each data point “(i)”, you need to find the minimum distance “(dij”) between point “i” and its nearest neighbour. Refer to the following code for the computation of the same.

 
delta(ordrho(ii)) = maxd;  % Set delta to a large initial value
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

Hope this helped.

Regards,

Anurag