function [class,type,clusteridx]=DBscan(x,k,Eps)
x=zscore(x);%standarlize
[m,~]=size(x);
if nargin<3||isempty(Eps)
[Eps]=epsilon(x,k);
end
x=[(1:m)',x];
[m,n]=size(x);
type=zeros(1,m);
no=1;
touched=zeros(m,1);
for i=1:m
if touched(i)==0;
ob=x(i,:);
D=dist(ob(2:n),x(:,2:n));
ind=find(D<=Eps);
if length(ind)>1 && length(ind)<k+1
type(i)=0;
class(i)=0;
end
if length(ind)==1
type(i)=-1;
class(i)=-1;
touched(i)=1;
end
if length(ind)>=k+1;
type(i)=1;
class(ind)=ones(length(ind),1)*max(no);
while ~isempty(ind)
ob=x(ind(1),:);
touched(ind(1))=1;
ind(1)=[];
D=dist(ob(2:n),x(:,2:n));
i1=find(D<=Eps);
if length(i1)>1
class(i1)=no;
if length(i1)>=k+1;
type(ob(1))=1;
else
type(ob(1))=0;
end
for k1=1:length(i1)
if touched(i1(k1))==0
touched(i1(k1))=1;
ind=[ind,i1(k1)];
class(i1(k1))=no;
end
end
end
end
no=no+1;
end
end
end
i1=find(class==0);
class(i1)=-1;
type(i1)=-1;
maxlab=max(class);
clusteridx=[];
clun=[];
for ck=1:maxlab
tidx=find(class==ck);
clusteridx=[clusteridx;[tidx,zeros(1,m-length(tidx))]];
clun=[clun,length(tidx)];
end
disp(clun);
%...........................................
function [Eps]=epsilon(x,k)
% Function: [Eps]=epsilon(x,k)
%
% Aim:
% Analytical way of estimating neighborhood radius for DBSCAN
%
% Input:
% x - data matrix (m,n); m-objects, n-variables
% k - number of objects in a neighborhood of an object
% (minimal number of objects considered as a cluster)
[m,n]=size(x);
Eps=((prod(max(x)-min(x))*k*gamma(.5*n+1))/(m*sqrt(pi.^n))).^(1/n);
disp('EPS:');
disp(Eps);
%............................................
function [D]=dist(i,x)
% function: [D]=dist(i,x)
%
% Aim:
% Calculates the Euclidean distances between the i-th object and all objects in x
%
% Input:
% i - an object (1,n)
% x - data matrix (m,n); m-objects, n-variables
%
% Output:
% D - Euclidean distance (m,1)
[m,n]=size(x);
D=sqrt(sum((((ones(m,1)*i)-x).^2)'));
if n==1
D=abs((ones(m,1)*i-x))';
end
%********************************************************
