dbscan的matlab代码实现

% -------------------------------------------------------------------------

% Function: [class,type]=dbscan(x,k,Eps)

% -------------------------------------------------------------------------

% Aim:

% Clustering the data with Density-Based Scan Algorithm with Noise (DBSCAN) % -------------------------------------------------------------------------

% Input:

% x - data set (m,n); m-objects, n-variables

% k - number of objects in a neighborhood of an object

% (minimal number of objects considered as a cluster)

% Eps - neighborhood radius, if not known avoid this parameter or put []

% -------------------------------------------------------------------------

% Output:

% class - vector specifying assignment of the i-th object to certain

% cluster (m,1)

% type - vector specifying type of the i-th object

% (core: 1, border: 0, outlier: -1)

% -------------------------------------------------------------------------

% Example of use:

% x=[randn(30,2)*.4;randn(40,2)*.5+ones(40,1)*[4 4]];

% [class,type]=dbscan(x,5,[])

% clusteringfigs('Dbscan',x,[1 2],class,type)

% -------------------------------------------------------------------------

% References:

% [1] M. Ester, H. Kriegel, J. Sander, X. Xu, A density-based algorithm for

% discovering clusters in large spatial databases with noise, proc.

% 2nd Int. Conf. on Knowledge Discovery and Data Mining, Portland, OR, 1996, % p. 226, available from:

% https://www.360docs.net/doc/e29723168.html,rmatik.uni-muenchen.de/cgi-bin/papers?query=--CO

% [2] M. Daszykowski, B. Walczak, D. L. Massart, Looking for

% Natural Patterns in Data. Part 1: Density Based Approach,

% Chemom. Intell. Lab. Syst. 56 (2001) 83-92

% -------------------------------------------------------------------------

% Written by Michal Daszykowski

% Department of Chemometrics, Institute of Chemistry,

% The University of Silesia

% December 2004

% https://www.360docs.net/doc/e29723168.html,.pl

function [class,type,clusteridx]=clu_dbscan_fn(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)

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

%********************************************************