Fuzzy c-mean clustering algorithm (principle +matlab code)

FCM Code

Function[center,u,obj_fun]=fcmcluster (data,n,options)% uses the fuzzy C-means to divide data into N-class% usage% 1 [center,u,obj_fcn]=fcmcluster (
Data,n,options);

% 2 [Center,u,obj_fcn]=fcmcluster (Data,n); % input% data n*m matrix, n samples, each sample has a dimension of M% n category% options 4*1 matrix% Options (1): Weighted index of Membership matrix U% Options (2): Max iterations% o Ptions (3): Minimum degree of membership change, iteration termination condition% options (4): Output information flag per iteration output% Center cluster center% U Membership matrix% obj_fun Target function value if Nargi
n~=2 && nargin~=3 Error (' Too many or Too few input arguments ');
End Data_n=size (data,1);

In_n=size (data,2);

% default parameter default_options=[2;100;1e-5;1];
  % parameter configuration% if only the first two parameters are selected, the default parameters are chosen, and if the number of parameters is less than 4, the other default parameters are selected if nargin==2 options=default_options;
           else if Length (options) <4 tmp=default_options;
           TMP (1:length (options)) =options;
       options=tmp;
       End Nan_index=find (isNaN (options) ==1);

       Options (Nan_index) =default_options (Nan_index); If options (1) <=1 error (' The exponent should be greater than1! ');
  End end% assigns the components in the options to four variables expo=options (1) respectively;
  Max_iter=options (2);
  Min_impro=options (3);

  Display=options (4);

  Obj_fun=zeros (max_iter,1);


  % initialization fuzzy distribution matrix U=INITFCM (N,data_n);
       % main program for I=1:max_iter [U,center,obj_fun (i)]=STEPFCM (Data,u,n,expo);
       If Display fprintf (' fcm:iteration count=%d,obj_fun=%f\n ', I,obj_fun (i));
           End% termination condition discriminant if i>1 if ABS (Obj_fun (i)-obj_fun (i-1)) <min_impro break;
   End End end Iter_n=i;
Obj_fun (Iter_n+1:max_iter) =[];
        % end percent of the sub function Fuzzy matrix initialization function u= INITFCM (n,data_n) U=rand (N,data_n);
        Col_sum=sum (U);
    U=u./col_sum (Ones (n,1),:);
            End-of-a-percent sub-function stepwise clustering functions [U_NEW,CENTER,OBJ_FUN]=STEPFCM (Data,u,n,expo) Mf=u.^expo;
            Center=mf*data./((Ones (Size (data,2), 1) *sum (MF '));
            DIST=DISTFCM (Center,data);
            Obj_fun=sum (sum ((dist.^2). *MF)); Tmp=dist.^ ( -2/(expo-1));
        U_new=tmp./(Ones (n,1) *sum (TMP));
                The end-of-count sub-function calculates the distance function OUT=DISTFCM (center,data) out=zeros (Size (center,1), size (data,1)); For K=1:size (center,1) out (k,:) =sqrt (Sum ((Data-ones (Size (data,1), 1) *center (k,:)). ^2) ', 1


                ));
 End END Algorithm Test

Data=rand (100,2);
[CENTER,U,OBJ_FCN] = Fcmcluster (data,2);
Plot (data (:, 1), Data (:, 2), ' O ');
Hold on;
Index1=find (U (1,:) ==max (u)),% find Data index divided into first class
Index2=find (U (2,:) ==max (u)),% find Data index divided into second class
Plot (data (index1,1), data (index1,2), ' g* ');
Hold on;
Plot (data (index2,1), data (index2,2), ' r* ');
Hold on;
Plot ([Center ([1 2],1)],[center ([1 2],2)], ' * ', ' color ', ' k ');

Experimental results show:
Original data distribution

Clustering results