function [center, U, obj_fcn] = kfcmFun(data, cluster_n,maxit, kernel_b,expo)

data_n = size(data, 1); % 求出data的第一维(rows)数,即样本个数

obj_fcn = zeros(100, 1);% 初始化输出参数obj_fcn

U = initkfcm(cluster_n, data_n);% 初始化模糊分配矩阵,使U满足列上相加为1

index = randperm(data_n); % 对样本序数随机排列

center_old = data(index(1:cluster_n),:); % 选取随机排列的序数的前cluster_n个

for i = 1:maxit

[U, center, obj_fcn(i)] = stepkfcm(data,U,center_old, expo, kernel_b);

fprintf('Iteration count = %d, obj. fcn = %f\n', i, obj_fcn(i));

center_old = center; % 用新的聚类中心代替老的聚类中心

% 终止条件判别

if i > 1

if abs(obj_fcn(i) - obj_fcn(i-1)) < 1e-5

break;

end

end

end

iter_n = i;

obj_fcn(iter_n+1:100) = [];

function U = initkfcm(cluster_n, data_n)

% 初始化fcm的隶属度函数矩阵

U = rand(cluster_n, data_n);

col_sum = sum(U);

U = U./col_sum(ones(cluster_n, 1), :);

function [U_new,center_new,obj_fcn] = stepkfcm(data,U,center,expo,kernel_b)

% 模糊C均值聚类时迭代的一步

feature_n = size(data,2); % 特征维数

cluster_n = size(center,1); % 聚类个数

mf = U.^expo;

% 计算新的聚类中心;

KernelMat = gaussKernel(center,data,kernel_b); % 计算高斯核矩阵

num = mf.*KernelMat * data;

den = sum(mf.*KernelMat,2);

center_new = num./(den*ones(1,feature_n));

% 计算新的隶属度矩阵；

kdist = distkfcm(center_new, data, kernel_b); % 计算距离矩阵

obj_fcn = sum(sum((kdist.^2).*mf)); % 计算目标函数值

tmp = kdist.^(-1/(expo-1));

U_new = tmp./(ones(cluster_n, 1)*sum(tmp));

function out = distkfcm(center, data, kernel_b)

% 计算样本点距离聚类中心的距离

cluster_n = size(center, 1);

data_n = size(data, 1);

out = zeros(cluster_n, data_n);

for i = 1:cluster_n % 对每个聚类中心

vi = center(i,:);

out(i,:) = 2-2*gaussKernel(vi,data,kernel_b);

end

function out = gaussKernel(center,data,kernel_b)

% 高斯核函数计算

dist = zeros(size(center, 1), size(data, 1));

for k = 1:size(center, 1)

dist(k, :) = sqrt(sum(((data-ones(size(data,1),1)*center(k,:)).^2)',1));

end

out = exp(-dist.^2/kernel_b^2);

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