求FCM算法在matlab中的实现

[zcw20004]

听说matlab7.0中已经有了FCM算法的实现，但是老师要求我们编写
各位高人能否告诉我该如何做

[UltraBejing]

等待牛人来答.

[qingmu1984]

在MATLAB7安装文件夹\toolbox\fuzzy\fuzzy下有几个m文件，其中fcm.m就是源码。

[yxw860516]

FCM的源代码：


function [center, U, obj_fcn] = fcm(data, cluster_n, options)
%FCM Data set clustering using fuzzy c-means clustering.
%
% [CENTER, U, OBJ_FCN] = FCM(DATA, N_CLUSTER) finds N_CLUSTER number of
% clusters in the data set DATA. DATA is size M-by-N, where M is the number of
% data points and N is the number of coordinates for each data point. The
% coordinates for each cluster center are returned in the rows of the matrix
% CENTER. The membership function matrix U contains the grade of membership of
% each DATA point in each cluster. The values 0 and 1 indicate no membership
% and full membership respectively. Grades between 0 and 1 indicate that the
% data point has partial membership in a cluster. At each iteration, an
% objective function is minimized to find the best location for the clusters
% and its values are returned in OBJ_FCN.
%
% [CENTER, ...] = FCM(DATA,N_CLUSTER,OPTIONS) specifies a vector of options
% for the clustering process:
% OPTIONS(1): exponent for the matrix U (default: 2.0)
% OPTIONS(2): maximum number of iterations (default: 100)
% OPTIONS(3): minimum amount of improvement (default: 1e-5)
% OPTIONS(4): info display during iteration (default: 1)
% The clustering process stops when the maximum number of iterations
% is reached, or when the objective function improvement between two
% consecutive iterations is less than the minimum amount of improvement
% specified. Use NaN to select the default value.
%
% Example
% data = rand(100,2);
% [center,U,obj_fcn] = fcm(data,2);
% plot(data(:,1), data(:,2),'o');
% hold on;
% maxU = max(U);
% % Find the data points with highest grade of membership in cluster 1
% index1 = find(U(1,:) == maxU);
% % Find the data points with highest grade of membership in cluster 2
% index2 = find(U(2,:) == maxU);
% line(data(index1,1),data(index1,2),'marker','*','color','g');
% line(data(index2,1),data(index2,2),'marker','*','color','r');
% % Plot the cluster centers
% plot([center([1 2],1)],[center([1 2],2)],'*','color','k')
% hold off;
%
% See also FCMDEMO, INITFCM, IRISFCM, DISTFCM, STEPFCM.

% Roger Jang, 12-13-94, N. Hickey 04-16-01
% Copyright 1994-2002 The MathWorks, Inc.
% $Revision: 1.13 $ $Date: 2002/04/14 22:20:38 $

if nargin ~= 2 & nargin ~= 3,
error('Too many or too few input arguments!');
end

data_n = size(data, 1);
in_n = size(data, 2);

% Change the following to set default options
default_options = [2; % exponent for the partition matrix U
100; % max. number of iteration
1e-5; % min. amount of improvement
1]; % info display during iteration

if nargin == 2,
options = default_options;
else
% If "options" is not fully specified, pad it with default values.
if length(options) < 4,
tmp = default_options;
tmp(1:length(options)) = options;
options = tmp;
end
% If some entries of "options" are nan's, replace them with defaults.
nan_index = find(isnan(options)==1);
options(nan_index) = default_options(nan_index);
if options(1) <= 1,
error('The exponent should be greater than 1!');
end
end

expo = options(1); % Exponent for U
max_iter = options(2); % Max. iteration
min_impro = options(3); % Min. improvement
display = options(4); % Display info or not

obj_fcn = zeros(max_iter, 1); % Array for objective function

U = initfcm(cluster_n, data_n); % Initial fuzzy partition
% Main loop
for i = 1:max_iter,
[U, center, obj_fcn(i)] = stepfcm(data, U, cluster_n, expo);
if display,
fprintf('Iteration count = %d, obj. fcn = %f\n', i, obj_fcn(i));
end
% check termination condition
if i > 1,
if abs(obj_fcn(i) - obj_fcn(i-1)) < min_impro, break; end,
end
end

iter_n = i; % Actual number of iterations
obj_fcn(iter_n+1:max_iter) = [];

[eblis88]

你先找一些理论知识看下。这里给出算法步骤，直接给你fast fcm，做论文，跑程序都方便。

参考文献：一种用于磁共振颅脑图像分割的快速模糊聚类算法 《中国生物医学工程学报》

1 确定参数c,n,m,e普西龙d,b=0
c是聚类数，m是模糊加权指数，e普西龙是迭代终止参数，或者叫收敛门限，n是总类数。这几个参数是没什么问题的，其他的解释下
n-像素总数，用来进行k均值的，目的是加快分割速度。
d-向量的特征数，这个应该知道的
b是迭代用的参数

其中，m=1，fcm就变成了hcm。很多文献上都说到这个

2 用k-均值聚类进行初始分割，把分割结果作为fcm的初始聚类中心V=(v1,v2,....,vc)
这步的好处是，让后面进行迭代的次数少了很多。毕竟fcm的复杂度是很大的。
k-均值步骤我后面说

这里后面和普通的fcm一样
3 更新U(b)到U(b+1)。 任取i,j
根据fcm定理。这个很多文献上都有的吧
uik=...一堆，这里不打了。关键字搜索，fcm定理。其中有一点

if (dij!=0,j=1,2,....c) //这里dij是数据点xk与第i类中心vi之间的距离，记得距离要取范数
根据fcm定理，更新uik
if (dij=0)
uik=1
if (dtj=0 , t!=i)
uik=0

要加两个边界条件

4 根据U(b+1)和fcm定理，计算c各均值矢量vi(b)
这步应该也没问题的，代公式就好

5 比较U(b)和U(b+1)，若||U(b)-U(b+1)||<e普西龙，停止迭代，否则b++，返回3。



上面是ffcm的步骤。下面给出k-means步骤，用伪代码给出

1 把图像随意分成nc个区域，并且进行标记，用1,2,3....nc
2 计算每一类的均值向量 mc[i][c],i=1.....d,c=1....nc
d 向量的特征数
3 进行下述为代码流程
change=false
for j=1...N do
Distmin=Bignumber,class=0
//寻找最近均值
for c=1...nc do // nc 聚类数
Dist=Distance(xj,mc) // xij 待聚类的像素向量，mc 每一类的均值向量
// 这步用来计算xj到均值mc的距离
if Dist<Distmin then Distmin=Dist
class=c
labj=class;
如果像素标记改变
change=True;
if change=ture
返回2，重新计算mc，并且进行上述操作

[guanqing1203]

谢谢O(∩_∩)O~

[laviewpbt]

http://blog.csdn.net/laviewpbt/archive/2006/11/01/1361548.aspx

模糊聚类算法（FCM）和硬聚类算法（HCM)的VB6.0实现及其应用

[kuaikaikai]

很详细，有用啊！谢谢先！

[blueskyr14]

很好，很详尽~~~