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function [y]=kmeans_C(m,k,rep) %%%%%%%%%%%%%%%% % % kMeansCluster - Simple k means clustering algorithm % Author: Kardi Teknomo, Ph.D. % % Purpose: classify the objects in data matrix based on the attributes % Criteria: minimize Euclidean distance between centroids and object points % For more explanation of the algorithm, see http://people.revoledu.com/kardi/tutorial/kMean/index.html % Output: matrix data plus an additional column represent the group of each object % % Example: m = [ 1 1; 2 1; 4 3; 5 4] or in a nice form % m = [ 1 1; % 2 1; % 4 3; % 5 4] % k = 2 % kMeansCluster(m,k) produces m = [ 1 1 1; % 2 1 1; % 4 3 2; % 5 4 2] % Input: % m - required, matrix data: objects in rows and attributes in columns % k - optional, number of groups (default = 1) % isRand - optional, if using random initialization isRand=1, otherwise input any number (default) % it will assign the first k data as initial centroids % % Local Variables % f - row number of data that belong to group i % c - centroid coordinate size (1:k, 1:maxCol) % g - current iteration group matrix size (1:maxRow) % i - scalar iterator % maxCol - scalar number of rows in the data matrix m = number of attributes % maxRow - scalar number of columns in the data matrix m = number of objects % temp - previous iteration group matrix size (1:maxRow) % z - minimum value (not needed) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if nargin<2, k=1; end [maxRow, maxCol]=size(m) %返回矩阵m的行数和列数 u=0; avg=0; avg1=0; for i=1:rep q=i; if maxRow<=k, %如果聚类的数量大于等于最大行数 y=[m,(1:maxRow)'] %把矩阵的每一行作为一个聚类中心，在最后一列添加一个矩阵标识。例如：X=[1 2 3;1 3 5;12 13 1] %kMeansCluster(X,4) 则产生y = % 1 2 3 1 % 1 3 5 2 % 12 13 1 3 else p = randperm(size(m,1)); % random initialization 用randperm产生一个行矩阵 数组元素是1到m的行数之间的整数。 for i=1:k p(i) c(i,:)=m(p(i),:); % 随机选择m中的K行作为聚类中心 end % initial value of centroid 初始化聚类中心 Z=c%用z来存储随机产生的聚类中心。 temp=zeros(maxRow,1); % initialize as zero vector 产生一个maxrow行1列的全0矩阵 count=0; tic while 1, d=DistMatrix(m,c); % calculate objcets-centroid distances 调用DistMatrix函数求矩阵m中的每行和聚类中心的距离 [z,g]=min(d,[],2); % find group matrix g 求矩阵d中每列的最小值作为一个行矩阵。例如：d=[11 2 24;14 23 4;1 26 8]则返回[1 2 4] %存储在z中并用g标识 if g==temp, break; % stop the iteration else temp=g; % copy group matrix to temporary variable end g; e=0; e1=0; count=count+1 for i=1:k f=find(g==i); if f % only compute centroid if f is not empty n=m(find(g==i),:); c(i,:)=mean(m(find(g==i),:),1); %求m的符合条件f的 每一列的平均值，产生一个行矩阵 作为聚类中心。例如： Example: If X = [0 1 2； 3 4 5] %每次迭代完成后的平均误差总和 end end v=c d=DistMatrix(m,v); [z,g]=min(d,[],2); for i=1:k w=m(find(g==i),:); %then mean(X,1) is [1.5 2.5 3.5] and mean(X,2) is [1；4] 求每一次找到的属于簇Ci的所有点 [a,b]=size(w); for j=1:a h=w(j,:)-v(i,:); l=h.*h; e1=e1+sum(l); end end e=e1 end u=u+e; avg1=u/rep; end toc g end function d=DistMatrix(A,B) %%%%%%%%%%%%%%%%%%%%%%%%% % DISTMATRIX return distance matrix between points in A=[x1 y1 ... w1] and in B=[x2 y2 ... w2] % Copyright (c) 2005 by Kardi Teknomo, http://people.revoledu.com/kardi/ % % Numbers of rows (represent points) in A and B are not necessarily the same. % It can be use for distance-in-a-slice (Spacing) or distance-between-slice (Headway), % % A and B must contain the same number of columns (represent variables of n dimensions), % first column is the X coordinates, second column is the Y coordinates, and so on. % The distance matrix is distance between points in A as rows % and points in B as columns. % example: Spacing= dist(A,A) % Headway = dist(A,B), with hA ~= hB or hA=hB % A=[1 2 3; 4 5 6; 2 4 6; 1 2 3]; B=[4 5 1; 6 2 0] % dist(A,B)= [ 4.69 5.83; % 5.00 7.00; % 5.48 7.48; % 4.69 5.83] % % dist(B,A)= [ 4.69 5.00 5.48 4.69; % 5.83 7.00 7.48 5.83] %repmat(A(:,k),1,hB)表示产生的矩阵是一行 hB列的行矩阵 形式如[A（:,k) A(:,k)。。。。] %例如k=1 则C{k}=[1 1;4 4;2 2;1 1] %欧氏距离：（∑（Xi-Yi）2）1/2，即两项间的差是每个变量值差的平方和再平方根，目的是计算其间的整体距离即不相似性。 %在二维和三维空间中的欧式距离的就是两点之间的距离，二维的公式是 %d = sqrt((x1-x2)^+(y1-y2)^) %三维的公式是 %d=sqrt(x1-x2)^+(y1-y2)^+z1-z2)^) % 推广到n维空间，欧式距离的公式是 %d=sqrt( ∑(xi1-xi2)^ ) 这里i=1,2..n %xi1表示第一个点的第i维坐标,xi2表示第二个点的第i维坐标 %例如A=[x1 y1 z1; B=[x5 y5 z5; % x2 y2 z2; x6 y5 z5] % x3 y3 z3; % x4 y4 z4] %C{1}=[x1 x1; D{1}'=[x5 x6; % x2 x2; x5 x6; % x3 x3; x5 x6; % x4 x4] x5 x6] %(C{1}-D{1}').^2+(C{2}-D{2}').^2+(C{3}-D{3}').^2这个结果和 %（x1-x2）.^2+(y1-y2).^2+(z1-z2).^2结果是一样的 %%%%%%%%%%%%%%%%%%%%%%%%%%%