| function [g, c, tmp, m]=kMeansCluster(m,k,isRand) | |
| % 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<3, isRand=0; end | |
| if nargin<2, k=1; end | |
| tmp = []; | |
| [maxRow, maxCol]=size(m); | |
| if maxRow<=k, | |
| y=[m, 1:maxRow]; | |
| else | |
| % initial value of centroid | |
| if isRand, | |
| p = randperm(size(m,1)); % random initialization | |
| for i=1:k | |
| c(i,:)=m(p(i),:) | |
| end | |
| else | |
| for i=1:k | |
| c(i,:)=m(i,:); % sequential initialization | |
| end | |
| end | |
| temp=zeros(maxRow,1); % initialize as zero vector | |
| while 1, | |
| d=DistMatrix(m,c); % calculate objcets-centroid distances | |
| [z,g]=min(d,[],2); % find group matrix g | |
| if g==temp, | |
| break; % stop the iteration | |
| else | |
| temp=g; % copy group matrix to temporary variable | |
| end | |
| for i=1:k | |
| f=find(g==i); | |
| if f % only compute centroid if f is not empty | |
| c(i,:)=mean(m(find(g==i),:),1); | |
| end | |
| end | |
| end | |
| y=[m,g]; | |
| end | |
| %The Matlab function kMeansCluster above call function DistMatrix as shown in the code below. It works for multi-dimensional Euclidean distance. Learn about other type of distance here. | |
| 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] | |
| %%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| [hA,wA]=size(A); | |
| [hB,wB]=size(B); | |
| if wA ~= wB, error(' second dimension of A and B must be the same'); end | |
| for k=1:wA | |
| C{k}= repmat(A(:,k),1,hB); | |
| D{k}= repmat(B(:,k),1,hA); | |
| end | |
| S=zeros(hA,hB); | |
| for k=1:wA | |
| S=S+(C{k}-D{k}').^2; | |
| end | |
| d=sqrt(S); | |