K-mean clustering 算法

作者在 2009-03-25 20:52:21 发布以下内容
K-MEANS算法:
  k-means 算法接受输入量 k ;然后将n个数据对象划分为 k个聚类以便使得所获得的聚类满足:同一聚类中的对象相似度较高;而不同聚类中的对象相似度较小。聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”(引力中心)来进行计算的。
  k-means 算法的工作过程说明如下:首先从n个数据对象任意选择 k 个对象作为初始聚类中心;而对于所剩下其它对象,则根据它们与这些聚类中心的相似度(距离),分别将它们分配给与其最相似的(聚类中心所代表的)聚类;然后再计算每个所获新聚类的聚类中心(该聚类中所有对象的均值);不断重复这一过程直到标准测度函数开始收敛为止。一般都采用均方差作为标准测度函数. k个聚类具有以下特点:各聚类本身尽可能的紧凑,而各聚类之间尽可能的分开。
  补充一个Matlab实现方法:
  function [cid,nr,centers] = cskmeans(x,k,nc)
  % CSKMEANS K-Means clustering - general method.
  %
  % This implements the more general k-means algorithm, where
  % HMEANS is used to find the initial partition and then each
  % observation is examined for further improvements in minimizing
  % the within-group sum of squares.
  %
  % [CID,NR,CENTERS] = CSKMEANS(X,K,NC) Performs K-means
  % clustering using the data given in X.
  %
  % INPUTS: X is the n x d matrix of data,
  % where each row indicates an observation. K indicates
  % the number of desired clusters. NC is a k x d matrix for the
  % initial cluster centers. If NC is not specified, then the
  % centers will be randomly chosen from the observations.
  %
  % OUTPUTS: CID provides a set of n indexes indicating cluster
  % membership for each point. NR is the number of observations
  % in each cluster. CENTERS is a matrix, where each row
  % corresponds to a cluster center.
  %
  % See also CSHMEANS
  % W. L. and A. R. Martinez, 9/15/01
  % Computational Statistics Toolbox
  warning off
  [n,d] = size(x);
  if nargin < 3
  % Then pick some observations to be the cluster centers.
  ind = ceil(n*rand(1,k));
  % We will add some noise to make it interesting.
  nc = x(ind,:) + randn(k,d);
  end
  % set up storage
  % integer 1,...,k indicating cluster membership
  cid = zeros(1,n);
  % Make this different to get the loop started.
  oldcid = ones(1,n);
  % The number in each cluster.
  nr = zeros(1,k);
  % Set up maximum number of iterations.
  maxiter = 100;
  iter = 1;
  while ~isequal(cid,oldcid) & iter < maxiter
  % Implement the hmeans algorithm
  % For each point, find the distance to all cluster centers
  for i = 1:n
  dist = sum((repmat(x(i,:),k,1)-nc).^2,2);
  [m,ind] = min(dist); % assign it to this cluster center
  cid(i) = ind;
  end
  % Find the new cluster centers
  for i = 1:k
  % find all points in this cluster
  ind = find(cid==i);
  % find the centroid
  nc(i,:) = mean(x(ind,:));
  % Find the number in each cluster;
  nr(i) = length(ind);
  end
  iter = iter + 1;
  end
  % Now check each observation to see if the error can be minimized some more.
  % Loop through all points.
  maxiter = 2;
  iter = 1;
  move = 1;
  while iter < maxiter & move ~= 0
  move = 0;
  % Loop through all points.
  for i = 1:n
  % find the distance to all cluster centers
  dist = sum((repmat(x(i,:),k,1)-nc).^2,2);
  r = cid(i); % This is the cluster id for x
  %%nr,nr+1;
  dadj = nr./(nr+1).*dist'; % All adjusted distances
  [m,ind] = min(dadj); % minimum should be the cluster it belongs to
  if ind ~= r % if not, then move x
  cid(i) = ind;
  ic = find(cid == ind);
  nc(ind,:) = mean(x(ic,:));
  move = 1;
  end
  end
  iter = iter+1;
  end
  centers = nc;
  if move == 0
  disp('No points were moved after the initial clustering procedure.')
  else
  disp('Some points were moved after the initial clustering procedure.')
  end
  warning on
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