MATLAB实例：聚类初始化方法与数据归一化方法
作者：凯鲁嘎吉 - 博客园 http://www.cnblogs.com/kailugaji/
初始化方法有：随机初始化，K-means初始化，FCM初始化。。。。。。
归一化方法有：不归一化，z-score归一化，最大最小归一化。。。。。。
1. 聚类初始化方法
init_methods.m
function label=init_methods(data, K, choose)
% 输入：无标签数据，聚类数，选择方法
% 输出：聚类标签
if choose==1
%随机初始化，随机选K行作为聚类中心，并用欧氏距离计算其他点到其聚类，将数据集分为K类，输出每个样例的类标签
[X_num, ~]=size(data);
rand_array=randperm(X_num); %产生1~X_num之间整数的随机排列
para_miu=data(rand_array(1:K), :); %随机排列取前K个数，在X矩阵中取这K行作为初始聚类中心
%欧氏距离，计算（X-para_miu）^2=X^2+para_miu^2-2*X*para_miu'，矩阵大小为X_num*K
distant=repmat(sum(data.*data,2),1,K)+repmat(sum(para_miu.*para_miu,2)',X_num,1)-2*data*para_miu';
%返回distant每行最小值所在的下标
[~,label]=min(distant,[],2);
elseif choose==2
%用kmeans进行初始化聚类，将数据集聚为K类，输出每个样例的类标签
label=kmeans(data, K);
elseif choose==3
%用FCM算法进行初始化
options=[NaN, NaN, NaN, 0];
[~, responsivity]=fcm(data, K, options); %用FCM算法求出隶属度矩阵
[~, label]=max(responsivity', [], 2);
elseif choose==4
label = litekmeans(data, K,'Replicates',20);
end
litekmeans.m
function [label, center, bCon, sumD, D] = litekmeans(X, k, varargin)
% [IDX, C] = litekmeans(data, K,'Replicates',20);
%LITEKMEANS K-means clustering, accelerated by matlab matrix operations.
%
% label = LITEKMEANS(X, K) partitions the points in the N-by-P data matrix
% X into K clusters. This partition minimizes the sum, over all
% clusters, of the within-cluster sums of point-to-cluster-centroid
% distances. Rows of X correspond to points, columns correspond to
% variables. KMEANS returns an N-by-1 vector label containing the
% cluster indices of each point.
%
% [label, center] = LITEKMEANS(X, K) returns the K cluster centroid
% locations in the K-by-P matrix center.
%
% [label, center, bCon] = LITEKMEANS(X, K) returns the bool value bCon to
% indicate whether the iteration is converged.
%
% [label, center, bCon, SUMD] = LITEKMEANS(X, K) returns the
% within-cluster sums of point-to-centroid distances in the 1-by-K vector
% sumD.
%
% [label, center, bCon, SUMD, D] = LITEKMEANS(X, K) returns
% distances from each point to every centroid in the N-by-K matrix D.
%
% [ ... ] = LITEKMEANS(..., 'PARAM1',val1, 'PARAM2',val2, ...) specifies
% optional parameter name/value pairs to control the iterative algorithm
% used by KMEANS. Parameters are:
%
% 'Distance' - Distance measure, in P-dimensional space, that KMEANS
% should minimize with respect to. Choices are:
% {'sqEuclidean'} - Squared Euclidean distance (the default)
% 'cosine' - One minus the cosine of the included angle
% between points (treated as vectors). Each
% row of X SHOULD be normalized to unit. If
% the intial center matrix is provided, it
% SHOULD also be normalized.
%
% 'Start' - Method used to choose initial cluster centroid positions,
% sometimes known as "seeds". Choices are:
% {'sample'} - Select K observations from X at random (the default)
% 'cluster' - Perform preliminary clustering phase on random 10%
% subsample of X. This preliminary phase is itself
% initialized using 'sample'. An additional parameter
% clusterMaxIter can be used to control the maximum
% number of iterations in each preliminary clustering
% problem.
% matrix - A K-by-P matrix of starting locations; or a K-by-1
% indicate vector indicating which K points in X
% should be used as the initial center. In this case,
% you can pass in [] for K, and KMEANS infers K from
% the first dimension of the matrix.
%
% 'MaxIter' - Maximum number of iterations allowed. Default is 100.
%
% 'Replicates' - Number of times to repeat the clustering, each with a
% new set of initial centroids. Default is 1. If the
% initial centroids are provided, the replicate will be
% automatically set to be 1.
%
% 'clusterMaxIter' - Only useful when 'Start' is 'cluster'. Maximum number
% of iterations of the preliminary clustering phase.
% Default is 10.
%
%
% Examples:
%
% fea = rand(500,10);
% [label, center] = litekmeans(fea, 5, 'MaxIter', 50);
%
% fea = rand(500,10);
% [label, center] = litekmeans(fea, 5, 'MaxIter', 50, 'Replicates', 10);
%
% fea = rand(500,10);
% [label, center, bCon, sumD, D] = litekmeans(fea, 5, 'MaxIter', 50);
% TSD = sum(sumD);
%
% fea = rand(500,10);
% initcenter = rand(5,10);
% [label, center] = litekmeans(fea, 5, 'MaxIter', 50, 'Start', initcenter);
%
% fea = rand(500,10);
% idx=randperm(500);
% [label, center] = litekmeans(fea, 5, 'MaxIter', 50, 'Start', idx(1:5));
%
%
% See also KMEANS
%
% [Cite] Deng Cai, "Litekmeans: the fastest matlab implementation of
% kmeans," Available at:
% http://www.zjucadcg.cn/dengcai/Data/Clustering.html, 2011.
%
% version 2.0 --December/2011
% version 1.0 --November/2011
%
% Written by Deng Cai (dengcai AT gmail.com)
if nargin < 2
error('litekmeans:TooFewInputs','At least two input arguments required.');
end
[n, p] = size(X);
pnames = { 'distance' 'start' 'maxiter' 'replicates' 'onlinephase' 'clustermaxiter'};
dflts = {'sqeuclidean' 'sample' [] [] 'off' [] };
[eid,errmsg,distance,start,maxit,reps,online,clustermaxit] = getargs(pnames, dflts, varargin{:});
if ~isempty(eid)
error(sprintf('litekmeans:%s',eid),errmsg);
end
if ischar(distance)
distNames = {'sqeuclidean','cosine'};
j = strcmpi(distance, distNames);
j = find(j);
if length(j) > 1
error('litekmeans:AmbiguousDistance', ...
'Ambiguous ''Distance'' parameter value: %s.', distance);
elseif isempty(j)
error('litekmeans:UnknownDistance', ...
'Unknown ''Distance'' parameter value: %s.', distance);
end
distance = distNames{j};
else
error('litekmeans:InvalidDistance', ...
'The ''Distance'' parameter value must be a string.');
end
center = [];
if ischar(start)
startNames = {'sample','cluster'};
j = find(strncmpi(start,startNames,length(start)));
if length(j) > 1
error(message('litekmeans:AmbiguousStart', start));
elseif isempty(j)
error(message('litekmeans:UnknownStart', start));
elseif isempty(k)
error('litekmeans:MissingK', ...
'You must specify the number of clusters, K.');
end
if j == 2
if floor(.1*n) < 5*k
j = 1;
end
end
start = startNames{j};
elseif isnumeric(start)
if size(start,2) == p
center = start;
elseif (size(start,2) == 1 || size(start,1) == 1)
center = X(start,:);
else
error('litekmeans:MisshapedStart', ...
'The ''Start'' matrix must have the same number of columns as X.');
end
if isempty(k)
k = size(center,1);
elseif (k ~= size(center,1))
error('litekmeans:MisshapedStart', ...
'The ''Start'' matrix must have K rows.');
end
start = 'numeric';
else
error('litekmeans:InvalidStart', ...
'The ''Start'' parameter value must be a string or a numeric matrix or array.');
end
% The maximum iteration number is default 100
if isempty(maxit)
maxit = 100;
end
% The maximum iteration number for preliminary clustering phase on random
% 10% subsamples is default 10
if isempty(clustermaxit)
clustermaxit = 10;
end
% Assume one replicate
if isempty(reps) || ~isempty(center)
reps = 1;
end
if ~(isscalar(k) && isnumeric(k) && isreal(k) && k > 0 && (round(k)==k))
error('litekmeans:InvalidK', ...
'X must be a positive integer value.');
elseif n < k
error('litekmeans:TooManyClusters', ...
'X must have more rows than the number of clusters.');
end
bestlabel = [];
sumD = zeros(1,k);
bCon = false;
for t=1:reps
switch start
case 'sample'
center = X(randsample(n,k),:);
case 'cluster'
Xsubset = X(randsample(n,floor(.1*n)),:);
[dump, center] = litekmeans(Xsubset, k, varargin{:}, 'start','sample', 'replicates',1 ,'MaxIter',clustermaxit);
case 'numeric'
end
last = 0;label=1;
it=0;
switch distance
case 'sqeuclidean'
while any(label ~= last) && it<maxit
last = label;
bb = full(sum(center.*center,2)');
ab = full(X*center');
D = bb(ones(1,n),:) - 2*ab;
[val,label] = min(D,[],2); % assign samples to the nearest centers
ll = unique(label);
if length(ll) < k
%disp([num2str(k-length(ll)),' clusters dropped at iter ',num2str(it)]);
missCluster = 1:k;
missCluster(ll) = [];
missNum = length(missCluster);
aa = sum(X.*X,2);
val = aa + val;
[dump,idx] = sort(val,1,'descend');
label(idx(1:missNum)) = missCluster;
end
E = sparse(1:n,label,1,n,k,n); % transform label into indicator matrix
center = full((E*spdiags(1./sum(E,1)',0,k,k))'*X); % compute center of each cluster
it=it+1;
end
if it<maxit
bCon = true;
end
if isempty(bestlabel)
bestlabel = label;
bestcenter = center;
if reps>1
if it>=maxit
aa = full(sum(X.*X,2));
bb = full(sum(center.*center,2));
ab = full(X*center');
D = bsxfun(@plus,aa,bb') - 2*ab;
D(D<0) = 0;
else
aa = full(sum(X.*X,2));
D = aa(:,ones(1,k)) + D;
D(D<0) = 0;
end
D = sqrt(D);
for j = 1:k
sumD(j) = sum(D(label==j,j));
end
bestsumD = sumD;
bestD = D;
end
else
if it>=maxit
aa = full(sum(X.*X,2));
bb = full(sum(center.*center,2));
ab = full(X*center');
D = bsxfun(@plus,aa,bb') - 2*ab;
D(D<0) = 0;
else
aa = full(sum(X.*X,2));
D = aa(:,ones(1,k)) + D;
D(D<0) = 0;
end
D = sqrt(D);
for j = 1:k
sumD(j) = sum(D(label==j,j));
end
if sum(sumD) < sum(bestsumD)
bestlabel = label;
bestcenter = center;
bestsumD = sumD;
bestD = D;
end
end
case 'cosine'
while any(label ~= last) && it<maxit
last = label;
W=full(X*center');
[val,label] = max(W,[],2); % assign samples to the nearest centers
ll = unique(label);
if length(ll) < k
missCluster = 1:k;
missCluster(ll) = [];
missNum = length(missCluster);
[dump,idx] = sort(val);
label(idx(1:missNum)) = missCluster;
end
E = sparse(1:n,label,1,n,k,n); % transform label into indicator matrix
center = full((E*spdiags(1./sum(E,1)',0,k,k))'*X); % compute center of each cluster
centernorm = sqrt(sum(center.^2, 2));
center = center ./ centernorm(:,ones(1,p));
it=it+1;
end
if it<maxit
bCon = true;
end
if isempty(bestlabel)
bestlabel = label;
bestcenter = center;
if reps>1
if any(label ~= last)
W=full(X*center');
end
D = 1-W;
for j = 1:k
sumD(j) = sum(D(label==j,j));
end
bestsumD = sumD;
bestD = D;
end
else
if any(label ~= last)
W=full(X*center');
end
D = 1-W;
for j = 1:k
sumD(j) = sum(D(label==j,j));
end
if sum(sumD) < sum(bestsumD)
bestlabel = label;
bestcenter = center;
bestsumD = sumD;
bestD = D;
end
end
end
end
label = bestlabel;
center = bestcenter;
if reps>1
sumD = bestsumD;
D = bestD;
elseif nargout > 3
switch distance
case 'sqeuclidean'
if it>=maxit
aa = full(sum(X.*X,2));
bb = full(sum(center.*center,2));
ab = full(X*center');
D = bsxfun(@plus,aa,bb') - 2*ab;
D(D<0) = 0;
else
aa = full(sum(X.*X,2));
D = aa(:,ones(1,k)) + D;
D(D<0) = 0;
end
D = sqrt(D);
case 'cosine'
if it>=maxit
W=full(X*center');
end
D = 1-W;
end
for j = 1:k
sumD(j) = sum(D(label==j,j));
end
end
function [eid,emsg,varargout]=getargs(pnames,dflts,varargin)
%GETARGS Process parameter name/value pairs
% [EID,EMSG,A,B,...]=GETARGS(PNAMES,DFLTS,'NAME1',VAL1,'NAME2',VAL2,...)
% accepts a cell array PNAMES of valid parameter names, a cell array
% DFLTS of default values for the parameters named in PNAMES, and
% additional parameter name/value pairs. Returns parameter values A,B,...
% in the same order as the names in PNAMES. Outputs corresponding to
% entries in PNAMES that are not specified in the name/value pairs are
% set to the corresponding value from DFLTS. If nargout is equal to
% length(PNAMES)+1, then unrecognized name/value pairs are an error. If
% nargout is equal to length(PNAMES)+2, then all unrecognized name/value
% pairs are returned in a single cell array following any other outputs.
%
% EID and EMSG are empty if the arguments are valid. If an error occurs,
% EMSG is the text of an error message and EID is the final component
% of an error message id. GETARGS does not actually throw any errors,
% but rather returns EID and EMSG so that the caller may throw the error.
% Outputs will be partially processed after an error occurs.
%
% This utility can be used for processing name/value pair arguments.
%
% Example:
% pnames = {'color' 'linestyle', 'linewidth'}
% dflts = { 'r' '_' '1'}
% varargin = {{'linew' 2 'nonesuch' [1 2 3] 'linestyle' ':'}
% [eid,emsg,c,ls,lw] = statgetargs(pnames,dflts,varargin{:}) % error
% [eid,emsg,c,ls,lw,ur] = statgetargs(pnames,dflts,varargin{:}) % ok
% We always create (nparams+2) outputs:
% one each for emsg and eid
% nparams varargs for values corresponding to names in pnames
% If they ask for one more (nargout == nparams+3), it's for unrecognized
% names/values
% Original Copyright 1993-2008 The MathWorks, Inc.
% Modified by Deng Cai (dengcai@gmail.com) 2011.11.27
% Initialize some variables
emsg = '';
eid = '';
nparams = length(pnames);
varargout = dflts;
unrecog = {};
nargs = length(varargin);
% Must have name/value pairs
if mod(nargs,2)~=0
eid = 'WrongNumberArgs';
emsg = 'Wrong number of arguments.';
else
% Process name/value pairs
for j=1:2:nargs
pname = varargin{j};
if ~ischar(pname)
eid = 'BadParamName';
emsg = 'Parameter name must be text.';
break;
end
i = strcmpi(pname,pnames);
i = find(i);
if isempty(i)
% if they've asked to get back unrecognized names/values, add this
% one to the list
if nargout > nparams+2
unrecog((end+1):(end+2)) = {varargin{j} varargin{j+1}};
% otherwise, it's an error
else
eid = 'BadParamName';
emsg = sprintf('Invalid parameter name: %s.',pname);
break;
end
elseif length(i)>1
eid = 'BadParamName';
emsg = sprintf('Ambiguous parameter name: %s.',pname);
break;
else
varargout{i} = varargin{j+1};
end
end
end
varargout{nparams+1} = unrecog;
2. 数据归一化方法：normlization.m
function data = normlization(data, choose)
% 数据归一化
if choose==0
% 不归一化
data = data;
elseif choose==1
% Z-score归一化
data = bsxfun(@minus, data, mean(data));
data = bsxfun(@rdivide, data, std(data));
elseif choose==2
% 最大-最小归一化处理
[data_num,~]=size(data);
data=(data-ones(data_num,1)*min(data))./(ones(data_num,1)*(max(data)-min(data)));
end
注意：可以在elseif后面添加自己的方法。