GMM-实现聚类的代码示例

Matlab 代码：

 % GMM code

 function varargout = gmm(X, K_or_centroids)

     % input X:N-by-D data matrix
     % input K_or_centroids: K-by-D centroids

     % 阈值
     threshold = 1e-15;
     % 读取数据维度
     [N, D] = size(X);
     % 判断输入质心是否为标量
     if isscalar(K_or_centroids)
         % 是标量，随机选取K个质心
         K = K_or_centroids;
         rnpm = randperm(N); % 打乱的N个序列
         centroids = X(rnpm(:K), :);
     else   % 矩阵，给出每一类的初始化
         K = size(K_or_centroids, );
         centroids = K_or_centroids;
     end

     % 定义模型初值
     [pMiu pPi pSigma] = init_params();

     Lprev = -inf;
     while true
         % E-step,估算出概率值
         % Px: N-by-K
         Px = calc_prob();

         % pGamma新的值,样本点所占的权重
         % pPi:-by-K     pGamma:N-by-K
         pGamma = Px ./ repmat(pPi, N, );
         % 对pGamma的每一行进行求和,sum(x,):每一行求和
         pGamma = pGamma ./ repmat(sum(pGamma, ) , , K);

         % M-step
         % 每一个组件给予新的值
         Nk = sum(pGamma,);
         pMiu = diag(./Nk)*pGamma'*X;
         pPi = Nk/N;
         for kk = 1:K
            Xshift = X - repmat(pMiu(kk, :) ,N, 1);
            pSigma(:,:,kk) = (Xshift'*(diag(pGamma(:,kk))*Xshift)) / Nk(kk);
         end

         % 观察收敛，convergence
         L = sum(log(Px*pPi'));
         if L-Lprev < threshold
             break;
         end
         Lprev = L;

     end

     % 输出参数判定
     if nargout == 1
         varargout = {Px};
     else
         model = [];
         model.Miu = pMiu;
         model.Sigma = pSigma;
         model.Pi = pPi;
         varargout = {Px, model};
     end

     function [pMiu pPi pSigma] = init_params()
        pMiu = centroids; % 均值，K类的中心
        pPi = zeros(1, K); % 概率
        pSigma = zeros(D, D, K); % 协方差，每一个都是D-by-D

        % (X - pMiu)^2 = X^2 + pMiu^2 - 2*X*pMiu
        distmat = repmat(sum(X.*X, 2), 1, K) + repmat(sum(pMiu.*pMiu, 2)', N, ) - *X*pMiu';
        [dummy labels] = min(distmat, [], 2); % 找出每一行的最小值,并标出列的位置

        for k=1:K   %初始化参数
            Xk = X(labels == k, :);
            pPi(k) = size(Xk, 1)/N;
            pSigma(:, :, k) = cov(Xk);
        end
     end

     % 计算概率值
     function Px = calc_prob()
         Px = zeros(N,K);
         for k=1:K
             Xshift = X - repmat(pMiu(k,:),N,1);
             inv_pSigma = inv(pSigma(:,:,k)+diag(repmat(threshold, 1, size(pSigma(:,:,k),1))));
             tmp = sum((Xshift*inv_pSigma).*Xshift, 2);
             coef = (2*pi)^(-D/2)*sqrt(det(inv_pSigma));
             Px(:,k) = coef * exp(-1/2*tmp);
         end
     end

 end

测试主程序：

 % 测试代码
 clear all
 clc

 data = load('testSet.txt');
 [PX, Model] = gmm(data, );
 [~,index] = max(PX'); % 每一列的最大值

 cent = Model.Miu;
 figure
 I = find(index == );
 scatter(data(I,), data(I,))
 hold on
 scatter(cent(,), cent(,) ,, 'filled');
 hold on
 I = find(index == );
 scatter(data(I,),data(I,))
 hold on
 scatter(cent(,),cent(,),,'filled')
 hold on
 I = find(index == );
 scatter(data(I,),data(I,))
 hold on
 scatter(cent(,),cent(,),,'filled')
 hold on
 I = find(index == );
 scatter(data(I,),data(I,))
 hold on
 scatter(cent(,),cent(,),,'filled')

示意图：

参考自：http://www.voidcn.com/blog/llp1992/article/p-2308490.html