【语音识别】基于高斯混合模型（GMM）的语音识别matlab源码-优快云博客

本文链接：https://blog.youkuaiyun.com/Matlab_dashi/article/details/140115733

一、简介

1 高斯混合模型概述

高斯密度函数估计是一种参数化模型。高斯混合模型(Gaussian Mixture Model, GMM)是单一高斯概率密度函数的延伸，GMM能够平滑地近似任意形状的密度分布。高斯混合模型种类有单高斯模型(Single Gaussian Model, SGM)和高斯混合模型(Gaussian Mixture Model, GMM)两类。类似于聚类，根据高斯概率密度函数(Probability Density Function, PDF)参数不同，每一个高斯模型可以看作一种类别，输入一个样本x，即可通过PDF计算其值，然后通过一个阈值来判断该样本是否属于高斯模型。很明显，SGM适合于仅有两类别问题的划分，而GMM由于具有多个模型，划分更为精细，适用于多类别的划分，可以应用于复杂对象建模。
1.1 单高斯模型【语音识别】基于高斯混合模型(GMM)的语音识别matlab源码_高斯混合模型
1.2 高斯混合模型
2 高斯混合模型参数估计

2.1 样本分类已知情况下的GMM 【语音识别】基于高斯混合模型(GMM)的语音识别matlab源码_高斯混合模型_05

二、源代码

function mix=gmm_init(ncentres,data,kiter,covar_type)
%% 输入：
% ncentres:混合模型数目
% train_data:训练数据
% kiter:kmeans的迭代次数
%% 输出：
% mix:gmm的初始参数集合
 
 
[dim,data_sz]=size(data');
 
mix.priors=ones(1,ncentres)./ncentres;
mix.centres=randn(ncentres,dim);
switch covar_type
case 'diag'
  % Store diagonals of covariance matrices as rows in a matrix
  mix.covars=ones(ncentres,dim);
case 'full'
  % Store covariance matrices in a row vector of matrices
  mix.covars=repmat(eye(dim),[1 1 ncentres]);
otherwise
  error(['Unknown covariance type ', mix.covar_type]);  
end
 
 
% Arbitrary width used if variance collapses to zero: make it 'large' so
% that centre is responsible for a reasonable number of points.
GMM_WIDTH=1.0;
 
%kmeans算法
% [mix.centres,options,post]=k_means(mix.centres,data);
[mix.centres,post]=k_means(mix.centres,data,kiter);
 
% Set priors depending on number of points in each cluster
cluster_sizes = max(sum(post,1),1);  % Make sure that no prior is zero
mix.priors = cluster_sizes/sum(cluster_sizes); % Normalise priors
 
switch covar_type
case 'diag'
  for j=1:ncentres
   % Pick out data points belonging to this centre
   c=data(find(post(:,j)),:);
   diffs=c-(ones(size(c,1),1)*mix.centres(j,:));
   mix.covars(j,:)=sum((diffs.*diffs),1)/size(c,1);
   % Replace small entries by GMM_WIDTH value
   mix.covars(j,:)=mix.covars(j,:)+GMM_WIDTH.*(mix.covars(j,:)<eps);
  end 
case 'full'
  for j=1:ncentres
   % Pick out data points belonging to this centre
   c=data(find(post(:,j)),:);
   diffs=c-(ones(size(c,1),1)*mix.centres(j,:));
   mix.covars(:,:,j)=(diffs'*diffs)/(size(c,1)+eps);
   % Add GMM_WIDTH*Identity to rank-deficient covariance matrices
   if rank(mix.covars(:,:,j))<dim
	mix.covars(:,:,j)=mix.covars(:,:,j)+GMM_WIDTH.*eye(dim);
   end
  end
otherwise
  error(['Unknown covariance type ', mix.covar_type]);
end
 
mix.ncentres=ncentres;
mix.covar_type=covar_type;
 
%=============================================================
function [centres,post]=k_means(centres,data,kiter)
 
[dim,data_sz]=size(data');
ncentres=size(centres,1); %簇的数目
[ignore,perm]=sort(rand(1,data_sz)); %产生任意顺序的随机数
perm = perm(1:ncentres); %取前ncentres个作为初始簇中心的序号
centres=data(perm,:); %指定初始中心点
id=eye(ncentres); %Matrix to make unit vectors easy to construct
for n=1:kiter
  % Save old centres to check for termination
  old_centres=centres; %存储旧的中心,便于计算终止条件
  
  % Calculate posteriors based on existing centres
  d2=(ones(ncentres,1)*sum((data.^2)',1))'+...
     ones(data_sz,1)* sum((centres.^2)',1)-2.*(data*(centres')); %计算距离
 
  % Assign each point to nearest centre
  [minvals, index]=min(d2', [], 1);
  post=id(index,:);
 
  num_points = sum(post, 1);
  % Adjust the centres based on new posteriors
  for j = 1:ncentres
    if (num_points(j) > 0)
      centres(j,:) = sum(data(find(post(:,j)),:), 1)/num_points(j);
    end
  end