高斯混合模型matlab代码肌电

### 高斯混合模型在MATLAB中的实现

对于肌电信号处理而言，高斯混合模型(GMM)是一种有效的工具。下面展示一段基于EM算法的GMM训练过程并应用于一维或多维数据集上的MATLAB代码[^1]。

function [weights,means,covariances,ll] = gmm_em(data,k,max_iter,tol)
% GMM_EM Fits a Gaussian mixture model to data using the EM algorithm.
%
% Inputs:
%   data     : NxD matrix of D-dimensional observations (one per row).
%   k        : Number of components in the mixture model.
%   max_iter : Maximum number of iterations for the EM algorithm.
%   tol      : Convergence tolerance on log likelihood change.

N = size(data, 1);
D = size(data, 2);

% Initialize parameters randomly or with K-means++
[~, means, ~] = kmeans(data, k); % Initial cluster centers from k-means++

covariances = repmat(cov(data), [k, 1]);
weights = ones(1, k)/k;

ll_old = -inf;
for iter=1:max_iter,
    % E-step: Compute responsibilities r_ik
    resp = zeros(N, k);
    
    for i=1:k,
        normpdf(:,i)=mvnpdf(data,means(i,:),squeeze(covariances(:,:,i)));
        resp(:,i) = weights(i)*normpdf(:,i);
    end
    
    ll_new=sum(log(sum(resp,2))); % Log-likelihood calculation
    
    if abs(ll_new-ll_old)<tol*abs(ll_old),
        break; % Stop when improvement is small enough
    end
    
    ll_old = ll_new;
    
    % M-step: Reestimate parameters based on current responsibility estimates
    resp = bsxfun(@rdivide,resp,sum(resp,2)); %#ok<BSXFUN>
    
    N_k = sum(resp,1);
    weights = N_k/N;
    means = diag(1./N_k)*(resp'*data);
    
    for j=1:k,
        diff = data-repmat(means(j,:),N,1);
        covariances(:,:,j) = ...
            (diff'*(bsxfun(@times,resp(:,j),diff)))/(N_k(j));
    end
end

此函数实现了完整的期望最大化（EM）迭代流程来拟合给定的数据分布。通过调整输入参数`k`,可以控制所建模的概率密度函数中正态分量的数量；而`max_iter`和`tol`则分别设定了最大循环次数以及收敛判据阈值[^1]。

为了适应特定于肌电图信号的特点，在实际应用之前可能还需要针对具体情况进行预处理操作，比如滤波去噪、特征提取等前置步骤，并且依据实验需求设定合适的组件数目\(K\)以达到最佳分类效果。