高斯混合聚类python实现

好的，下面是高斯混合聚类的Python实现代码：

import numpy as np
from scipy.stats import multivariate_normal

class GaussianMixture:
    def __init__(self, n_components, max_iter=100, tol=1e-3):
        self.n_components = n_components
        self.max_iter = max_iter
        self.tol = tol

    def _init_params(self, X):
        self.n_samples, self.n_features = X.shape
        self.weights = np.ones(self.n_components) / self.n_components
        self.means = X[np.random.choice(self.n_samples, self.n_components, replace=False)]
        self.covs = np.array([np.eye(self.n_features)] * self.n_components)

    def _e_step(self, X):
        self.responsibilities = np.zeros((self.n_samples, self.n_components))
        for k in range(self.n_components):
            self.responsibilities[:, k] = self.weights[k] * multivariate_normal.pdf(X, self.means[k], self.covs[k])
        self.responsibilities /= np.sum(self.responsibilities, axis=1, keepdims=True)

    def _m_step(self, X):
        Nk = np.sum(self.responsibilities, axis=0)
        self.weights = Nk / self.n_samples
        self.means = np.dot(self.responsibilities.T, X) / Nk.reshape(-1, 1)
        for k in range(self.n_components):
            diff = X - self.means[k]
            self.covs[k] = np.dot(self.responsibilities[:, k] * diff.T, diff) / Nk[k]
    
    def fit(self, X):
        self._init_params(X)
        for i in range(self.max_iter):
            weights_prev = self.weights.copy()
            self._e_step(X)
            self._m_step(X)
            if np.allclose(self.weights, weights_prev, atol=self.tol):
                break

其中，`n_components`是高斯混合模型的成分数，`max_iter`是最大迭代次数，`tol`是收敛阈值。`_init_params`函数用于初始化模型参数，`_e_step`函数用于进行E步，计算每个样本属于每个成分的后验概率，`_m_step`函数用于进行M步，更新模型参数。`fit`函数用于训练模型，输入数据`X`，并进行迭代优化，直到满足收敛条件为止。