端元混合模型的代码

端元混合模型（Mixture Model）是一种常用的聚类算法，其代码实现如下：

import numpy as np
from sklearn.cluster import KMeans

class MixtureModel:
    def __init__(self, n_components = 2):
        self.n_components = n_components
        self.weights = None
        self.means = None
        self.covariances = None

    def fit(self, X, n_iter = 100):
        n_samples, n_features = X.shape

        # 初始化混合模型参数
        self.weights = np.ones(self.n_components) / self.n_components
        self.means = KMeans(n_clusters = self.n_components).fit(X).cluster_centers_
        self.covariances = np.tile(np.identity(n_features), (self.n_components, 1, 1))

        # EM算法迭代
        for i in range(n_iter):
            # E步骤：计算每个样本属于每个混合成分的概率
            likelihood = np.zeros((n_samples, self.n_components))
            for j in range(self.n_components):
                likelihood[:, j] = self.weights[j] * multivariate_normal.pdf(X, mean = self.means[j], cov = self.covariances[j])
            responsibility = likelihood / np.sum(likelihood, axis = 1, keepdims = True)

            # M步骤：重新估计混合模型参数
            Nk = np.sum(responsibility, axis = 0)
            self.weights = Nk / n_samples
            self.means = np.dot(responsibility.T, X) / Nk.reshape(-1, 1)
            for j in range(self.n_components):
                diff = X - self.means[j]
                self.covariances[j] = np.dot(responsibility[:, j] * diff.T, diff) / Nk[j]

    def predict(self, X):
        likelihood = np.zeros((X.shape[0], self.n_components))
        for j in range(self.n_components):
            likelihood[:, j] = self.weights[j] * multivariate_normal.pdf(X, mean = self.means[j], cov = self.covariances[j])
        return np.argmax(likelihood, axis = 1)

其中，`fit`方法是针对训练数据进行混合模型的参数估计，`predict`方法则是对新数据进行分类预测。这里使用`scikit-learn`库中的`KMeans`算法来初始化混合模型的均值参数。在迭代过程中，使用`EM`算法来更新混合模型的参数。