我正在尝试为24维和32维特征向量实现GMM聚类，其中初始参数的分配由Kmeans算法完成（K均值聚类仅提供聚类中心 – MU）。我参考了这个链接，那里只为2D特征向量实现了预定义的Mu和sigma。

如果有人有GMM聚类的代码，请发布出来。

sklearn中也有预定义的GMM库，但它不提供每次迭代的似然值。sklearn GMM

回答：

def kmeans(dataSet, k, c):    # 1. 随机选择聚类    rng = np.random.RandomState(c)    p = rng.permutation(dataSet.shape[0])[:k]    centers = dataSet[p]    while True:        labels = pairwise_distances_argmin(dataSet, centers)        new_centers = np.array([dataSet[labels == i].mean(0) for i in range(k)])        if np.all(centers == new_centers):            break        centers = new_centers    cluster_data = [dataSet[labels == i] for i in range(k)]    l = []    covs = []    for i in range(k):        l.append(len(cluster_data[i]) * 1.0 / len(dataSet))        covs.append(np.cov(np.array(cluster_data[i]).T))    return centers, l, covs, cluster_datareturn new_mu, new_covs, cluster_dataclass gaussian_Mix_Model:    def __init__(self, k = 8, eps = 0.0000001):        self.k = k ## 聚类数量        self.eps = eps ## 停止阈值 `epsilon`    def calculate_Exp_Maxim(self, X, max_iters = 1000):        # n = 数据点数量, d = 数据点维度                n, d = X.shape        mu, Cov = [], []        for i in range(1,k):            new_mu, new_covs, cluster_data = kmeans(dataSet, k, c)            # 初始化新参数                     mu[k] = new_mu            Cov[k]= new_cov            # 初始化权重            w = [1./self.k] * self.k            R = np.zeros((n, self.k))            ### 似然值            LLhoods = []            P = lambda mu, s: np.linalg.det(s) ** -.5 ** (2 * np.pi) ** (-X.shape[1]/2.) \                * np.exp(-.5 * np.einsum('ij, ij -> i',\                        X - mu, np.dot(np.linalg.inv(s) , (X - mu).T).T ) )             # 迭代至最大迭代次数                    while len(LLhoods) < max_iters:            # 期望计算             ## 每个K聚类的成员关系            for k in range(self.k):                R[:, k] = w[k] * P(mu[k], Cov[k])            # 计算对数似然值            LLhood = np.sum(np.log(np.sum(R, axis = 1)))            # 现在将对数似然值存储到列表中             LLhoods.append(LLhood)            # 计算每个聚类的数据点数量            R = (R.T / np.sum(R, axis = 1)).T                               N_ks = np.sum(R, axis = 0)            # 最大化并计算新参数             for k in range(self.k):                # 计算新均值                mu[k] = 1. / N_ks[k] * np.sum(R[:, k] * X.T, axis = 1).T                x_mu = np.matrix(X - mu[k])                # 计算新协方差                Cov[k] = np.array(1 / N_ks[k] * np.dot(np.multiply(x_mu.T,  R[:, k]), x_mu))                # 计算新PiK                w[k] = 1. / n * N_ks[k]            # 检查是否收敛            if (np.abs(LLhood - LLhoods[-2]) < self.eps) and (iteration < max_iters): break            else:                Continue    from collections import namedtuple    self.params = namedtuple('params', ['mu', 'Cov', 'w', 'LLhoods', 'num_iters'])    self.params.mu = mu    self.params.Cov = Cov    self.params.w = w    self.params.LLhoods = LLhoods    self.params.num_iters = len(LLhoods)           return self.params# 调用GMM来查找模型 gmm = gaussian_Mix_Model(3, 0.000001)params = gmm.fit_EM(X, max_iters= 150)# 绘制对数似然值与迭代次数的关系图 plt.plot(LLhoods[0])plt.savefig('Dataset_2A_GMM_Class_1_K_16.png')plt.clf()plt.plot(LLhoods[1])plt.savefig('Dataset_2A_GMM_Class_2_K_16.png')plt.clf()plt.plot(LLhoods[2])plt.savefig('Dataset_2A_GMM_Class_3_K_16.png')plt.clf()