如何在python中实现EM-GMM？

如何在python中实现EM-GMM？

正如我在评论中提到的，我看到的关键点是“手段”`初始化。遵循[sk]的默认实现
混合物,
我没有随机初始化，而是切换到KMeans。

import numpy as npimport seaborn as snsimport matplotlib.pyplot as pltplt.style.use('seaborn')eps=1e-8def PDF(data, means, variances):    return 1/(np.sqrt(2 * np.pi * variances) + eps) * np.exp(-1/2 * (np.square(data - means) / (variances + eps)))def EM_GMM(data, k=3, iterations=100, init_strategy='kmeans'):    weights = np.ones((k, 1)) / k # shape=(k, 1)    if init_strategy=='kmeans':        from sklearn.cluster import KMeans        km = KMeans(k).fit(data[:, None])        means = km.cluster_centers_ # shape=(k, 1)    else: # init_strategy=='random'        means = np.random.choice(data, k)[:, np.newaxis] # shape=(k, 1)    variances = np.random.random_sample(size=k)[:, np.newaxis] # shape=(k, 1)    data = np.repeat(data[np.newaxis, :], k, 0) # shape=(k, n)    for step in range(iterations):        # Expectation step        likelihood = PDF(data, means, np.sqrt(variances)) # shape=(k, n)        # Maximization step        b = likelihood * weights # shape=(k, n)        b /= np.sum(b, axis=1)[:, np.newaxis] + eps        # updage means, variances, and weights        means = np.sum(b * data, axis=1)[:, np.newaxis] / (np.sum(b, axis=1)[:, np.newaxis] + eps)        variances = np.sum(b * np.square(data - means), axis=1)[:, np.newaxis] / (np.sum(b, axis=1)[:, np.newaxis] + eps)        weights = np.mean(b, axis=1)[:, np.newaxis]    return means, variances

This seems to yield the desired output much more consistently:

s = np.array([25.31      , 24.31      , 24.12      , 43.46      , 41.48666667,   41.48666667, 37.54      , 41.175     , 44.81      , 44.44571429,   44.44571429, 44.44571429, 44.44571429, 44.44571429, 44.44571429,   44.44571429, 44.44571429, 44.44571429, 44.44571429, 44.44571429,   44.44571429, 44.44571429, 39.71      , 26.69      , 34.15      ,   24.94      , 24.75      , 24.56      , 24.38      , 35.25      ,   44.62      , 44.94      , 44.815     , 44.69      , 42.31      ,   40.81      , 44.38      , 44.56      , 44.44      , 44.25      ,   43.66666667, 43.66666667, 43.66666667, 43.66666667, 43.66666667,   40.75      , 32.31      , 36.08      , 30.135     , 24.19      ])k=3n_iter=100means, variances = EM_GMM(s, k, n_iter)print(means,variances)[[44.42596231] [24.509301  ] [35.4137508 ]] [[0.07568723] [0.10583743] [0.52125856]]# Plotting the resultscolors = ['green', 'red', 'blue', 'yellow']bins = np.linspace(np.min(s)-2, np.max(s)+2, 100)plt.figure(figsize=(10,7))plt.xlabel('$x$')plt.ylabel('pdf')sns.scatterplot(s, [0.05] * len(s), color='navy', s=40, marker=2, label='Series data')for i, (m, v) in enumerate(zip(means, variances)):    sns.lineplot(bins, PDF(bins, m, v), color=colors[i], label=f'Cluster {i+1}')plt.legend()plt.plot()

最后我们可以看到，纯随机初始化会产生不同的结果；让我们看看结果“means”：

for _ in range(5):    print(EM_GMM(s, k, n_iter, init_strategy='random')[0], 'n')[[44.42596231] [44.42596231] [44.42596231]][[44.42596231] [24.509301  ] [30.1349997 ]][[44.42596231] [35.4137508 ] [44.42596231]][[44.42596231] [30.1349997 ] [44.42596231]][[44.42596231] [44.42596231] [44.42596231]]

在某些情况下，结果是如何不同的呢是常量，意味着选择了3个相似的值而没有
迭代时会有很大的变化。在

EMGMM中添加一些打印语句

我会澄清的。