高斯混合

class sklearn.mixture.GaussianMixture(n_components=1, covariance_type='full', tol=0.001, reg_covar=1e-06, max_iter=100,
n_init=1, init_params='kmeans', weights_init=None, means_init=None, precisions_init=None, random_state=None, warm_start=False,
verbose=0, verbose_interval=10)

1. n_components: 混合高斯模型个数，默认为 1
2. covariance_type: 协方差类型，包括 {‘full’,‘tied’, ‘diag’, ‘spherical’} 四种，full 指每个分量有各自不同的标准协方差矩阵，完全协方差矩阵（元素都不为零）， tied 指所有分量有相同的标准协方差矩阵（HMM 会用到），diag 指每个分量有各自不同对角协方差矩阵（非对角为零，对角不为零）， spherical 指每个分量有各自不同的简单协方差矩阵，球面协方差矩阵（非对角为零，对角完全相同，球面特性），默认‘full’ 完全协方差矩阵
3. tol：EM 迭代停止阈值，默认为 1e-3.
4. reg_covar: 协方差对角非负正则化，保证协方差矩阵均为正，默认为 0
5. max_iter: 最大迭代次数，默认 100
6. n_init: 初始化次数，用于产生最佳初始参数，默认为 1
7. init_params: {‘kmeans’, ‘random’}, defaults to ‘kmeans’. 初始化参数实现方式，默认用 kmeans 实现，也可以选择随机产生
8. weights_init: 各组成模型的先验权重，可以自己设，默认按照 7 产生
9. means_init: 初始化均值，同 8
10. precisions_init: 初始化精确度（模型个数，特征个数），默认按照 7 实现
11. random_state : 随机数发生器
12. warm_start : 若为 True，则 fit（）调用会以上一次 fit（）的结果作为初始化参数，适合相同问题多次 fit 的情况，能加速收敛，默认为 False。
13. verbose : 使能迭代信息显示，默认为 0，可以为 1 或者大于 1（显示的信息不同）
14. verbose_interval : 与 13 挂钩，若使能迭代信息显示，设置多少次迭代后显示信息，默认 10 次。

参考代码

import matplotlib as mpl
import matplotlib.pyplot as plt

import numpy as np

from sklearn import datasets
from sklearn.mixture import GaussianMixture
from sklearn.model_selection import StratifiedKFold

print(__doc__)

colors = ['navy', 'turquoise', 'darkorange']


def make_ellipses(gmm, ax):
    for n, color in enumerate(colors):
        if gmm.covariance_type == 'full':
            covariances = gmm.covariances_[n][:2, :2]
        elif gmm.covariance_type == 'tied':
            covariances = gmm.covariances_[:2, :2]
        elif gmm.covariance_type == 'diag':
            covariances = np.diag(gmm.covariances_[n][:2])
        elif gmm.covariance_type == 'spherical':
            covariances = np.eye(gmm.means_.shape[1]) * gmm.covariances_[n]
        v, w = np.linalg.eigh(covariances)
        u = w[0] / np.linalg.norm(w[0])
        angle = np.arctan2(u[1], u[0])
        angle = 180 * angle / np.pi  # convert to degrees
        v = 2. * np.sqrt(2.) * np.sqrt(v)
        ell = mpl.patches.Ellipse(gmm.means_[n, :2], v[0], v[1],
                                  180 + angle, color=color)
        ell.set_clip_box(ax.bbox)
        ell.set_alpha(0.5)
        ax.add_artist(ell)
        ax.set_aspect('equal', 'datalim')

iris = datasets.load_iris()

# Break up the dataset into non-overlapping training (75%) and testing
# (25%) sets.
skf = StratifiedKFold(n_splits=4)
# Only take the first fold.
train_index, test_index = next(iter(skf.split(iris.data, iris.target)))


X_train = iris.data[train_index]
y_train = iris.target[train_index]
X_test = iris.data[test_index]
y_test = iris.target[test_index]

n_classes = len(np.unique(y_train))

# Try GMMs using different types of covariances.
# print(n_classes)
estimators = {cov_type: GaussianMixture(n_components=n_classes,
              covariance_type=cov_type, max_iter=20, random_state=0)
              for cov_type in ['spherical', 'diag', 'tied', 'full']}

n_estimators = len(estimators)

plt.figure(figsize=(3 * n_estimators // 2, 6))
plt.subplots_adjust(bottom=.01, top=0.95, hspace=.15, wspace=.05,
                    left=.01, right=.99)


for index, (name, estimator) in enumerate(estimators.items()):
    # Since we have class labels for the training data, we can
    # initialize the GMM parameters in a supervised manner.
    estimator.means_init = np.array([X_train[y_train == i].mean(axis=0)
                                    for i in range(n_classes)])

    # Train the other parameters using the EM algorithm.
    estimator.fit(X_train)

    h = plt.subplot(2, n_estimators // 2, index + 1)
    make_ellipses(estimator, h)

    for n, color in enumerate(colors):
        data = iris.data[iris.target == n]
        plt.scatter(data[:, 0], data[:, 1], s=0.8, color=color,
                    label=iris.target_names[n])
    # Plot the test data with crosses
    for n, color in enumerate(colors):
        data = X_test[y_test == n]
        plt.scatter(data[:, 0], data[:, 1], marker='x', color=color)

    y_train_pred = estimator.predict(X_train)
    train_accuracy = np.mean(y_train_pred.ravel() == y_train.ravel()) * 100
    plt.text(0.05, 0.9, 'Train accuracy: %.1f' % train_accuracy,
             transform=h.transAxes)

    y_test_pred = estimator.predict(X_test)
    test_accuracy = np.mean(y_test_pred.ravel() == y_test.ravel()) * 100
    plt.text(0.05, 0.8, 'Test accuracy: %.1f' % test_accuracy,
             transform=h.transAxes)

    plt.xticks(())
    plt.yticks(())
    plt.title(name)

plt.legend(scatterpoints=1, loc='lower right', prop=dict(size=12))


plt.show()