高斯混合模型橢圓體#

繪製透過期望最大化（GaussianMixture 類別）和變分推論（具有狄利克雷過程先驗的 BayesianGaussianMixture 類別模型）獲得的兩個高斯混合的信賴橢圓體。

這兩個模型都可以存取五個元件來擬合資料。請注意，期望最大化模型將必須使用所有五個元件，而變分推論模型實際上只會使用足夠好的擬合所需的元件數量。在這裡，我們可以看到期望最大化模型任意地分割某些元件，因為它試圖擬合太多元件，而狄利克雷過程模型則會自動調整其狀態數量。

這個範例沒有顯示出來，因為我們處於低維空間，但狄利克雷過程模型的另一個優點是，由於推論演算法的正規化特性，即使每個叢集的範例數量少於資料中的維度數量，它也能有效地擬合完整共變異數矩陣。

Gaussian Mixture, Bayesian Gaussian Mixture with a Dirichlet process prior

/home/circleci/project/sklearn/mixture/_base.py:269: ConvergenceWarning:

Best performing initialization did not converge. Try different init parameters, or increase max_iter, tol, or check for degenerate data.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

import itertools

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
from scipy import linalg

from sklearn import mixture

color_iter = itertools.cycle(["navy", "c", "cornflowerblue", "gold", "darkorange"])


def plot_results(X, Y_, means, covariances, index, title):
    splot = plt.subplot(2, 1, 1 + index)
    for i, (mean, covar, color) in enumerate(zip(means, covariances, color_iter)):
        v, w = linalg.eigh(covar)
        v = 2.0 * np.sqrt(2.0) * np.sqrt(v)
        u = w[0] / linalg.norm(w[0])
        # as the DP will not use every component it has access to
        # unless it needs it, we shouldn't plot the redundant
        # components.
        if not np.any(Y_ == i):
            continue
        plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], 0.8, color=color)

        # Plot an ellipse to show the Gaussian component
        angle = np.arctan(u[1] / u[0])
        angle = 180.0 * angle / np.pi  # convert to degrees
        ell = mpl.patches.Ellipse(mean, v[0], v[1], angle=180.0 + angle, color=color)
        ell.set_clip_box(splot.bbox)
        ell.set_alpha(0.5)
        splot.add_artist(ell)

    plt.xlim(-9.0, 5.0)
    plt.ylim(-3.0, 6.0)
    plt.xticks(())
    plt.yticks(())
    plt.title(title)


# Number of samples per component
n_samples = 500

# Generate random sample, two components
np.random.seed(0)
C = np.array([[0.0, -0.1], [1.7, 0.4]])
X = np.r_[
    np.dot(np.random.randn(n_samples, 2), C),
    0.7 * np.random.randn(n_samples, 2) + np.array([-6, 3]),
]

# Fit a Gaussian mixture with EM using five components
gmm = mixture.GaussianMixture(n_components=5, covariance_type="full").fit(X)
plot_results(X, gmm.predict(X), gmm.means_, gmm.covariances_, 0, "Gaussian Mixture")

# Fit a Dirichlet process Gaussian mixture using five components
dpgmm = mixture.BayesianGaussianMixture(n_components=5, covariance_type="full").fit(X)
plot_results(
    X,
    dpgmm.predict(X),
    dpgmm.means_,
    dpgmm.covariances_,
    1,
    "Bayesian Gaussian Mixture with a Dirichlet process prior",
)

plt.show()