# !/usr/bin/python
# -*- coding:utf-8 -*-
import numpy as np
from scipy.stats import multivariate_normal
from sklearn.mixture import GaussianMixture
from mpl_toolkits.mplot3d import Axes3D
import matplotlib as mpl
import matplotlib.pyplot as plt
from sklearn.metrics.pairwise import pairwise_distances_argmin
mpl.rcParams['font.sans-serif'] = ['SimHei']
mpl.rcParams['axes.unicode_minus'] = False
if __name__ == '__main__':
style = 'myself'
np.random.seed(0)
mu1_fact = (0, 0, 0)
cov1_fact = np.diag((1, 2, 3))
data1 = np.random.multivariate_normal(mu1_fact, cov1_fact, 400)
mu2_fact = (2, 2, 1)
cov2_fact = np.array(((1, 1, 3), (1, 2, 1), (0, 0, 1)))
data2 = np.random.multivariate_normal(mu2_fact, cov2_fact, 100)
data = np.vstack((data1, data2))
y = np.array([True] * 400 + [False] * 100)
if style == 'sklearn':
g = GaussianMixture(n_components=2, covariance_type='full', tol=1e-6, max_iter=1000)
g.fit(data)
print('类别概率:\t', g.weights_[0])
print('均值:\n', g.means_, '\n')
print('方差:\n', g.covariances_, '\n')
mu1, mu2 = g.means_
sigma1, sigma2 = g.covariances_
else:
num_iter = 100
n, d = data.shape
# 随机指定
# mu1 = np.random.standard_normal(d)
# print mu1
# mu2 = np.random.standard_normal(d)
# print mu2
mu1 = data.min(axis=0)
mu2 = data.max(axis=0)
sigma1 = np.identity(d)
sigma2 = np.identity(d)
pi = 0.5
# EM
for i in range(num_iter):
# E Step
norm1 = multivariate_normal(mu1, sigma1)
norm2 = multivariate_normal(mu2, sigma2)
tau1 = pi * norm1.pdf(data)
tau2 = (1 - pi) * norm2.pdf(data)
gamma = tau1 / (tau1 + tau2)
# M Step
mu1 = np.dot(gamma, data) / np.sum(gamma)
mu2 = np.dot((1 - gamma), data) / np.sum((1 - gamma))
sigma1 = np.dot(gamma * (data - mu1).T, data - mu1) / np.sum(gamma)
sigma2 = np.dot((1 - gamma) * (data - mu2).T, data - mu2) / np.sum(1 - gamma)
pi = np.sum(gamma) / n
print(i, ":\t", mu1, mu2)
print('类别概率:\t', pi)
print('均值:\t', mu1, mu2)
print('方差:\n', sigma1, '\n\n', sigma2, '\n')
# 预测分类
norm1 = multivariate_normal(mu1, sigma1)
norm2 = multivariate_normal(mu2, sigma2)
tau1 = norm1.pdf(data)
tau2 = norm2.pdf(data)
fig = plt.figure(figsize=(10, 5), facecolor='w')
ax = fig.add_subplot(121, projection='3d')
ax.scatter(data[:, 0], data[:, 1], data[:, 2], c='b', s=30, marker='o', edgecolors='k', depthshade=True)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('原始数据', fontsize=15)
ax = fig.add_subplot(122, projection='3d')
order = pairwise_distances_argmin([mu1_fact, mu2_fact], [mu1, mu2], metric='euclidean')
print(order)
if order[0] == 0:
c1 = tau1 > tau2
else:
c1 = tau1 < tau2
c2 = ~c1
acc = np.mean(y == c1)
print('准确率：%.2f%%' % (100*acc))
ax.scatter(data[c1, 0], data[c1, 1], data[c1, 2], c='r', s=30, marker='o', edgecolors='k', depthshade=True)
ax.scatter(data[c2, 0], data[c2, 1], data[c2, 2], c='g', s=30, marker='^', edgecolors='k', depthshade=True)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('EM算法分类', fontsize=15)
plt.suptitle('EM算法的实现', fontsize=18)
plt.subplots_adjust(top=0.90)
plt.tight_layout()
plt.show()
