1.多维GMM聚类

#!usr/bin/env python
# -*- coding:utf-8 -*-
"""
@author: admin
@file: EM.py
@time: 2021/02/03
@desc:
"""import numpy as np
from scipy.stats import multivariate_normal
from sklearn.mixture import GaussianMixture
import matplotlib as mpl
import matplotlib.pyplot as plt
from sklearn.metrics.pairwise import pairwise_distances_argminmpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = Falseif __name__ == '__main__':style = 'myself'np.random.seed(0)mu1_fact = (0, 0, 0)# np.diag((1, 2, 3))生成对角线数组，除对角线外，其余位置为0cov1_fact = np.diag((1, 2, 3))# 生成一个多元正态分布矩阵data1 = np.random.multivariate_normal(mu1_fact, cov1_fact, 400) # (400,3)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,check_valid='ignore') # (100,3)data = np.vstack((data1, data2))y = np.array([True] * 400 + [False] * 100)if style == 'sklearn':# n_components表示混合高斯模型的个数# covariance_type描述协方差的类型;默认‘full’ ,完全协方差矩阵# tol：EM迭代停止阈值，默认为1e-3.# max_iter:最大迭代次数，默认100gm = GaussianMixture(n_components=2, covariance_type='full', tol=1e-6, max_iter=1000)gm.fit(data)print('类别概率:\t', gm.weights_[0])print('均值:\n', gm.means_, '\n')print('方差:\n', gm.covariances_, '\n')mu1, mu2 = gm.means_sigma1, sigma2 = gm.covariances_else:num_iter = 100n, d = data.shape# 随机指定# mu1 = np.random.standard_normal(d)# print mu1# mu2 = np.random.standard_normal(d)# print mu2mu1 = data.min(axis=0)mu2 = data.max(axis=0)sigma1 = np.identity(d)sigma2 = np.identity(d)pi = 0.5# EMfor i in range(num_iter):# E Stepnorm1 = 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 Stepmu1 = 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) / nprint(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=(13, 7), facecolor='w')ax = fig.add_subplot(121, projection='3d')ax.scatter(data[:, 0], data[:, 1], data[:, 2], c='b', s=30, marker='o', depthshade=True)ax.set_xlabel('X')ax.set_ylabel('Y')ax.set_zlabel('Z')ax.set_title(u'原始数据', fontsize=18)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 > tau2else:c1 = tau1 < tau2c2 = ~c1acc = np.mean(y == c1)print(u'准确率：%.2f%%' % (100*acc))ax.scatter(data[c1, 0], data[c1, 1], data[c1, 2], c='r', s=30, marker='o', depthshade=True)ax.scatter(data[c2, 0], data[c2, 1], data[c2, 2], c='g', s=30, marker='^', depthshade=True)ax.set_xlabel('X')ax.set_ylabel('Y')ax.set_zlabel('Z')ax.set_title(u'EM算法分类', fontsize=18)plt.suptitle(u'EM算法的实现', fontsize=21)plt.subplots_adjust(top=0.90)plt.tight_layout()plt.show()

提取码：h676

# !/usr/bin/python
# -*- coding:utf-8 -*-import numpy as np
from sklearn.mixture import GaussianMixture
from sklearn.model_selection import train_test_split
import matplotlib as mpl
import matplotlib.colors
import matplotlib.pyplot as pltmpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False# from matplotlib.font_manager import FontProperties
# font_set = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=15)
# fontproperties=font_setdef expand(a, b):d = (b - a) * 0.05return a - d, b + dif __name__ == '__main__':data = np.loadtxt('HeightWeight.csv', dtype=np.float, delimiter=',', skiprows=1)print(data.shape)y, x = np.split(data, [1, ], axis=1)x, x_test, y, y_test = train_test_split(x, y, train_size=0.6, random_state=0)gmm = GaussianMixture(n_components=2, covariance_type='full', random_state=0)gmm.fit(x)print('均值 = \n', gmm.means_)print('方差 = \n', gmm.covariances_)y_hat = gmm.predict(x)y_test_hat = gmm.predict(x_test)x_min = np.min(x, axis=0)x_max = np.max(x, axis=0)# 确保类1的身高高于类2change = (gmm.means_[0][0] > gmm.means_[1][0])if change:z = y_hat == 0y_hat[z] = 1y_hat[~z] = 0z = y_test_hat == 0y_test_hat[z] = 1y_test_hat[~z] = 0acc = np.mean(y_hat.ravel() == y.ravel())acc_test = np.mean(y_test_hat.ravel() == y_test.ravel())acc_str = u'训练集准确率：%.2f%%' % (acc * 100)acc_test_str = u'测试集准确率：%.2f%%' % (acc_test * 100)print(acc_str)print(acc_test_str)cm_light = mpl.colors.ListedColormap(['#FF8080', '#77E0A0'])cm_dark = mpl.colors.ListedColormap(['r', 'g'])# 画决策边界图x1_min, x1_max = x[:, 0].min(), x[:, 0].max()x2_min, x2_max = x[:, 1].min(), x[:, 1].max()x1_min, x1_max = expand(x1_min, x1_max)x2_min, x2_max = expand(x2_min, x2_max)x1, x2 = np.mgrid[x1_min:x1_max:500j, x2_min:x2_max:500j]grid_test = np.stack((x1.flat, x2.flat), axis=1)grid_hat = gmm.predict(grid_test)grid_hat = grid_hat.reshape(x1.shape)if change:z = grid_hat == 0grid_hat[z] = 1grid_hat[~z] = 0plt.figure(figsize=(9, 7), facecolor='w')plt.pcolormesh(x1, x2, grid_hat, cmap=cm_light, shading='auto')plt.scatter(x[:, 0], x[:, 1], s=50, c=y, marker='o', cmap=cm_dark, edgecolors='k')plt.scatter(x_test[:, 0], x_test[:, 1], s=60, c=y_test, marker='^', cmap=cm_dark, edgecolors='k')# 概率p = gmm.predict_proba(grid_test)print(p)p = p[:, 0].reshape(x1.shape)CS = plt.contour(x1, x2, p, levels=(0.1, 0.5, 0.8), colors=list('rgb'), linewidths=2)plt.clabel(CS, fontsize=15, fmt='%.1f', inline=True)ax1_min, ax1_max, ax2_min, ax2_max = plt.axis()xx = 0.9 * ax1_min + 0.1 * ax1_maxyy = 0.1 * ax2_min + 0.9 * ax2_maxplt.text(xx, yy, acc_str, fontsize=18)yy = 0.15 * ax2_min + 0.85 * ax2_maxplt.text(xx, yy, acc_test_str, fontsize=18)plt.xlim((x1_min, x1_max))plt.ylim((x2_min, x2_max))plt.xlabel(u'身高(cm)', fontsize='large')plt.ylabel(u'体重(kg)', fontsize='large')plt.title(u'EM算法估算GMM的参数', fontsize=20)plt.grid()plt.show()

2.GMM调参

# !/usr/bin/python
# -*- coding:utf-8 -*-import numpy as np
from sklearn.mixture import GaussianMixture
import matplotlib as mpl
import matplotlib.colors
import matplotlib.pyplot as pltmpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = Falsedef expand(a, b, rate=0.05):d = (b - a) * ratereturn a-d, b+ddef accuracy_rate(y1, y2):acc = np.mean(y1 == y2)return acc if acc > 0.5 else 1-accif __name__ == '__main__':np.random.seed(0)cov1 = np.diag((1, 2))print(cov1)N1 = 500N2 = 300N = N1 + N2x1 = np.random.multivariate_normal(mean=(1, 2), cov=cov1, size=N1)m = np.array(((1, 1), (1, 3)))x1 = x1.dot(m)x2 = np.random.multivariate_normal(mean=(-1, 10), cov=cov1, size=N2)x = np.vstack((x1, x2))y = np.array([0]*N1 + [1]*N2)types = ('spherical', 'diag', 'tied', 'full')err = np.empty(len(types))bic = np.empty(len(types))for i, type in enumerate(types):gmm = GaussianMixture(n_components=2, covariance_type=type, random_state=0)gmm.fit(x)err[i] = 1 - accuracy_rate(gmm.predict(x), y)bic[i] = gmm.bic(x)print('错误率：', err.ravel())print('BIC：', bic.ravel())xpos = np.arange(4)plt.figure(facecolor='w')ax = plt.axes()b1 = ax.bar(xpos-0.3, err, width=0.3, color='#77E0A0')b2 = ax.twinx().bar(xpos, bic, width=0.3, color='#FF8080')# print(b1[0])plt.grid(True)bic_min, bic_max = expand(bic.min(), bic.max())plt.ylim((bic_min, bic_max))plt.xticks(xpos, types)plt.legend([b1[0], b2[0]], (u'错误率', u'BIC'))plt.title(u'不同方差类型的误差率和BIC', fontsize=18)plt.show()optimal = bic.argmin()# print(optimal)gmm = GaussianMixture(n_components=2, covariance_type=types[optimal], random_state=0)gmm.fit(x)print('均值 = \n', gmm.means_)print('方差 = \n', gmm.covariances_)y_hat = gmm.predict(x)cm_light = mpl.colors.ListedColormap(['#FF8080', '#77E0A0'])cm_dark = mpl.colors.ListedColormap(['r', 'g'])x1_min, x1_max = x[:, 0].min(), x[:, 0].max()x2_min, x2_max = x[:, 1].min(), x[:, 1].max()x1_min, x1_max = expand(x1_min, x1_max)x2_min, x2_max = expand(x2_min, x2_max)x1, x2 = np.mgrid[x1_min:x1_max:500j, x2_min:x2_max:500j]grid_test = np.stack((x1.flat, x2.flat), axis=1)grid_hat = gmm.predict(grid_test)grid_hat = grid_hat.reshape(x1.shape)if gmm.means_[0][0] > gmm.means_[1][0]:z = grid_hat == 0grid_hat[z] = 1grid_hat[~z] = 0plt.figure(figsize=(9, 7), facecolor='w')plt.pcolormesh(x1, x2, grid_hat, cmap=cm_light,shading='auto')plt.scatter(x[:, 0], x[:, 1], s=30, c=y, marker='o', cmap=cm_dark, edgecolors='k')ax1_min, ax1_max, ax2_min, ax2_max = plt.axis()plt.xlim((x1_min, x1_max))plt.ylim((x2_min, x2_max))plt.title(u'GMM调参：covariance_type=%s' % types[optimal], fontsize=20)plt.grid()plt.show()

3. 鸢尾花数据集

import numpy as np
import pandas as pd
from sklearn.mixture import GaussianMixture
import matplotlib as mpl
import matplotlib.colors
import matplotlib.pyplot as plt
from sklearn.metrics.pairwise import pairwise_distances_argminmpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = Falseiris_feature = u'花萼长度', u'花萼宽度', u'花瓣长度', u'花瓣宽度'def expand(a, b, rate=0.05):d = (b - a) * ratereturn a-d, b+dif __name__ == '__main__':path = 'iris.data'data = pd.read_csv(path, header=None)x_prime, y = data[np.arange(4)], data[4]y = pd.Categorical(y).codesn_components = 3feature_pairs = [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]]plt.figure(figsize=(10, 9), facecolor='#FFFFFF')for k, pair in enumerate(feature_pairs):x = x_prime[pair]m = np.array([np.mean(x[y == i], axis=0) for i in range(3)])  # 均值的实际值print('实际均值 = \n', m)gmm = GaussianMixture(n_components=n_components, covariance_type='full', random_state=0)gmm.fit(x)print('预测均值 = \n', gmm.means_)print('预测方差 = \n', gmm.covariances_)y_hat = gmm.predict(x)order = pairwise_distances_argmin(m, gmm.means_, axis=1, metric='euclidean')# 实际对应标签print('顺序：\t', order)n_sample = y.sizen_types = 3change = np.empty((n_types, n_sample), dtype=np.bool)# 交换顺序for i in range(n_types):change[i] = y_hat == order[i]for i in range(n_types):y_hat[change[i]] = iacc = u'准确率：%.2f%%' % (100*np.mean(y_hat == y))print(acc)# 画决策边界图cm_light = mpl.colors.ListedColormap(['#FF8080', '#77E0A0', '#A0A0FF'])cm_dark = mpl.colors.ListedColormap(['r', 'g', '#6060FF'])x1_min, x2_min = x.min()x1_max, x2_max = x.max()x1_min, x1_max = expand(x1_min, x1_max)x2_min, x2_max = expand(x2_min, x2_max)x1, x2 = np.mgrid[x1_min:x1_max:500j, x2_min:x2_max:500j]grid_test = np.stack((x1.flat, x2.flat), axis=1)grid_hat = gmm.predict(grid_test)change = np.empty((n_types, grid_hat.size), dtype=np.bool)for i in range(n_types):change[i] = grid_hat == order[i]for i in range(n_types):grid_hat[change[i]] = igrid_hat = grid_hat.reshape(x1.shape)plt.subplot(3, 2, k+1)plt.pcolormesh(x1, x2, grid_hat, cmap=cm_light)plt.scatter(x[pair[0]], x[pair[1]], s=30, c=y, marker='o', cmap=cm_dark, edgecolors='k')xx = 0.95 * x1_min + 0.05 * x1_maxyy = 0.1 * x2_min + 0.9 * x2_maxplt.text(xx, yy, acc, fontsize=14)plt.xlim((x1_min, x1_max))plt.ylim((x2_min, x2_max))plt.xlabel(iris_feature[pair[0]], fontsize=14)plt.ylabel(iris_feature[pair[1]], fontsize=14)plt.grid()plt.tight_layout(2)plt.suptitle(u'EM算法无监督分类鸢尾花数据', fontsize=20)plt.subplots_adjust(top=0.92)plt.show()

4.GMM与DPGMM比较

import numpy as np
from sklearn.mixture import GaussianMixture, BayesianGaussianMixture
import scipy as sp
import matplotlib as mpl
import matplotlib.colors
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipsedef expand(a, b, rate=0.05):d = (b - a) * ratereturn a-d, b+dmatplotlib.rcParams['font.sans-serif'] = [u'SimHei']
matplotlib.rcParams['axes.unicode_minus'] = Falseif __name__ == '__main__':np.random.seed(0)cov1 = np.diag((1, 2))N1 = 500N2 = 300N = N1 + N2x1 = np.random.multivariate_normal(mean=(3, 2), cov=cov1, size=N1)m = np.array(((1, 1), (1, 3)))# 点乘x1 = x1.dot(m)x2 = np.random.multivariate_normal(mean=(-1, 10), cov=cov1, size=N2)x = np.vstack((x1, x2))y = np.array([0]*N1 + [1]*N2)n_components = 3# 绘制决策边界图colors = '#A0FFA0', '#2090E0', '#FF8080'cm = mpl.colors.ListedColormap(colors)x1_min, x1_max = x[:, 0].min(), x[:, 0].max()x2_min, x2_max = x[:, 1].min(), x[:, 1].max()x1_min, x1_max = expand(x1_min, x1_max)x2_min, x2_max = expand(x2_min, x2_max)x1, x2 = np.mgrid[x1_min:x1_max:500j, x2_min:x2_max:500j]grid_test = np.stack((x1.flat, x2.flat), axis=1)plt.figure(figsize=(9, 9), facecolor='w')plt.suptitle(u'GMM/DPGMM比较', fontsize=23)ax = plt.subplot(211)gmm = GaussianMixture(n_components=n_components, covariance_type='full', random_state=0)gmm.fit(x)centers = gmm.means_covs = gmm.covariances_print('GMM均值 = \n', centers)print('GMM方差 = \n', covs)y_hat = gmm.predict(x)grid_hat = gmm.predict(grid_test)grid_hat = grid_hat.reshape(x1.shape)plt.pcolormesh(x1, x2, grid_hat, cmap=cm)plt.scatter(x[:, 0], x[:, 1], s=30, c=y, cmap=cm, marker='o')clrs = list('rgbmy')for i, (center, cov) in enumerate(zip(centers, covs)):value, vector = sp.linalg.eigh(cov)width, height = value[0], value[1]v = vector[0] / sp.linalg.norm(vector[0])angle = 180* np.arctan(v[1] / v[0]) / np.pie = Ellipse(xy=center, width=width, height=height,angle=angle, color=clrs[i], alpha=0.5, clip_box = ax.bbox)ax.add_artist(e)ax1_min, ax1_max, ax2_min, ax2_max = plt.axis()plt.xlim((x1_min, x1_max))plt.ylim((x2_min, x2_max))plt.title(u'GMM', fontsize=20)plt.grid(True)# DPGMMdpgmm = BayesianGaussianMixture(n_components=n_components, covariance_type='full', max_iter=1000, n_init=5,weight_concentration_prior_type='dirichlet_process', weight_concentration_prior=0.1)dpgmm.fit(x)centers = dpgmm.means_covs = dpgmm.covariances_print('DPGMM均值 = \n', centers)print('DPGMM方差 = \n', covs)y_hat = dpgmm.predict(x)print(y_hat)ax = plt.subplot(212)grid_hat = dpgmm.predict(grid_test)grid_hat = grid_hat.reshape(x1.shape)plt.pcolormesh(x1, x2, grid_hat, cmap=cm)plt.scatter(x[:, 0], x[:, 1], s=30, c=y, cmap=cm, marker='o')for i, cc in enumerate(zip(centers, covs)):if i not in y_hat:continuecenter, cov = ccvalue, vector = sp.linalg.eigh(cov)width, height = value[0], value[1]v = vector[0] / sp.linalg.norm(vector[0])angle = 180* np.arctan(v[1] / v[0]) / np.pie = Ellipse(xy=center, width=width, height=height,angle=angle, color='m', alpha=0.5, clip_box = ax.bbox)ax.add_artist(e)plt.xlim((x1_min, x1_max))plt.ylim((x2_min, x2_max))plt.title('DPGMM', fontsize=20)plt.grid(True)plt.tight_layout()plt.subplots_adjust(top=0.9)plt.show()

5. GMM似然函数值

import numpy as np
from sklearn.mixture import GaussianMixture
import scipy as sp
import matplotlib as mpl
import matplotlib.colors
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse
import warningsdef expand(a, b, rate=0.05):d = (b - a) * ratereturn a-d, b+dif __name__ == '__main__':warnings.filterwarnings(action='ignore', category=RuntimeWarning)np.random.seed(0)cov1 = np.diag((1, 2))N1 = 500N2 = 300N = N1 + N2x1 = np.random.multivariate_normal(mean=(3, 2), cov=cov1, size=N1)m = np.array(((1, 1), (1, 3)))x1 = x1.dot(m)x2 = np.random.multivariate_normal(mean=(-1, 10), cov=cov1, size=N2)x = np.vstack((x1, x2))y = np.array([0]*N1 + [1]*N2)gmm = GaussianMixture(n_components=2, covariance_type='full', random_state=0)gmm.fit(x)centers = gmm.means_covs = gmm.covariances_print('GMM均值 = \n', centers)print('GMM方差 = \n', covs)y_hat = gmm.predict(x)colors = '#A0FFA0', '#E080A0',levels = 10cm = mpl.colors.ListedColormap(colors)x1_min, x1_max = x[:, 0].min(), x[:, 0].max()x2_min, x2_max = x[:, 1].min(), x[:, 1].max()x1_min, x1_max = expand(x1_min, x1_max)x2_min, x2_max = expand(x2_min, x2_max)x1, x2 = np.mgrid[x1_min:x1_max:500j, x2_min:x2_max:500j]grid_test = np.stack((x1.flat, x2.flat), axis=1)print(gmm.score_samples(grid_test))grid_hat = -gmm.score_samples(grid_test)grid_hat = grid_hat.reshape(x1.shape)plt.figure(figsize=(9, 7), facecolor='w')ax = plt.subplot(111)cmesh = plt.pcolormesh(x1, x2, grid_hat, cmap=plt.cm.Spectral)plt.colorbar(cmesh, shrink=0.9)CS = plt.contour(x1, x2, grid_hat, levels=np.logspace(0, 2, num=levels, base=10), colors='w', linewidths=1)plt.clabel(CS, fontsize=9, inline=True, fmt='%.1f')plt.scatter(x[:, 0], x[:, 1], s=30, c=y, cmap=cm, marker='o')for i, cc in enumerate(zip(centers, covs)):center, cov = ccvalue, vector = sp.linalg.eigh(cov)width, height = value[0], value[1]v = vector[0] / sp.linalg.norm(vector[0])angle = 180* np.arctan(v[1] / v[0]) / np.pie = Ellipse(xy=center, width=width, height=height,angle=angle, color='m', alpha=0.5, clip_box = ax.bbox)ax.add_artist(e)plt.xlim((x1_min, x1_max))plt.ylim((x2_min, x2_max))mpl.rcParams['font.sans-serif'] = [u'SimHei']mpl.rcParams['axes.unicode_minus'] = Falseplt.title(u'GMM似然函数值', fontsize=20)plt.grid(True)plt.show()

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