利用Python实现高斯混合模型（GMM）
Python代码
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.preprocessing import Normalizer
from sklearn.metrics import accuracy_score
class GMM:
def __init__(self,Data,K,weights = None,means = None,covars = None):
"""
这是GMM（高斯混合模型）类的构造函数
:param Data: 训练数据
:param K: 高斯分布的个数
:param weigths: 每个高斯分布的初始概率（权重）
:param means: 高斯分布的均值向量
:param covars: 高斯分布的协方差矩阵集合
"""
self.Data = Data
self.K = K
if weights is not None:
self.weights = weights
else:
self.weights = np.random.rand(self.K)
self.weights /= np.sum(self.weights) # 归一化
col = np.shape(self.Data)[1]
if means is not None:
self.means = means
else:
self.means = []
for i in range(self.K):
mean = np.random.rand(col)
#mean = mean / np.sum(mean) # 归一化
self.means.append(mean)
if covars is not None:
self.covars = covars
else:
self.covars = []
for i in range(self.K):
cov = np.random.rand(col,col)
#cov = cov / np.sum(cov) # 归一化
self.covars.append(cov) # cov是np.array,但是self.covars是list
def Gaussian(self,x,mean,cov):
"""
这是自定义的高斯分布概率密度函数
:param x: 输入数据
:param mean: 均值数组
:param cov: 协方差矩阵
:return: x的概率
"""
dim = np.shape(cov)[0]
# cov的行列式为零时的措施
covdet = np.linalg.det(cov + np.eye(dim) * 0.001)
covinv = np.linalg.inv(cov + np.eye(dim) * 0.001)
xdiff = (x - mean).reshape((1,dim))
# 概率密度
prob = 1.0/(np.power(np.power(2*np.pi,dim)*np.abs(covdet),0.5))*\
np.exp(-0.5*xdiff.dot(covinv).dot(xdiff.T))[0][0]
return prob
def GMM_EM(self):
"""
这是利用EM算法进行优化GMM参数的函数
:return: 返回各组数据的属于每个分类的概率
"""
loglikelyhood = 0
oldloglikelyhood = 1
len,dim = np.shape(self.Data)
# gamma表示第n个样本属于第k个混合高斯的概率
gammas = [np.zeros(self.K) for i in range(len)]
while np.abs(loglikelyhood-oldloglikelyhood) > 0.00000001:
oldloglikelyhood = loglikelyhood
# E-step
for n in range(len):
# respons是GMM的EM算法中的权重w，即后验概率
respons = [self.weights[k] * self.Gaussian(self.Data[n], self.means[k], self.covars[k])
for k in range(self.K)]
respons = np.array(respons)
sum_respons = np.sum(respons)
gammas[n] = respons/sum_respons
# M-step
for k in range(self.K):
#nk表示N个样本中有多少属于第k个高斯
nk = np.sum([gammas[n][k] for n in range(len)])
# 更新每个高斯分布的概率
self.weights[k] = 1.0 * nk / len
# 更新高斯分布的均值
self.means[k] = (1.0/nk) * np.sum([gammas[n][k] * self.Data[n] for n in range(len)], axis=0)
xdiffs = self.Data - self.means[k]
# 更新高斯分布的协方差矩阵
self.covars[k] = (1.0/nk)*np.sum([gammas[n][k]*xdiffs[n].reshape((dim,1)).dot(xdiffs[n].reshape((1,dim))) for n in range(len)],axis=0)
loglikelyhood = []
for n in range(len):
tmp = [np.sum(self.weights[k]*self.Gaussian(self.Data[n],self.means[k],self.covars[k])) for k in range(self.K)]
tmp = np.log(np.array(tmp))
loglikelyhood.append(list(tmp))
loglikelyhood = np.sum(loglikelyhood)
for i in range(len):
gammas[i] = gammas[i]/np.sum(gammas[i])
self.posibility = gammas
self.prediction = [np.argmax(gammas[i]) for i in range(len)]
def run_main():
"""
这是主函数
"""
# 导入Iris数据集
iris = load_iris()
label = np.array(iris.target)
data = np.array(iris.data)
print("Iris数据集的标签：\n",label)
# 对数据进行预处理
data = Normalizer().fit_transform(data)
# 解决画图是的中文乱码问题
mpl.rcParams['font.sans-serif'] = [u'simHei']
mpl.rcParams['axes.unicode_minus'] = False
# 数据可视化
plt.scatter(data[:,0],data[:,1],c = label)
plt.title("Iris数据集显示")
plt.show()
# GMM模型
K = 3
gmm = GMM(data,K)
gmm.GMM_EM()
y_pre = gmm.prediction
print("GMM预测结果：\n",y_pre)
print("GMM正确率为：\n",accuracy_score(label,y_pre))
plt.scatter(data[:, 0], data[:, 1], c=y_pre)
plt.title("GMM结果显示")
plt.show()
if __name__ == '__main__':
run_main()