【GMM】理论与实现
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【GMM】理论与实现
2017年11月10日Author: Guofei
文章归类: 3-2-聚类 ,文章编号: 304
版权声明:本文作者是郭飞。转载随意,但需要标明原文链接,并通知本人
原文链接:https://www.guofei.site/2017/11/10/gmm.html
模型介绍
GMM(高斯混合模型,Gaussian misture model)是一个聚类模型,特点是可以得出概率值
P(y∣θ)=∑k=1Kαkϕ(y∣θ)P(y∣θ)=∑k=1Kαkϕ(y∣θ)
其中,∑kKαk=1∑kKαk=1
ϕ(y∣θk)=12π−−√σkexp(−(y−uk)22σ2k)ϕ(y∣θk)=12πσkexp(−(y−uk)22σk2)
参数计算
用MLE方法1
为求解MLE,引入EM算法2
Python实现
from sklearn.mixture import GaussianMixture
pca_scaled_data=PCA(n_components=2).fit_transform(data)
gm = GaussianMixture(n_components=3, n_init=3)
gm.fit(pca_scaled_data)
GaussianMixture(covariance_type=’full’, init_params=’kmeans’, max_iter=100, means_init=None, n_components=3, n_init=3, precisions_init=None, random_state=None, reg_covar=1e-06, tol=0.001, verbose=0, verbose_interval=10, warm_start=False, weights_init=None)
gm.predict(pca_scaled_data)
gm.predict_proba(pca_scaled_data)
gm.bic(pca_scaled_data)
参考资料
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