Gaussian mixture model
Hybrid model, by definition is the probability distribution density of a few mixed together, and the Gaussian mixture model is the most common hybrid model;
GMM, the full name of Gaussian Mixture Model, Chinese name Gaussian mixture model, which is composed of a plurality of Gaussian distribution model mix;
Probability density function
K represents the number of Gaussian distribution, [alpha] K represents a coefficient of each Gaussian distribution, [alpha] K > 0, and Σα K =. 1,
Ø (Y | [theta] K ) represents each Gaussian distribution, [theta] K represents a Gaussian distribution for each parameter, [theta] K = (U K , [sigma] K 2 );
for example
Men and women are subject to their own height Gaussian distribution, the men and women mix together, then their height on the Gaussian mixture distribution;
Gaussian mixture model is to use height data mixed together, men and women estimated their Gaussian distribution
summary
GMM fact divided into two steps, the first step is to choose a Gaussian distribution, a data set such as man, to take this to a probability distribution, [alpha] K ,
A sample is then taken from this distribution, equivalent to a normal Gaussian distribution
GMM commonly used in cluster, that is, the probability density distribution for each clustered together; if the probability density distribution is known, it becomes a parameter estimation problem
EM interpretation GMM
EM is the core of hidden variables and the likelihood function
Derivative results were as follows
GMM EM algorithm
Algorithmic process
References:
https://blog.csdn.net/jinping_shi/article/details/59613054
"Statistical learning methods" Lee Hang