gaussianhidden-markov-modelsmixture-model

Difference between GMM and HMM


From what I understand:

If these two informations are correct, what is the difference between GMM and HMM ?

Also, in time series case (continuous data), each state is one and only one Gaussian distribution ? there is no emission probability matrix ?

Thanks for your help !!! :)


Solution

  • Those two pieces of information are NOT correct. First, you have to understand the 'process' versus random variable (RV). HMM, even its name is 'model' actually it is a (stochastic) process that RV(s) change over time index t. GMM is usually used for the emission of the process (HMM). Comparing HMM to GMM is not apple to apple, one HMM is a stochastic process even its name is a model. and GMM is related to the distribution of random variables. HMM need time index (t or n) while GMM doesn't.

    Q: Also, in time series case (continuous data), each state is one and only one Gaussian distribution? there is no emission probability matrix? A: This question is not understandable