gaussian mixture model

1.  A Gaussian Mixture Model (GMM) is a parametric
representation of a probability density function, based
on a weighted sum of multi-variate Gaussian
distributions
 GMMs are commonly used as a parametric model of
the probability distribution of continuous
measurements or features in a biometric system
 GMM parameters are estimated from training data
using the iterative Expectation-Maximization (EM)
algorithm or Maximum A Posteriori (MAP)
estimation from a well-trained prior model

2.  GMM is computationally inexpensive, does not require
phonetically labeled training speech, and is well suited
for text-independent tasks, where there is no strong
prior knowledge of the spoken text.
 GMM is used in Signal Processing , Speaker
Recognition, Language Identification, Classification etc
 Big phoneme or vocabulary database no needed.
 Text independent verification.
 HMM doesn’t shown advantage over GMM.

3.  An Expectation–Maximization (EM) algorithm is
an iterative method for finding Maximum
Likelihood or Maximum A Posteriori(MAP)
estimates of parameters in statistical models, where
the model depends on unobserved latent variables
 EM Algorithm consists of two major steps:
1st --E (Expectation) step
2nd--M (Maximization) step

4. E (Expectation) step:
In the E-step, the expected value of the log-likelihood
function is calculated given the observed data and current
estimate of the model parameters.
M (Maximization) step:
The M-step computes the parameters which maximize the
expected log-likelihood found on the E-step. These
parameters are then used to determine the distribution of
the latent variables in the next E-step until the algorithm
has converged.

5. Overview of EM
Algorithm

6.  A maximum a posteriori probability (MAP)
estimate is a mode of the posterior distribution
 The MAP estimation is a two step estimation process:
1st-- Estimates of the sufficient statistics of the training
data are computed for each mixture in the prior model.
2nd-- For adaptation these ‘new’ sufficient statistic
estimates are then combined with the ‘old’ sufficient
statistics from the prior mixture parameters using a
data-dependent mixing coefficient.

7. In statistics, maximum-likelihood estimation (MLE) is a
method of estimating the parameters of a statistical model.
When applied to a data set and given a statistical model,
maximum-likelihood estimation provides estimates for the
model's parameters

8. 1. Language Identification:A Tutorial(Eliathamby
Ambikairajah,Haizhou Li, Liang Wang,Bo Yin, and
Vidhyasaharan Sethu)
2. Language Identification of Indian Languages Based on
Gaussian Mixture Models(Pinki Roy, Pradip K. Das)
3. Gaussian Mixture Models(Douglas Reynolds)
4. wikipedia