2019-01-13[Stay Sharp]Gaussian m

2019-01-13 本文已影响4人三千雨点

What is gaussian mixture model ?

Gaussian mixture models are a probabilistic model for representing normally distributed subpopulations within an overall population.

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The model is parameterized by two types of values:

the mixture component weights
the component means and variances.
For a Gaussian mixture model with $K$ components.

$\begin{aligned} p ( x ) & = \sum _ { i = 1 } ^ { K } \phi _ { i } \mathcal { N } ( x | \mu _ { i } , \sigma _ { i } ) \\ \mathcal { N } ( x | \mu _ { i } , \sigma _ { i } ) & = \frac { 1 } { \sigma _ { i } \sqrt { 2 \pi } } \exp \left( - \frac { \left( x - \mu _ { i } \right) ^ { 2 } } { 2 \sigma _ { i } ^ { 2 } } \right) \\ \sum _ { i = 1 } ^ { K } \phi _ { i } & = 1 \end{aligned}$
where $\mu_{i}$ and $\sigma_{i}$ is the mean and variance to the $k^{th}$ components, and $\phi_{i}$ is the correspoing component weight. from the last equation we get the total probability distribution normalizes to 1.

clustering with Gaussian mixture models

we assume that the data points are gaussian distributed, each gaussian distribution is assigned to a single cluster.

we often use Expectation-Maximization(EM) to find the parameters of the Gaussian model for each cluster.

References

https://people.csail.mit.edu/rameshvs/content/gmm-em.pdf

https://brilliant.org/wiki/gaussian-mixture-model/

2019-01-13[Stay Sharp]Gaussian m

What is gaussian mixture model ?

clustering with Gaussian mixture models

References

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