2019-01-13[Stay Sharp]Gaussian m

作者: 三千雨点 | 来源:发表于2019-01-13 20:22 被阅读4次

2019-01-13[Stay Sharp]Gaussian m
[Stay Sharp]Gaussian Naive Bayes
2019-01-03[Stay Sharp]Gaussian D
面对无果的实相，如何努力而不麻木倦怠
要与什么在一以让自己保持敏锐
[Stay Sharp]Perceptron
[Stay Sharp]SVM基础
从0实现高斯混合模型（EM-GMM）
[Stay Sharp]SVM Python实现
[Stay Sharp]Naive Bayes Algorith

What is gaussian mixture model ?

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

image.png

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.