# Gaussian Mixture Model Clustering

Softsampling: everypoint in our dataset will belong to every clusterthat we have, but they will have different levels of membership. 

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-LmuqxmpOyE-7k65RcIw%2Fimage.png?alt=media\&token=77fa8abd-23ab-4a59-9bec-28836f1fed00)

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmur7bI7QrmiYKUvwDG%2Fimage.png?alt=media\&token=49b9e66d-08e0-463a-a8e1-f1cc246b7a25)

Works in 2d as well.

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-LmurCuPDmG4kt6S_KEa%2Fimage.png?alt=media\&token=56775cd5-39c4-4d84-a50b-10db7ad30578)

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-LmutHwcxRJ4DeCoPP5n%2Fimage.png?alt=media\&token=e5aac1ac-f273-4246-91ee-9396ef86e6fd)

### 2d Gaussian Distribution

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-LmutddsUuB2xQeQLK0P%2Fimage.png?alt=media\&token=cfcb082e-c853-438e-9fc6-7eb8442c687f)

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmutr-lZ1uAz9Ht7w-m%2Fimage.png?alt=media\&token=9e929509-0aab-4e90-8ddd-51a2018f9fe2)

First concentric certicle = 1 std dev away from the mean (68% of the data), etc. 

### Expectation - Maximization for Gaussian Mixture

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-LmuxteOE7WchMQVb-lj%2Fimage.png?alt=media\&token=2f6d83f5-49e5-4fec-b45c-3a36c1222409)

Step1

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmv-7PLu2pMatyXi0GH%2Fimage.png?alt=media\&token=b7792e42-795e-4096-9fcb-5e969f91492d)

step 2

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmv46b64zjRbUDTPSsz%2Fimage.png?alt=media\&token=eab9ebcb-f512-4340-98fc-b40bde88a4c9)

step 3

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmv3wUPmc_ZrmE0Jvm9%2Fimage.png?alt=media\&token=3aa1371d-166f-4632-9e75-f0caf879e10c)

step 4

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmv40CYHMmUtnlpvnrm%2Fimage.png?alt=media\&token=8a537932-8bf0-4482-8e60-871ae78c7729)

We can also change the covariance type from spherical, to full - which can make it have an elipse shape

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmv4wBwpcQOYDc2RzZj%2Fimage.png?alt=media\&token=e56fb896-f496-4565-b54a-405484d73fee)

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-LmpDXaJYiI3aUWErGxL%2F-Lmv4syN8SgDSmqiztLV%2Fimage.png?alt=media\&token=37d228ea-6b4e-4184-8904-090f6fe7fd30)