# Independant Component Analysis

PCA works to maximize variance, ICA assumes that the features are mixtures of independant sources. It tries to isolate these independant sources that are mixed in this dataset.&#x20;

Ex: say you only have 3 recordings of a piano, cello and tv that were played but not playing the same musique:&#x20;

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-Ln41l11hC8FBWgb6AAk%2F-Ln46xxhOh1wekFAjCFR%2Fimage.png?alt=media\&token=b3f82de9-8a13-41c5-8a20-e57a27aedefc)

With ICA, it is possible to retrieve each tune independantly.&#x20;

Blind source separation

![](https://846345873-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LagOeJ2nL90MQERwhxy%2F-Ln41l11hC8FBWgb6AAk%2F-Ln47OMZba4U8RH4j8Iy%2Fimage.png?alt=media\&token=f1e771a3-36fe-409f-88b8-a8a7c13cd4ff)

### Algorithm

![](broken-reference)

g is tanh function, but can be other functions, we have different options. The decorrelation matrix is W.&#x20;

ICA Assumptions:

The components are statistically independant.&#x20;

Components have non Gaussian distributions. Very important.&#x20;

The algo tries to maximise the non gaussianity. One way to calculate this is the w+ above. It is called negentropy. w+ is how we approximate it.&#x20;



Applications&#x20;

Brain scan data, retail earnings to find patterns.&#x20;
