I know there are a couple posts asking about why we whiten the data for ICA. I understand why we whiten to fix scaling invariants between the sources and to increase the computationally efficiency.
But most answers mention something saying we want to decorrelate our data before running ICA or it should be orthogonal. Could someone please explain the intuition behind this as well as the example in this link https://arnauddelorme.com/ica_for_dummies/.
Specifically, why does our data need to be decorrelated? The ICA assumption is that our data is statistically independent. Decorrelating our data does not create statistical independence just a form of linear independence.
As for the example in the link, I do not understand it all. If someone could break it down clearly that would be a huge help. One of the many questions I have about it is why do they apply a linear transformation to the data in the example.
A clear geometric intuition would be beyond appreciated. Thank you for the clarification.
I saw someone else had a similar question, so after I did some research and felt like I had a decent intuition, I provided an explanation that I think should clear up both questions. It can be found here Whitening/Decorrelation - why does it work?.
Please take all of this with a grain of salt until someone can confirm it.