Principle Component Analysis and and my drive into Dimensional Reduction Alley

I was set in motion by one of the Math Assignment in Mathematics for data foundation course. 

The question under consideration is whether we can do dimensional reduction? or not post SVD. What parameter and components should look out for post SVD analysis.

I started with this document  - http://courses.cs.tamu.edu/rgutier/cs790_w02/l5.pdf. A PPT with good insight into error post PCA and clarifying that Dominant Eigen Value, and corresponding Eigen Vector to be considered for Dimensional Reduction.

I did not get the difference between 2 principle axis (highest spread axis & residual error axis), until I read the paper https://blog.paperspace.com/dimension-reduction-with-principal-component-analysis/

Apart from PCA, ICA and other Dimensional reduction techniques are revealing various dimensional worlds to me. They lead me until deep learning (autoencoders) with the related links in above paper.

 

I had been getting an hit related to Co-relation and SVD. The below paper clarified the relationship

https://towardsdatascience.com/principal-component-analysis-for-dimensionality-reduction-115a3d157bad

SVD and PCA are linear analysis, I also got to know that Independent component means Independent both linearly and non linearly. (Note: Correlation only show linear relationships only, it does not compare non linear relationships)

There are lot of wonderful comprehensions of DIMENSIONAL REDUCTION and a lot to learn.

Below are the Summary of good links to browse through.

PCA

http://courses.cs.tamu.edu/rgutier/cs790_w02/l5.pdf

https://blog.paperspace.com/dimension-reduction-with-principal-component-analysis/

https://blog.paperspace.com/dimension-reduction-with-autoencoders/

https://github.com/asdspal/dimRed

How Co-relation is related to MATH SVD and PCA?

https://towardsdatascience.com/principal-component-analysis-for-dimensionality-reduction-115a3d157bad

DIMENSIONAL REDUCTION - WONDERFUL COMPREHENSION.

https://lvdmaaten.github.io/publications/papers/TR_Dimensionality_Reduction_Review_2009.pdf

https://www.analyticsvidhya.com/blog/2018/08/dimensionality-reduction-techniques-python/

https://blog.paperspace.com/dimension-reduction-with-principal-component-analysis/