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Start Introduction:
-- pca
-- pga
-- pns

Step by Step upgrade and additions to the algorithm.
What is PCA, how does it work, when does it not give good results
Why PGA?
Explaining terms in details as geodesic distances, adding formulas explaining log map and exp map,
Approximation in PGA.
Why PNS?
How it works.
Projection formulae,
Finding principal directions on spheres

Run with new variances on Rat Skull Data set.

Lets try to report the results for Rat skull data set Today.
I have updated the code to give the new variances, we should observe the expected trend.

-- IMP: When I ran it on the simulated dataset, I got variances equal in all the directions!!.. Which is a plus point as in every dimension I am adding an equal amount of noise to the dimension.
We should observe better trends on Rat skull.

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