A question for principal components analysis (pca)

Dear All,

I have a question about principal components analysis.

The scenario is,

I have a ellipsoid with semi major axis (length=1) and two equal length (=0.5) semi minor axes.

Despite I already know the magnitudes of three axes, I would like to try to use the pca command to find the magnitudes of semi_axes as well as the corresponding vectors.

The ellipsoid stl file in attached.

I use the stlread command to read this simple stl file.

Then perform the pca to the vertices.

T=stlread('ell.stl')
[coeff,score,latent,tsquared,explained,mu] =pca(T.Points)

I believe that the ''coeff'' matrix gives me three principal directions (the unit vectors of three semi axes) in terms of column vectors of the ellipsoid.

However, I don't know how to find the ''magnitude of semi axes'' (i.e. max_principal value=1, other tow=0.5) of this ellipsoid from pca data.

After I refer the documentation of pca command, I still fail to find the information could answer my question.

https://www.mathworks.com/help/stats/pca.html#btkjq7h-1

Could anyone give me the hint about it?

Really appreciate for that!!!

Sincerely

Daniel Chou

Answer 1

[Gaurav Garg]

Hi Daniel,

plot (score(:,1), score(:,2))

On running the above function, you will find a 2-D ellipse which has magnitude same as the magnitude of the original 3-D ellipsoid.

You can also plot the other principal axis by -

plot (score(:,1), score(:,3))
plot (score(:,3), score(:,2))