Intuition behind the use of Eigen vectors in PCA

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ninjapunit
Posts: 20
Joined: Fri Sep 16, 2011 5:12 am

Re: Intuition behind the use of Eigen vectors in PCA

Postby ninjapunit » Tue Aug 07, 2012 3:26 pm

Hi Carol,

I guess what I am really asking is,

1. the fact that eigenvectors happen to be the axes of choice for PCA for explaining most "variance"
2. These are the eigenvectors of "covariance" matrix (which the covariance matrix can't rotate)

Do these two facts have anything to do with each other intuitively/geometrically?

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Intuition behind the use of Eigen vectors in PCA

Postby coalexander » Tue Aug 07, 2012 3:37 pm

Maybe this has the intuition you require?

http://www.cs.princeton.edu/picasso/mat ... ion_jp.pdf

Carol

ninjapunit
Posts: 20
Joined: Fri Sep 16, 2011 5:12 am

Re: Intuition behind the use of Eigen vectors in PCA

Postby ninjapunit » Tue Aug 07, 2012 7:49 pm

Amazing material. The author had exactly same thought process of building the concepts that I had in mind. I guess the "intuitive" aspect was staring in my face all along from your book -
• the principal components are uncorrelated with each other (this is necessary to ensure 0 redundancy in data observation)
• the first principal component explains the most variation (this is necessary so that we can choose the significant first few)

Eigen-vectors fit these two needs!

Thanks again for your kind guidance.

Puneet


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