[robert00700]

Nice to see PCA in an HN article, it's a very powerful tool.

For those struggling to get the example in this article, I find PCA easier to understand given visual examples, and in less dimensions (try http://en.wikipedia.org/wiki/File:GaussianScatterPCA.png)

Note how this dataset is two dimensional in nature, and PCA yields two vectors. The first gives the direction of the greatest variation, and the next gives the variation orthogonally to the first.

An awesome use of PCA is for facial detection, a method called 'Eigenfaces' http://en.wikipedia.org/wiki/Eigenface

[j2kun]

I wrote a blog post with more detail, and lots of intuitive examples. see http://jeremykun.wordpress.com/2011/07/27/eigenfaces/

[apu]

FYI Eigenfaces was a ground-breaking theory when introduced...almost 25 years ago. It's no longer used in any serious way for practical face recognition applications.

[misiti3780]

eigenfaces are very cool. i did a bunch of work with them a few years ago.