From: s_d_lew@my-dejanews.com
Subject: Re: Principal Component Analysis
Date: Tue, 06 Apr 1999 14:12:49 -0800
Newsgroups: sci.math
Keywords: Lay person's description of PCA

The way I like to teach eigen-vector/values simplify it to say
that it is a way to change the coordinate system so that
it is easiest to measure the effects that we are interested in.
The eigen values measure the importance of the eigen vector
and, the eigen vectors themselves indicate how much of each
of the original components contribute to the new "good"
coordinate system.

Admittedly, this is a pretty gross simplification, but most people
understand "change in coordinates".

I usually follow it up with my guns-vs-butter economic analogy
where the evil professor throws in a bread dimension.

I say something like, "Wouldn't it be nice to use the same analysis
as guns-vs-butter when we don't have this extra 'bread' dimension."
Then I say, "Common sense says a good coordinates for a
guns-vs-bread-vs-butter analysis would be something like
guns vs (alpha*bread+beta*butter)  where alpha and beta tell you how
much butter the average person puts on the bread."  Then I say
something like, "Eigen-vector/value analysis incorporates the
information about how much butter the average person puts on
bread to select this new coordinate system using alpha and beta."
This usually goes on to discuss how this creates eigen value
degeneracies, etc, but I usually skip this part for a non-tech audience.

I don't know if this is usable in your audience or not, but I thought
I'd throw it out there for grins.

-slew



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