Re: "Sphere the data"

From: Ross Clement (clemenr_at_wmin.ac.uk)
Date: 10/28/04 

Date: 28 Oct 2004 05:02:41 -0700

Bruce Weaver <bweaver@lakeheadu.ca> wrote in message news:<2uahppF29dnm1U1@uni-berlin.de>...
> Ross Clement wrote:
>
> > Hi. I'm trying to understand the term "Sphere the data" that has
> > turned up in several things that I've read recently.
> >
>
>
> Have you tried contacting any of the authors of the material you've been
> reading? Surely they must know what they meant. ;-)

Actually I did think of that after I posted, and was planning to do so
after . However, events have over-taken me...

Answering a number of points in other postings in this thread:

I first ran across the term 'sphere the data' in the book _Elements of
Statistical Learning_ by Hastie, Tibshirani, and Friedman, Chapter 4,
page 91.

However, I was thinking of performing massive amounts of
dimensionality reduction, and was thinking of "sphere-ing" the data in
order to reduce the effects of range differences and correlations
between variables. However, since I started this general thread, I've
learnt of the existence of principle co-ordinate analysis. From what I
can see, if I want to do massive dimensionality reduction for data
where I can calculate distance metrics (e.g. Euclidean, Mahalanobis),
then principle co-ordinate analysis seems to be the way to go. Firstly
because it appears to be a standard and obvious technique, and since I
can see the sizes of the eignvalues for the dimenions I'm dropping, I
know how much of the variance of the full data set (n x n matrix of
distances) is explained by the one or two dimensions I have left.

In any case, now that I know of the search term "multidimensional
scaling", I should be reading introductory material on that topic
before trying anything specific, no?

Cheers,

Ross-c