Re: Angles between vectors

From: Aleks Jakulin (a_jakulin_at_@hotmail.com)
Date: 10/21/04 

Date: Thu, 21 Oct 2004 10:57:37 +0200

Ross Clement wrote:
> Hi. I'm interested in measuring angles between vectors. I'm
> aware of the standard formula for this:
>
> A.B = ||A||.||B||.cos(t)

It depends on what is your goal. If your goal is classification, you
should pick such a distance measure that will help you classify
better, e.g., http://www.stat.cmu.edu/~minka/papers/metric/ and the
references therein. If your goal is description, you should pick a
distance that captures the intuitive similarity best.

You list several problems of metrics, and provide solutions for each
of them. The 'Mahalonobis angle' metric will result if you transform
the space in which A and B are vectors, and then apply your metric
above. But deciding upon the transform comes under the "it depends" of
my previous paragraph.

Aleks 

-- 
mag. Aleks Jakulin
http://www.ailab.si/aleks/
Artificial Intelligence Laboratory,
Faculty of Computer and Information Science,
University of Ljubljana, Slovenia.