Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: how to compute length of principal axis
Replies: 6   Last Post: Oct 31, 2011 6:04 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Ray Koopman

Posts: 3,382
Registered: 12/7/04
Re: how to compute length of principal axis
Posted: Oct 31, 2011 2:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Oct 30, 11:07 pm, MBALOVER <mbalov...@gmail.com> wrote:
> Hi all,
>
> I have a data set and I can compute the vector of the principal axis.
> However i do not know if there is an equation to compute the length of
> the first principal axis. I know that it related to the largest
> eigenvalue. But what is exactly the equation?
>
> For now, I just compute very expensively by projecting all data points
> to the principal axis and compute the maximum distance between every
> pair of projected points. However it is not efficient.
>
> I tried to find the equation in books but could not find it.
>
> Could you please help?
>
> Thank you.


The first eigenvalue is the sum of squares of the projections of
the points onto the first principal axis. If by "length" you mean
the difference between the maximum and minimum projections onto
the axis then the eigenvalue only bounds the length; to get the
actual length you need to find the maximum and minimum projections.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.