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

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Kaba

Posts: 289
Registered: 5/23/11
Re: how to compute length of principal axis
Posted: Oct 31, 2011 3:45 PM
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MBALOVER 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.


You will probably want to have a look at the PASTD algorithm:

"Projection approximation subspace tracking"

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=365290

Simple and efficient, though in principle only approximate. But it might
be what you are looking for.

--
http://kaba.hilvi.org



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