Re: eigen analysis : how to recompose the signal?

Olivier Delrieu wrote:
> Hello,
>
> Let's imagine I am using an eigen analysis to decompose n variables
observed
> p times. This will produce a subset of c components, c<<n, explaining
most
> of the signal : a vector of [c] eigenvalues, a matrix of [n,c]
loadings and
> a matrix of [p,c] scores.
>
> Now, I would like to use only the variables having the greatest
loadings in
> order to estimate what the 'real' observation would be. How do I
recompose
> the signal ? How can I better characterize this estimatation (e.g.
> confidence interval) ?
>
> Is it something like :
> observation = sum(1 to c)
> [sqrt(eigenvalue(c)).loading(variable,c).measure(variable)]
>
> Thanks
>
> Olivier.


My feeling is that your idea is basically the same as "Proper
Orthogonal Decomposition". Search Google or
(http://scholar.google.com/) for this term and you will find a lot of
papers on this.

If you original system is linear, there are better approaches to reduce
the model dimension. Check refrences at

http://www.imtek.uni-freiburg.de/simulation/mor4ansys/

in particular a review

http://www.imtek.uni-freiburg.de/simulation/mor4ansys/pdf/rudnyi02SU.pdf

where you will find many references including POD.

Best wishes,

Evgenii Rudnyi
--
http://Evgenii.Rudnyi.Ru/

.