[Eeglablist] Eigenvalues generation

[Matt Gerhold]

Hi Ibtissem,

ARFit is a toolbox for fitting vector autoregressive timeseries models. It
uses QR factorisation to solve for a least-squares fit. One can use the QR
factors to compute the covariance matrix for progressively lower model
orders, thus enabling a step-wise least-square approach. It has
computational advantages over OLS and Yule-Walker fitting algorithms.

The ARFit provides a (chan X chan*order) matrix of coefficients in the
instance of a higher order model. For a higher-order model one would
compute the companion form matrix denoted, F.

% fit model to a bivariate timeseries data in variable ts

>>[w, A, C, sbc, fpe, th]=arfit(ts', 4, 4, 'sbc', 'zero');

 % build companion form matrix

>> rw_2 = [eye(2) zeros(2,2) zeros(2,2) zeros(2,2)];

>> rw_3 = [zeros(2,2) eye(2) zeros(2,2) zeros(2,2)];

>> rw_4 = [zeros(2,2) zeros(2,2) eye(2) zeros(2,2)];

>> F = [A; rw_2; rw_3; rw_4]; % final companion form matrix

 % check stability

>> eig_vals = abs(diag(jordan(F))) % jordan canonical form of A
>> max(eig_vals) < 1 % should give a 1 if the system is stable

That’s pretty much it.

Rgds,

Matthew

On Fri, May 13, 2016 at 12:57 PM, Ibtissem KHOUAJA BENFRADJ <
ibtissem.khouaja at live.fr> wrote:

> Hi Matt,
>
> I thank you so much for your reply.
>
> Really, you have undersatand very well my goal.
> In fact, I'd like to know if you have applied a specific algorithm for
> the generation of the AR matrix (A).
> In my work, I applied the algorithm 'arfit', and it gives me a vector of
> p AR parameters for each signal.
>
> In this case, how can I present my matrix to extract the eigenvalues?
>
> Thank's a lot for your reply, Ibtissem
>
> ----------------------------------------------------------
> ----------------------------------------------------------
> Ibtissem KHOUAJA BENFRADJ
> PhD in computer science
> Speciality: Biomedical Signal Processing
> Laboratory: LTIM, University of Monastir, Tunisia
> http://www.labtim.org/accueil.php
> Laboratory: LIGM, Univerisity of Paris-East, France
> http://ligm.u-pem.fr/
>
>
>
>
> ------------------------------
> Date: Tue, 3 May 2016 21:09:01 +0200
> Subject: Re: [Eeglablist] Eigenvalues generation
> From: matt.gerhold at gmail.com
> To: ibtissem.khouaja at live.fr
> CC: eeglablist at sccn.ucsd.edu
>
>
> Hi,
>
> One would compute the eigenvalues for the autoregressive parameter
> matrix--your estimated beta coefficients. This would be to assess the
> stability of the system. One only needs to compute these eigenvalues for
> this matrix; nothing more nothing less... Then take the modulus of the
> eigenvalues, they should all be less than one. Following Lutkepohl (2005),
> a simple way to do this is:
>
> if A = autoregressive parameters (K x K), where K is number of
> data-channels:
>
> >> eig_vals = abs(diag(jordan(A))) % jordan canonical form of A
> >> eig_vals < 1 % should give a vector of 1's if the system is stable
>
> Regards,
>
> Matthew
>
>
> On Mon, May 2, 2016 at 6:20 PM, Ibtissem KHOUAJA BENFRADJ <
> ibtissem.khouaja at live.fr> wrote:
>
> Dear list,
>
>
> I applied the ARFIT algorithm in the generation of autoregressive
> parameters
> corresponding to the time-varying of EEG.
> Nest, in order to generate the eigenvalues of the AR matrix I used ARMODE
> algorithm.
>
> I need your help to generate differently the eigenvalues for the AR
> parameters of each signal (AR vector) and all of signal (AR matrix).
>
> Thank you for your help, Ibtissem
>
> ----------------------------------------------------------
> ----------------------------------------------------------
> Ibtissem KHOUAJA BENFRADJ
> PhD in computer science
> Speciality: Biomedical Signal Processing
> Laboratory: LTIM, University of Monastir, Tunisia
> http://www.labtim.org/accueil.php
> Laboratory: LIGM, Univerisity of Paris-East, France
> http://ligm.u-pem.fr/
>
>
>
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