Question about how to check stationary sources separated by SSA

[Dan Choi]

Dear SSA

Hi all! I am using SSA toolbox for my personal project. I have my own
input data and I want to find how many stationary and non-stationary
sources my data have. Here, I don't know “dimensionality of stationary
subspace” (d) of my data.

My method to find correct “dimensionality of stationary subspace” is
trying all the possible values for dimensionality of stationary
subspace and If all the stationary sources (s_src) separated by SSA
are real staionary and all non-staionary sources (n_src) are all real
non-stationary. If all of sources are real then it is correct
dimensionality of stationary subspace.

I came up with own algorithm to calculate mean and variance to find if
signal is stationary or non-stationary, but when I tested with toy
data, my function was not working. s_src should be stationary but my
algorithm said non-stationary and n_src should be non-stationary but
my algorithm said stationary with correct toy data.

I want to check stationary source (s_src) and non-stationary source
(n_src) separated by SSA are real stationary and non-stationary. Is
there function or way to check the if siganl is stationary or non-
staionary? or way to find number of dimensionality of stationary
subspace of data.

Thanks

Best regards

Dan Choi

[Paul Bünau]

Dear Dan, 

finding the "true" number of stationary resp. non-stationary sources is a difficult problem. Essentially, it is an unsupervised model selection task.

On real data, epoch mean and covariance matrices will never be exactly equal and therefore no time series is stationary in a strict sense. The best way to assess the degree of stationarity is probably to compare the minimum/maximum objective function value found by optimization against the distribution of the objective function value over repeated random shuffles of the dataset. 

See for example:

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6151166

Paul 

--
Paul von Bünau
Machine Learning (ML) Group

http://www.user.tu-berlin.de/paulbuenau

Tel: +49 (0)30 314 78628
Fax: +49 (0)30 314 78622

Berlin Institute of Technology (TU Berlin)

Dept. Computer Science
Sekr. FR 6-9, Room 6059
Franklinstr. 28/29
10587 Berlin

[Ying Li]

Dear Paul,

I am also using the SSA and wondering how to figure out the number of stationary sources. I'm trying to use different d (num of stationary sources) and check the value of "ssa_results.loss_s". Does the "ssa_results.loss_s" represent the objective function value or normalized objective function value?

If it is the latter, do you think I can only use "ssa_results.loss_s" to determine d? I.e. I first set a range [-10,10], when I tried d=3, ssa_results.loss_s = -4 (within the range), then I say there're at least 3 stationary sources; when I tried d = 5, and ssa_results.loss_s=20 (out of the range), then I say there are less than 5 stationary sources. Does that make sense? Or I need to divide ssa_results.loss_s by N, etc. ?

Thanks a lot!

Best wishes,

Ying

在 2012年5月29日星期二UTC-7上午10时45分29秒，Paul Bünau写道：

[Paul Bünau]

Dear Ying, 

on real data, I would rather use a "normalization" based on resampling. Please see the discussion on page 44 of my Ph.D. thesis:

http://opus.kobv.de/tuberlin/volltexte/2012/3694/

Please don't hesitate to contact me again.

Best wishes, 

Paul

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Paul von Bünau
Machine Learning (ML) Group

http://www.user.tu-berlin.de/paulbuenau

Tel: +49 (0)30 314 78628
Fax: +49 (0)30 314 78622

Berlin Institute of Technology (TU Berlin)

Dept. Computer Science
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10587 Berlin

[YING LI]

Dear Paul,

Thanks for your reply. Your thesis is a great reference and is very educational. : )

So the objective function (loss_s & loss_n) reported by SSA software is not just -2log(LH0/LHA), but is the the normalized one (2X)^1/2 - (2k-1)^1/2, right? 

Thanks,

Ying

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[Jan Saputra Müller]

Dear Ying,

this is correct, the objective function value returned by the SSA toolbox is the normalized one!

Best wishes, Jan

Am 5/20/13 9:22 PM, schrieb YING LI:

-- 
Jan Saputra Müller
Machine Learning Group

Tel: +49 30 314 75742

Berlin Institute of Technology (TU Berlin)
Dept. Computer Science
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Marchstr. 23
10587 Berlin

http://www.ml.tu-berlin.de