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let us consider following graph of singular values

enter image description here

i want to make some kind of clustering of these data,namely to seperate main components from non main components,let say signal components from noise components,i would like to do like this(any software matlab,etc is great,better matlab)let us start like this ,first do linear regression with first point,then do regression analysis with first two point and so on,point is that one want to create two group,in first group coefficients of regression lines should be close to each other, also in another group regression coefficients should be close to each other,but regression coefficients in one group must be different then coefficients in another group,that means that we should find such point which separate this group optimally, in other word i should stop regression analysis at some point which well separate two group,and another regression will start from this stop point till other rest points,please help me how to do it programaticaly

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  • $\begingroup$ By the way, it's common to present SVD eigenvalues in decrasing order, not as on your images. You can also try to use log-scale on Y axis when displaying SVD eigenvalues. $\endgroup$ – werediver Apr 18 '14 at 9:55
  • $\begingroup$ it is cumulative,not itself singular value $\endgroup$ – dato datuashvili Apr 18 '14 at 10:54
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I would use the SVD (Singular Value Decomposition). By looking at the Singular Values I'd determine which vectors spread the data and which spread the noise.

Practically, they both do both, but if we speak which are dominant, this would be a great starting point.

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  • $\begingroup$ i have got SVD exacting and they are singular values $\endgroup$ – dato datuashvili Apr 17 '14 at 12:20
  • $\begingroup$ What do you mean? $\endgroup$ – Royi Oct 27 at 11:20
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You question is pretty broad and you didn't even mentioned that you're using SSA (at the moment).

You're asking for interpretaion of SSA decomposition. This topic is rather complex and pretty difficult to automate, but there are much information on this in chapter 2.4 "Choice of Parameters in Basic SSA" of the book Singular Spectrum Analysis for Time Series by N. Golyandina & A. Zhigljavsky (chapter 2 is freely available).

You may also search by keywoard "AutoSSA" to get some related information.

By the way, SSA can not separate everything because there can be nonseparable components in the signal. Even noise can be nonseparable from the signal.

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