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I have given a time-series in various channels. There are two major oscillations "hidden" in the time-series and distributed over all channels. I want to extract these oscillations using multivariate Singular Spectrum (mSSA) Analysis.

I am new to SSA and it seems to me that SSA is not really a dimensionality reduction method but more a "denoising" method. I.e. is it true that I cannot really extract the major oscillations, as after grouping, backprojection and diagonal averaging, I get signal in all channels, but not really a single signal which is the major oscillation (as PCA would provide)?

On the other hand, the eigenvectors (altough shrinked in time due to hankelization) seem to be exactly the oscillations that I am looking for. Can I use SSA for dimensionality reduction by simply treating the eigenvectors as the major oscillations?

Bharata
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refle
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  • What do you mean "a time series in various channels"? You either have a single time series or multiple time series (different from eachother). If you have one time series, regular SSA. If you have multiple time series then multi channel SSA (AKA multivariate SSA). SSA in general uses the sub-space method concepts (similar to PCA). – Ash Jul 01 '23 at 02:43

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I found an article dealing with exactly the problem i was facing: https://arxiv.org/pdf/1812.09057.pdf

It introduces a technique called "Singular Spectrum Analysis for advanced reduction of dimensionality" (SSA-FARI).

refle
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I would suggest you read this post on kaggle as a primer.

As I understand it, SSA effectively seeks to find periodicities in the autocorrelation of a function. The single time-series is broken down into three types of signal: trend, periodic, and noise. This allows, e.g. examination of the underlying oscillatory modes which make up the original signal. In this sense, it is broadly comparable with Empirical Mode Decomposition (EMD), although the latter emphasises oscillations as opposed to periodicity. SSA has been found to be superior in certain applications to EMD.

Matti Wens
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  • Thanks a lot. Very interesting article! However, not yet exactly what I need – refle Jan 04 '19 at 11:29
  • That is not right. SSA decomposes the autocovariance matrix of a given window length. There is no three types of signal etc what so ever. There are signal and noise. So basically S+N=Time series. SSA is not comparable with Empirical Mode Decomposition. SSA is mainly useful in dyanmical systems that are operating near their steay states, which means the time series is almost stationary. EMD has not physical interpretation, but SSA extracts the physical properties of the subspace and gives you an idea abut the noise in the signal. You can effectively remove noise from the signal using SSA. – Ash Jul 01 '23 at 02:52
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I would refer you to look into dynamic mode decomposition which similarly to SSA, it uses singular value decomposition, then it extracts the modes based on eigenvalues of a koopman operator. It was created for non-linear dynamical systems. https://en.m.wikipedia.org/wiki/Dynamic_mode_decomposition

DomIsAwesomee
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