CODEWITHSUNDEEP
time-seriespcadimensionality-reductionssa
refle
refle

Reputation: 593

Dimensionality reduction using (multivariat) Singular Spectrum Analysis

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?

Upvotes: 0

Views: 946

Answers (3)

DomIsAwesomee
DomIsAwesomee

Reputation: 97

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

Upvotes: -1

refle
refle

Reputation: 593

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).

Upvotes: 1

Matti Wens
Matti Wens

Reputation: 750

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.

Upvotes: 0

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