SSA and subspace-based methods in signal processing

SSA is closely linked with the subspace-based methods of signal processing and the members of the group are actively trying to formalize the connections and differences. For example, the "signal plus noise" model is often obligatory in signal processing and consequently the main aim of most signal processing methods is the estimation of parameters of a specified model; on the contrary, in SSA the aims of the analysis are often different (for example, forecasting) and the parameters of the approximatory time series are of secondary importance. Specific current projects include:

Improvement or replacement of the SVD

There are two main reasons why it may be worthwhile to replace the SVD operation in SSA with an alternative.

  1. Simplicity: In problems where the trajectory matrix is very large, the SVD may be too costly to perform.
  2. Accuracy: When separating signal from noise, some parts of the noise often remain in the SVD components mostly related to the signal. A small adjustment of the eigenvalues and eigenvectors may diminish this effect.

Low-rank matrix approximations

As an approximation to the trajectory matrix, SSA yields a Hankel matrix, obtained by diagonally averaging a lower rank approximation of the original trajectory matrix. Due to this diagonal averaging, it is likely that the Hankel matrix is of full rank.

In many signal processing applications, the parametric form of an approximation is often of primary importance. Hence one may wish to find a Hankel approximation to the original trajectory matrix, of specified lower rank. This is the problem of structured low-rank approximation.

Selected publications