Singular Spectrum Analysis | BioSSA - Tool For Analysis of Gene Expression

The theory and algorithms of SSA and its extensions, which are used in BioSSA, can be found in the following papers supported by the NG13-083 grant of Dynasty Foundation:

N. Golyandina, A. Korobeynikov, A. Shlemov, K. Usevich. Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package. Journal of Statistical Software, 67(2):1–78, 2015
A. Shlemov, N. Golyandina. Shaped extensions of singular spectrum analysis. In proceedings of The 21st International Symposium on Mathematical Theory of Networks and Systems, July 7–11, 2014. Groningen, The Netherlands, pages 1813–1820, 2014

Singular spectrum analysis as a method of time series analysis has well-elaborated theory and solves various problems: time series decomposition, trend extraction, periodicity detection and extraction, signal extraction, denoising, filtering, forecasting, missing data imputation, change point detection, spectral analysis among them. Since the method does not need a model given a priori, it is called nonparametric and is well suited for exploratory analysis of time series.

SSA was originally proposed for time series, but was extended to 2D digital images. 2D-SSA and related subspace based methods find applications in texture analysis, seismology, spatial gene expression data, medical imaging, etc., and are gaining increasing popularity.

The SSA and 2D-SSA methods deal with series and rectangular images and have subseries and rectangles as moving windows. This can limit applications of the methods; for example, the methods hardly process circular-shaped images, images with gaps and so on. Due to this reason, Shaped 2D-SSA can be proposed, which can deal with images of arbitrary shape and arbitrary window shapes.