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Shaped extension of singular spectrum analysis
 in Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), July 711, 2014
, 2014
"... Extensions of singular spectrum analysis (SSA) for processing of nonrectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid. The ..."
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Extensions of singular spectrum analysis (SSA) for processing of nonrectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid. The constructed Shaped SSA method with planar or circular topology is able to produce lowrank approximations for images of complex shapes. Together with Shaped SSA, a shaped version of the subspacebased ESPRIT method for frequency estimation is developed. Examples of 2D circular SSA and 2D Shaped ESPRIT are presented. 1
Research Article Shaped 3D Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the Early Zebrafish Embryo
, 2015
"... Copyright © 2015 Alex Shlemov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recent progress in microscopy technologies, biol ..."
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Copyright © 2015 Alex Shlemov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recent progress in microscopy technologies, biological markers, and automated processing methods is making possible the development of gene expression atlases at cellularlevel resolution over whole embryos. Raw data on gene expression is usually very noisy. This noise comes from both experimental (technical/methodological) and true biological sources (from stochastic biochemical processes). In addition, the cells or nuclei being imaged are irregularly arranged in 3D space. This makes the processing, extraction, and study of expression signals and intrinsic biological noise a serious challenge for 3D data, requiring new computational approaches. Here, we present a new approach for studying gene expression in nuclei located in a thick layer around a spherical surface.Themethod includes depth equalization on the sphere, flattening, interpolation to a regular grid, pattern extraction by Shaped 3D singular spectrum analysis (SSA), and interpolation back to original nuclear positions. The approach is demonstrated on several examples of gene expression in the zebrafish egg (a model system in vertebrate development).Themethod is tested on several different data geometries (e.g., nuclear positions) and different forms of gene expression patterns. Fully 3D datasets for developmental gene expression are becoming increasingly available; we discuss the prospects of applying 3DSSA to
Basic Singular Spectrum Analysis and Forecasting with R
"... Singular Spectrum Analysis (SSA) is a powerful tool of analysis and forecasting of time series. In this paper we describe the main features of the Rssa package, which efficiently implements the SSA algorithms and methodology in R. Analysis, forecasting and parameter estimation are demonstrated usin ..."
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Singular Spectrum Analysis (SSA) is a powerful tool of analysis and forecasting of time series. In this paper we describe the main features of the Rssa package, which efficiently implements the SSA algorithms and methodology in R. Analysis, forecasting and parameter estimation are demonstrated using case studies. These studies are supplemented with accompanying codes in R.
Variations of Singular Spectrum Analysis for separability improvement: nonorthogonal decompositions of time series
"... Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two variat ..."
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Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two variations of SSA, which weaken the separability conditions, are proposed. Both proposed approaches consider inner products corresponding to oblique coordinate systems instead of the conventional Euclidean inner product. One of the approaches performs iterations to obtain separating inner products. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and reallife data. Keywords: Singular Spectrum Analysis, time series, time series analysis, time series decomposition, separability
Fast ESPRIT algorithms based on partial singular value decompositions
"... Abstract Let h(x) be a nonincreasing exponential sum of order M . For N given noisy sampled values h n = h(n) + e n (n = 0, . . . , N − 1) with error terms e n , all parameters of h(x) can be estimated by the known ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method ..."
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Abstract Let h(x) be a nonincreasing exponential sum of order M . For N given noisy sampled values h n = h(n) + e n (n = 0, . . . , N − 1) with error terms e n , all parameters of h(x) can be estimated by the known ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method. The ESPRIT method is based on singular value decomposition (SVD) of the L , where the window length L fulfills M ≤ L ≤ N − M + 1. The computational cost of the ESPRIT algorithm is dominated by the cost of SVD. In the case L ≈