scholarly journals Shaped 3D Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the Early Zebrafish Embryo

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Alex Shlemov ◽  
Nina Golyandina ◽  
David Holloway ◽  
Alexander Spirov
Keyword(s):  
Gene Expression ◽  
Spectrum Analysis ◽  
Spherical Surface ◽  
Expression Patterns ◽  
Singular Spectrum Analysis ◽  
Thick Layer ◽  
Cellular Level ◽  
Grid Pattern ◽  
Developmental Gene Expression ◽  
Singular Spectrum

Recent progress in microscopy technologies, biological markers, and automated processing methods is making possible the development of gene expression atlases at cellular-level 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. The method 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). The method 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 3D-SSA to data processing and analysis in this growing field.

scholarly journals Shaped Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the EarlyDrosophilaEmbryo

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Alex Shlemov ◽  
Nina Golyandina ◽  
David Holloway ◽  
Alexander Spirov
Keyword(s):  
Gene Expression ◽  
Spectrum Analysis ◽  
Expression Patterns ◽  
Singular Spectrum Analysis ◽  
Image Data ◽  
Fruit Fly ◽  
Biological Data ◽  
Singular Spectrum ◽  
Cylindrical Projection ◽  
2D And 3D

In recent years, with the development of automated microscopy technologies, the volume and complexity of image data on gene expression have increased tremendously. The only way to analyze quantitatively and comprehensively such biological data is by developing and applying new sophisticated mathematical approaches. Here, we present extensions of 2D singular spectrum analysis (2D-SSA) for application to 2D and 3D datasets of embryo images. These extensions, circular and shaped 2D-SSA, are applied to gene expression in the nuclear layer just under the surface of theDrosophila(fruit fly) embryo. We consider the commonly used cylindrical projection of the ellipsoidalDrosophilaembryo. We demonstrate how circular and shaped versions of 2D-SSA help to decompose expression data into identifiable components (such as trend and noise), as well as separating signals from different genes. Detection and improvement of under- and overcorrection in multichannel imaging is addressed, as well as the extraction and analysis of 3D features in 3D gene expression patterns.

scholarly journals Singular Spectrum Analysis of Gene Expression Profiles of EarlyDrosophila embryo: Exponential-in-Distance Patterns

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
T. Alexandrov ◽  
N. Golyandina ◽  
A. Spirov
Keyword(s):  
Gene Expression ◽  
Spectrum Analysis ◽  
Expression Profiles ◽  
Singular Spectrum Analysis ◽  
Gene Expression Profiles ◽  
Analytical Approximation ◽  
Similar Data ◽  
Singular Spectrum ◽  
Trend Extraction ◽  
The Given

We present investigation of gene expression profiles by means of singular spectrum analysis (SSA). The biological problem under investigation is the decomposition ofbicoidprotein profiles ofDrosophila melanogasterinto the sum of a signal and noise, where the former consists of an exponential-in-distance pattern and is close to constant nonspecific component, or “background.” The signal processing problems addressed are (i) trend extraction from a noisy signal, (ii) batch processing of similar data, and (iii) analytical approximation of the signal components by the sum of exponential and constant-like functions. The proposed methods are evaluated on the given 17 series.

scholarly journals Multi-Channel Singular Spectrum Analysis on Geocenter Motion and Its Precise Prediction

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1403
Author(s):  
Xin Jin ◽  
Xin Liu ◽  
Jinyun Guo ◽  
Yi Shen
Keyword(s):  
Solid Earth ◽  
Spectrum Analysis ◽  
Mean Squared Error ◽  
Moving Average ◽  
Singular Spectrum Analysis ◽  
Singular Spectrum ◽  
Autoregressive Moving Average Model ◽  
Seasonal Characteristics ◽  
Geocenter Motion ◽  
Moving Average Model

Geocenter is the center of the mass of the Earth system including the solid Earth, ocean, and atmosphere. The time-varying characteristics of geocenter motion (GCM) reflect the redistribution of the Earth’s mass and the interaction between solid Earth and mass loading. Multi-channel singular spectrum analysis (MSSA) was introduced to analyze the GCM products determined from satellite laser ranging data released by the Center for Space Research through January 1993 to February 2017 for extracting the periods and the long-term trend of GCM. The results show that the GCM has obvious seasonal characteristics of the annual, semiannual, quasi-0.6-year, and quasi-1.5-year in the X, Y, and Z directions, the annual characteristics make great domination, and its amplitudes are 1.7, 2.8, and 4.4 mm, respectively. It also shows long-period terms of 6.09 years as well as the non-linear trends of 0.05, 0.04, and –0.10 mm/yr in the three directions, respectively. To obtain real-time GCM parameters, the MSSA method combining a linear model (LM) and autoregressive moving average model (ARMA) was applied to predict GCM for 2 years into the future. The precision of predictions made using the proposed model was evaluated by the root mean squared error (RMSE). The results show that the proposed method can effectively predict GCM parameters, and the prediction precision in the three directions is 1.53, 1.08, and 3.46 mm, respectively.

Application of singular spectrum analysis in reconstruction of the annual signal from GRACE

2020 ◽  
Vol 14 (3) ◽  
pp. 295-302
Author(s):  
Chuandong Zhu ◽  
Wei Zhan ◽  
Jinzhao Liu ◽  
Ming Chen
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Mixture Effect ◽  
Singular Spectrum ◽  
Grace Data ◽  
Terrestrial Water ◽  
Annual Signal ◽  
Long Term Variations

AbstractThe mixture effect of the long-term variations is a main challenge in single channel singular spectrum analysis (SSA) for the reconstruction of the annual signal from GRACE data. In this paper, a nonlinear long-term variations deduction method is used to improve the accuracy of annual signal reconstructed from GRACE data using SSA. Our method can identify and eliminate the nonlinear long-term variations of the equivalent water height time series recovered from GRACE. Therefore the mixture effect of the long-term variations can be avoided in the annual modes of SSA. For the global terrestrial water recovered from GRACE, the peak to peak value of the annual signal is between 1.4 cm and 126.9 cm, with an average of 11.7 cm. After the long-term and the annual term have been deducted, the standard deviation of residual time series is between 0.9 cm and 9.9 cm, with an average of 2.1 cm. Compared with the traditional least squares fitting method, our method can reflect the dynamic change of the annual signal in global terrestrial water, more accurately with an uncertainty of between 0.3 cm and 2.9 cm.

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