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 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 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.

MULTIDIMENSIONAL EXTENSION OF SINGULAR SPECTRUM ANALYSIS BASED ON FILTERING INTERPRETATION

2014 ◽  
Vol 06 (01) ◽  
pp. 1450005 ◽  
Author(s):  
KENJI KUME ◽  
NAOKO NOSE-TOGAWA
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Arbitrary Dimension ◽  
Singular Spectrum Analysis ◽  
Simple Algorithm ◽  
Image Data ◽  
Multidimensional Data ◽  
Data Series ◽  
Singular Spectrum ◽  
Original Time

Singular spectrum analysis is a nonparametric spectral decomposition of a time series. The singular spectrum analysis can be viewed as the two-step filtering with the complete set of eigenfilter adaptively constructed from the original time series. Based on this viewpoint, we present a flexible and quite simple algorithm for the singular spectrum analysis which can be applied to the multidimensional data series with arbitrary dimension. We have carried out the decomposition of two-dimensional image data, and the optimally constructed filters are found to be the smoothing or the edge enhancement filters of various type. We have also examined a simple example for the decomposition of 3D data.

scholarly journals Filter Characteristics in Image Decomposition with Singular Spectrum Analysis

2016 ◽  
Vol 08 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Kenji Kume ◽  
Naoko Nose-Togawa
Keyword(s):  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Low Frequency ◽  
Image Data ◽  
Original Data ◽  
Multidimensional Data ◽  
Singular Spectrum ◽  
Symmetry Properties ◽  
Frequency Components ◽  
Differential Type

Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this viewpoint, the singular spectrum analysis can be understood as the adaptive and optimal generation of the filters and their two-step point-symmetric operation to the original data. In this paper, we point out that, when applied to the multidimensional data, the adaptively generated filters exhibit symmetry properties resulting from the bisymmetric nature of the lag-covariance matrices. The eigenvectors of the lag-covariance matrix are either symmetric or antisymmetric, and for the 2D image data, these lead to the differential-type filters with even- or odd-order derivatives. The dominant filter is a smoothing filter, reflecting the dominance of low-frequency components of the photo images. The others are the edge-enhancement or the noise filters corresponding to the band-pass or the high-pass filters. The implication of the decomposition to the image denoising is briefly discussed.

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