Computation- and space-efficient implementation of SSA

Korobeynikov, Anton

doi:10.4310/sii.2010.v3.n3.a9

Cited by 81 publications

(75 citation statements)

References 31 publications

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“…This is because the unchanged grouping transformation part dominates the computational cost in this stage due to p K  . According to an introductory computational complexity analysis of the SSA algorithm in [35], step-wise complexity of the techniques presented in terms of multiplicate-accumulates (MACs) is given in Table VIII for comparisons. The embedding stage only consists of relocating the elements from a vector array into a matrix, so no MACs are involved.…”

Section: E Computational Complexity For Ssa and F-ssamentioning

confidence: 99%

Fast Implementation of Singular Spectrum Analysis for Effective Feature Extraction in Hyperspectral Imaging

Zabalza

Ren

Wang

et al. 2015

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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This version is available at https://strathprints.strath.ac.uk/53416/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract-As a recent approach for time series analysis, singular spectrum analysis (SSA) has been successfully applied for feature extraction in hyperspectral imaging (HSI), leading to increased accuracy in pixel-based classification tasks. However, one of the main drawbacks of conventional SSA in HSI is the extremely high computational complexity, where each pixel requires individual and complete singular value decomposition (SVD) analysis. To address this issue, a fast implementation of SSA (F-SSA) is proposed for efficient feature extraction in HSI. Rather than applying pixel-based SVD as conventional SSA does, the fast implementation only needs one SVD applied to a representative pixel, i.e. either the median or the mean spectral vector of the HSI hypercube. The result of SVD is employed as a unique transform matrix for all the pixels within the hypercube. As demonstrated in experiments using two well-known publicly available data sets, almost identical results are produced by the fast implementation in terms of accuracy of data classification, using the support vector machine (SVM) classifier. However, the overall computational complexity has been significantly reduced.

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Section: E Computational Complexity For Ssa and F-ssamentioning

confidence: 99%

Fast Implementation of Singular Spectrum Analysis for Effective Feature Extraction in Hyperspectral Imaging

Zabalza

Ren

Wang

et al. 2015

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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“…The Hankel structure of H implies that applying this matrix to a vector is equivalent to computing the convolution of the data series with this vector. Thanks to the properties of the fast digital Fourier transform (FFT), fast Hankel matrix product algorithms can be designed that perform this operation much more rapidly and with a much smaller memory footprint than direct multiplication (13,29). This approach presents a processing cost proportional to OðL logðLÞÞ rather than OðMNÞ.…”

Section: Methodsmentioning

confidence: 99%

Efficient denoising algorithms for large experimental datasets and their applications in Fourier transform ion cyclotron resonance mass spectrometry

Chiron¹,

Agthoven

Kieffer

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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Modern scientific research produces datasets of increasing size and complexity that require dedicated numerical methods to be processed. In many cases, the analysis of spectroscopic data involves the denoising of raw data before any further processing. Current efficient denoising algorithms require the singular value decomposition of a matrix with a size that scales up as the square of the data length, preventing their use on very large datasets. Taking advantage of recent progress on random projection and probabilistic algorithms, we developed a simple and efficient method for the denoising of very large datasets. Based on the QR decomposition of a matrix randomly sampled from the data, this approach allows a gain of nearly three orders of magnitude in processing time compared with classical singular value decomposition denoising. This procedure, called urQRd (uncoiled random QR denoising), strongly reduces the computer memory footprint and allows the denoising algorithm to be applied to virtually unlimited data size. The efficiency of these numerical tools is demonstrated on experimental data from high-resolution broadband Fourier transform ion cyclotron resonance mass spectrometry, which has applications in proteomics and metabolomics. We show that robust denoising is achieved in 2D spectra whose interpretation is severely impaired by scintillation noise. These denoising procedures can be adapted to many other data analysis domains where the size and/or the processing time are crucial. big data | noise reduction | matrix rank reduction | FT-ICR MS

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“…Fig. 2 [19]), while the other two models performed using the forecast package [20]. For each approach, the following performance indexes related to the forecasting errors are offered: MAE, MSE, RMSE and MAPE, and residuals test statistics.…”

Section: Application To Real Datamentioning

confidence: 99%

A Singular Spectrum Analysis Technique to Electricity Consumption Forecasting

Iqelan¹

2017

IJERA

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Singular Spectrum Analysis (SSA) is a relatively new and powerful nonparametric tool for analyzing and forecasting economic data. SSA is capable of decomposing the main time series into independent components like trends, oscillatory manner and noise. This paper focuses on employing the performance of SSA approach to the monthly electricity consumption of the Middle Province in Gaza Strip\Palestine. The forecasting results are compared with the results of exponential smoothing state space (ETS) and ARIMA models. The three techniques do similarly well in forecasting process. However, SSA outperforms the ETS and ARIMA techniques according to forecasting error accuracy measures.

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Computation- and space-efficient implementation of SSA

Cited by 81 publications

References 31 publications

Fast Implementation of Singular Spectrum Analysis for Effective Feature Extraction in Hyperspectral Imaging

Fast Implementation of Singular Spectrum Analysis for Effective Feature Extraction in Hyperspectral Imaging

Efficient denoising algorithms for large experimental datasets and their applications in Fourier transform ion cyclotron resonance mass spectrometry

A Singular Spectrum Analysis Technique to Electricity Consumption Forecasting

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