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.

INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250023 ◽  
Author(s):  
KENJI KUME
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Original Time Series ◽  
Singular Vectors ◽  
Singular Spectrum ◽  
Original Time ◽  
Value Decomposition ◽  
Insight Into

Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.

scholarly journals PERAMALAN JUMLAH KUNJUNGAN WISATAWAN MANCANEGARA KE BALI MENGGUNAKAN METODE SINGULAR SPECTRUM ANALYSIS

2019 ◽  
Vol 8 (4) ◽  
pp. 303
Author(s):  
MIRA AYU NOVITA SARI ◽  
I WAYAN SUMARJAYA ◽  
MADE SUSILAWATI
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Window Length ◽  
Original Time Series ◽  
Number Of Components ◽  
Singular Spectrum ◽  
Original Time

Singular spectrum analysis (SSA) is a method to decompose the original time series into a summation of a small number of components that can be interpreted as varied trends, oscillatory, and noise components. The purpose of this research is to model and to find out the results of forecasting the number of foreign tourists arrival to Bali using SSA method. In this research, the accuracy of forecasting results will be calculated using the SSA model with reccurent singular spectrum analysis (RSSA) method. The best SSA model was obtained with a window length (L=94) and produces MAPE value of 7,65%.

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.

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.

scholarly journals Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis

2018 ◽  
Vol 17 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Mahdi Kalantari ◽  
Masoud Yarmohammadi ◽  
Hossein Hassani ◽  
Emmanuel Sirimal Silva
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Missing Values ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
L1 Norm ◽  
Nonparametric Approach ◽  
Singular Spectrum ◽  
Simulated Time

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the [Formula: see text] norm-based version of Singular Spectrum Analysis (SSA), namely [Formula: see text]-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially [Formula: see text]-SSA can provide better imputation in comparison to other methods.

Sign in / Sign up

Export Citation Format

Share Document