Characteristic Lengths and Distances: Fast and Robust Features for Nonlinear Time Series

2012 ◽  
Author(s):  
Son Hai Nguyen ◽  
David Chelidze
Keyword(s):  
Time Series ◽  
Vector Fields ◽  
Fractal Dimensions ◽  
Large Data ◽  
Practical Applications ◽  
Force Microscopy ◽  
Birkhoff Ergodic Theorem ◽  
Long Time ◽  
Computational Resources ◽  
Simple Features

Estimation of most of the metrics used to characterize dynamical systems’ output require fairly long time series (e.g., Lyapunov Exponents, Fractal Dimensions), or substantial computational resources (e.g., phase space warping metrics, sensitivity vector fields). In many practical applications, when there is abundance of data (e.g., in Atomic Force Microscopy) fast and simple features are needed, and when there is sparsity of data (e.g., in many Structural Health Monitoring situations) robust features are needed. Here, we propose a new class of features based on Birkhoff Ergodic Theorem, which are fast to calculate and do not require large data or computational resources. Applications of these metrics, in conjunction with the smooth orthogonal decomposition, to identifying underlying processes causing nonstationarity both in simulations and actual experiments are demonstrated.

The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions

1998 ◽  
Vol 06 (02) ◽  
pp. 107-116 ◽  
Author(s):  
Sepp Hochreiter
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Time Lag ◽  
Neural Nets ◽  
Alternative Methods ◽  
Reasonable Time ◽  
Practical Applications ◽  
Learning Time ◽  
Long Time ◽  
Gradient Based

Recurrent nets are in principle capable to store past inputs to produce the currently desired output. Because of this property recurrent nets are used in time series prediction and process control. Practical applications involve temporal dependencies spanning many time steps, e.g. between relevant inputs and desired outputs. In this case, however, gradient based learning methods take too much time. The extremely increased learning time arises because the error vanishes as it gets propagated back. In this article the de-caying error flow is theoretically analyzed. Then methods trying to overcome vanishing gradients are briefly discussed. Finally, experiments comparing conventional algorithms and alternative methods are presented. With advanced methods long time lag problems can be solved in reasonable time.

scholarly journals A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Franz Konstantin Fuss
Keyword(s):  
Time Series ◽  
Time Derivative ◽  
Fractal Dimensions ◽  
Human Movement ◽  
Robust Algorithm ◽  
Practical Applications ◽  
Linear Effect ◽  
Scaling Methods ◽  
The Difference ◽  
Nowhere Differentiable Functions

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

scholarly journals Sea Ice Concentration Products over Polar Regions with Chinese FY3C/MWRI Data

2021 ◽  
Vol 13 (11) ◽  
pp. 2174
Author(s):  
Lijian Shi ◽  
Sen Liu ◽  
Yingni Shi ◽  
Xue Ao ◽  
Bin Zou ◽  
...  
Keyword(s):  
Time Series ◽  
Sea Ice ◽  
Ocean Circulation ◽  
The Arctic ◽  
Retrieval Algorithm ◽  
Atmospheric Effects ◽  
Observation Data ◽  
Long Time Series ◽  
Ice Concentration ◽  
Long Time

Polar sea ice affects atmospheric and ocean circulation and plays an important role in global climate change. Long time series sea ice concentrations (SIC) are an important parameter for climate research. This study presents an SIC retrieval algorithm based on brightness temperature (Tb) data from the FY3C Microwave Radiation Imager (MWRI) over the polar region. With the Tb data of Special Sensor Microwave Imager/Sounder (SSMIS) as a reference, monthly calibration models were established based on time–space matching and linear regression. After calibration, the correlation between the Tb of F17/SSMIS and FY3C/MWRI at different channels was improved. Then, SIC products over the Arctic and Antarctic in 2016–2019 were retrieved with the NASA team (NT) method. Atmospheric effects were reduced using two weather filters and a sea ice mask. A minimum ice concentration array used in the procedure reduced the land-to-ocean spillover effect. Compared with the SIC product of National Snow and Ice Data Center (NSIDC), the average relative difference of sea ice extent of the Arctic and Antarctic was found to be acceptable, with values of −0.27 ± 1.85 and 0.53 ± 1.50, respectively. To decrease the SIC error with fixed tie points (FTPs), the SIC was retrieved by the NT method with dynamic tie points (DTPs) based on the original Tb of FY3C/MWRI. The different SIC products were evaluated with ship observation data, synthetic aperture radar (SAR) sea ice cover products, and the Round Robin Data Package (RRDP). In comparison with the ship observation data, the SIC bias of FY3C with DTP is 4% and is much better than that of FY3C with FTP (9%). Evaluation results with SAR SIC data and closed ice data from RRDP show a similar trend between FY3C SIC with FTPs and FY3C SIC with DTPs. Using DTPs to present the Tb seasonal change of different types of sea ice improved the SIC accuracy, especially for the sea ice melting season. This study lays a foundation for the release of long time series operational SIC products with Chinese FY3 series satellites.

scholarly journals Meso- and microscale sea-ice motion in the East Siberian Sea as determined from ERS-1 SAR Data

1999 ◽  
Vol 45 (150) ◽  
pp. 370-383 ◽  
Author(s):  
Kim Morris ◽  
Shusun Li ◽  
Martin Jeffries
Keyword(s):  
Time Series ◽  
Sea Ice ◽  
Large Scale ◽  
Vector Fields ◽  
Lateral Displacement ◽  
Motion Vector ◽  
Sar Interferometry ◽  
East Siberian Sea ◽  
Pack Ice ◽  
Sar Data

Abstract Synthetic aperture radar- (SAR-)derived ice-motion vectors and SAR interferometry were used to study the sea-ice conditions in the region between the coast and 75° N (~ 560 km) in the East Siberian Sea in the vicinity of the Kolyma River. ERS-1 SAR data were acquired between 24 December 1993 and 30 March 1994 during the 3 day repeat Ice Phase of the satellite. The time series of the ice-motion vector fields revealed rapid (3 day) changes in the direction and displacement of the pack ice. Longer-term (≥ 1 month) trends also emerged which were related to changes in large-scale atmospheric circulation. On the basis of this time series, three sea-ice zones were identified: the near-shore, stationary-ice zone; a transitional-ice zone;and the pack-ice zone. Three 3 day interval and one 9 day interval interferometric sets (amplitude, correlation and phase diagrams) were generated for the end of December, the begining of February and mid-March. They revealed that the stationary-ice zone adjacent to the coast is in constant motion, primarily by lateral displacement, bending, tilting and rotation induced by atmospheric/oceanic forcing. The interferogram patterns change through time as the sea ice becomes thicker and a network of cracks becomes established in the ice cover. It was found that the major features in the interferograms were spatially correlated with sea-ice deformation features (cracks and ridges) and major discontinuities in ice thickness.

scholarly journals Performance stability of the MODIS and VIIRS LAI algorithms inferred from analysis of long time series of products

2021 ◽  
Vol 260 ◽  
pp. 112438
Author(s):  
Kai Yan ◽  
Jiabin Pu ◽  
Taejin Park ◽  
Baodong Xu ◽  
Yelu Zeng ◽  
...  
Keyword(s):  
Time Series ◽  
Long Time Series ◽  
Long Time

Cloud Properties over the North Slope of Alaska: Identifying the Prevailing Meteorological Regimes

2012 ◽  
Vol 25 (23) ◽  
pp. 8238-8258 ◽  
Author(s):  
Johannes Mülmenstädt ◽  
Dan Lubin ◽  
Lynn M. Russell ◽  
Andrew M. Vogelmann
Keyword(s):  
Time Series ◽  
Climate Model ◽  
North Slope ◽  
Test Cases ◽  
Synoptic Scale ◽  
Long Time Series ◽  
The North ◽  
Cloud Properties ◽  
North Slope Of Alaska ◽  
Long Time

Abstract Long time series of Arctic atmospheric measurements are assembled into meteorological categories that can serve as test cases for climate model evaluation. The meteorological categories are established by applying an objective k-means clustering algorithm to 11 years of standard surface-meteorological observations collected from 1 January 2000 to 31 December 2010 at the North Slope of Alaska (NSA) site of the U.S. Department of Energy Atmospheric Radiation Measurement Program (ARM). Four meteorological categories emerge. These meteorological categories constitute the first classification by meteorological regime of a long time series of Arctic meteorological conditions. The synoptic-scale patterns associated with each category, which include well-known synoptic features such as the Aleutian low and Beaufort Sea high, are used to explain the conditions at the NSA site. Cloud properties, which are not used as inputs to the k-means clustering, are found to differ significantly between the regimes and are also well explained by the synoptic-scale influences in each regime. Since the data available at the ARM NSA site include a wealth of cloud observations, this classification is well suited for model–observation comparison studies. Each category comprises an ensemble of test cases covering a representative range in variables describing atmospheric structure, moisture content, and cloud properties. This classification is offered as a complement to standard case-study evaluation of climate model parameterizations, in which models are compared against limited realizations of the Earth–atmosphere system (e.g., from detailed aircraft measurements).

scholarly journals Mixed Models as a Tool for Comparing Groups of Time Series in Plant Sciences

Plants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 362
Author(s):  
Ioannis Spyroglou ◽  
Jan Skalák ◽  
Veronika Balakhonova ◽  
Zuzana Benedikty ◽  
Alexandros G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Model ◽  
Repeated Measurements ◽  
Time Series Models ◽  
Additional Time ◽  
Biotic Stresses ◽  
Viable Solution ◽  
Long Time

Plants adapt to continual changes in environmental conditions throughout their life spans. High-throughput phenotyping methods have been developed to noninvasively monitor the physiological responses to abiotic/biotic stresses on a scale spanning a long time, covering most of the vegetative and reproductive stages. However, some of the physiological events comprise almost immediate and very fast responses towards the changing environment which might be overlooked in long-term observations. Additionally, there are certain technical difficulties and restrictions in analyzing phenotyping data, especially when dealing with repeated measurements. In this study, a method for comparing means at different time points using generalized linear mixed models combined with classical time series models is presented. As an example, we use multiple chlorophyll time series measurements from different genotypes. The use of additional time series models as random effects is essential as the residuals of the initial mixed model may contain autocorrelations that bias the result. The nature of mixed models offers a viable solution as these can incorporate time series models for residuals as random effects. The results from analyzing chlorophyll content time series show that the autocorrelation is successfully eliminated from the residuals and incorporated into the final model. This allows the use of statistical inference.

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