Dataset Information

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

ABSTRACT: A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized 'events'. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event's 'region of influence' within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis, is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry.

SUBMITTER: Lilly JM

PROVIDER: S-EPMC5415685 | biostudies-literature | 2017 Apr

REPOSITORIES: biostudies-literature

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Publications

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

Lilly Jonathan M JM

Proceedings. Mathematical, physical, and engineering sciences 20170426 2200

A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized 'events'. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its ...[more]

PMID: 28484325

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Project description:BackgroundIt is a daunting task to discontinue pertussis completely in China owing to its growing increase in the incidence. While basic to any formulation of prevention and control measures is early response for future epidemic trends. Discrete wavelet transform(DWT) has been emerged as a powerful tool in decomposing time series into different constituents, which facilitates better improvement in prediction accuracy. Thus we aim to integrate modeling approaches as a decision-making supportive tool for formulating health resources.MethodsWe constructed a novel hybrid method based on the pertussis morbidity cases from January 2004 to May 2018 in China, where the approximations and details decomposed by DWT were forecasted by a seasonal autoregressive integrated moving average (SARIMA) and nonlinear autoregressive network (NAR), respectively. Then, the obtained values were aggregated as the final results predicted by the combined model. Finally, the performance was compared with the SARIMA, NAR and traditional SARIMA-NAR techniques.ResultsThe hybrid technique at level 2 of db2 wavelet including a SARIMA(0,1,3)(1,0,0)12modelfor the approximation-forecasting and NAR model with 12 hidden units and 4 delays for the detail d1-forecasting, along with another NAR model with 11 hidden units and 5 delays for the detail d2-forecasting notably outperformed other wavelets, SARIMA, NAR and traditional SARIMA-NAR techniques in terms of the mean square error, root mean square error, mean absolute error and mean absolute percentage error. Descriptive statistics exhibited that a substantial rise was observed in the notifications from 2013 to 2018, and there was an apparent seasonality with summer peak. Moreover, the trend was projected to continue upwards in the near future.ConclusionsThis hybrid approach has an outstanding ability to improve the prediction accuracy relative to the others, which can be of great help in the prevention of pertussis. Besides, under current trend of pertussis morbidity, it is required to urgently address strategically within the proper policy adopted.

Dataset Information

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

Publications

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

Similar Datasets

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