Entropy-Based Wavelet De-noising Method for Time Series Analysis

Adaptive wavelet base selection for deep learning-based ECG diagnosis: A reinforcement learning approach

Electrocardiogram (ECG) signals are crucial in diagnosing cardiovascular diseases (CVDs). While wavelet-based feature extraction has demonstrated effectiveness in deep learning (DL)-based ECG diagnosis, selecting the optimal wavelet base poses a significant challenge, as it directly influences feature quality and diagnostic accuracy. Traditional methods typically rely on fixed wavelet bases chosen heuristically or through trial-and-error, which can fail to cover the distinct characteristics of individual ECG signals, leading to suboptimal performance. To address this limitation, we propose a reinforcement learning-based wavelet base selection (RLWBS) framework that dynamically customizes the wavelet base for each ECG signal. In this framework, a reinforcement learning (RL) agent iteratively optimizes its wavelet base selection (WBS) strategy based on successive feedback of classification performance, aiming to achieve progressively optimized feature extraction. Experiments conducted on the clinically collected PTB-XL dataset for ECG abnormality classification show that the proposed RLWBS framework could obtain more detailed time-frequency representation of ECG signals, yielding enhanced diagnostic performance compared to traditional WBS approaches.

Application of a Novel Hybrid Wavelet-ANFIS/Fuzzy C-Means Clustering Model to Predict Groundwater Fluctuations

In order to optimize the management of groundwater resources, accurate estimates of groundwater level (GWL) fluctuations are required. In recent years, the use of artificial intelligence methods based on data mining theory has increasingly attracted attention. The goal of this research is to evaluate and compare the performance of adaptive network-based fuzzy inference system (ANFIS) and Wavelet-ANFIS models based on FCM for simulation/prediction of monthly GWL in the Maragheh plain in northwestern Iran. A 22-year dataset (1996–2018) including hydrological parameters such as monthly precipitation (P) and GWL from 25 observation wells was used as models input data. To improve the prediction accuracy of hybrid Wavelet-ANFIS model, different mother wavelets and different numbers of clusters and decomposition levels were investigated. The new hybrid model with Sym4-mother wavelet, two clusters and a decomposition level equal to 3 showed the best performance. The maximum values of R2 in the training and testing phases were 0.997 and 0.994, respectively, and the best RMSE values were 0.05 and 0.08 m, respectively. By comparing the results of the ANFIS and hybrid Wavelet-ANFIS models, it can be deduced that a hybrid model is an acceptable method in modeling of GWL because it employs both the wavelet transform and FCM clustering technique.

Spatiotemporal Variability of Monthly and Annual Snow Depths in Xinjiang, China over 1961–2015 and the Potential Effects

The spatiotemporal variability of snow depth supplies important information for snow disaster prevention. The monthly and annual snow depths and weather data (from Xinjiang Meteorological Observatory) at 102 meteorological stations in Xinjiang, China over 1961–2015 were used to analyze the spatiotemporal characteristics of snow depths from different aspects. The empirical orthogonal function (EOF), the modified Mann–Kendall method, Morlet wavelet, Daubechies wavelet decomposition and cross wavelet transform were applied to investigate the trend and significance, spatial structure, periods, decomposed series and coherence of monthly and annual snow depths. The results indicated that: (1) The value of EOF first spatial mode (EOF1) of the monthly and annual snow depths in north Xinjiang were larger than south Xinjiang, indicating greater variability of snow depths in north Xinjiang. (2) The change points of annual snow depth mainly occurred during 1969–1979 and 1980–1990. The annual snow depth of most sites showed increasing trends, but with different slope magnitudes. (3) The sites that had main periods of 2–8 and 9–14 years of monthly and annual snow depths (detected by the Morlet wavelet) mainly distributed in northern Xinjiang. The sites that had main periods of 15–20 years of monthly and annual snow depths mainly distributed in southwestern Xinjiang. (4) By using the Daubechies wavelet, the decomposed annual snow depth in entire Xinjiang tended to increase. (5) Through the cross wavelet transform, annual snow depths in entire Xinjiang had good correlations with annual precipitation or relative humidity, and showed a low negative correlation with minimum temperature or sunshine hours. In conclusion, the monthly and annual snow depths had comprehensive spatiotemporal variability but had overall increasing trend during 1961–2015.

Energy-based wavelet de-noising of hydrologic time series

De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed.