A Quantum Wavelet Uncertainty Principle

In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some q-quantum wavelet, is established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is used for exploring a wavelet uncertainty principle in the q-calculus framework.

Comparison of wavelet transformations to enhance convolutional neural network performance in brain tumor segmentation

Introduction and goal to background Due to the importance of segmentation of MRI images in identifying brain tumors, various methods including deep learning have been introduced for automatic brain tumor segmentation. On the other hand, using a combination of methods can improve their performance. Among them is the use of wavelet transform as an auxiliary element in deep networks. The analysis of the requirements of such combinations has been addressed in this study. Method In this developmental study, different wavelet functions were used to compress brain MRI images and finally as an auxiliary element in improving the performance of the convolutional neural network in brain tumor segmentation. Results Based on the results of the tests performed, the Daubechies1 function was most effective in enhancing network performance in segmenting MRI images and was able to balance the performance and computational overload. Conclusion Choosing the wavelet function to optimize the performance of a convolutional neural network should be based on the requirements of the problem, also taking into account some considerations such as computational load, processing time, and performance of the wavelet function in optimizing CNN output in the intended task.

The wave packet transform in the framework of linear canonical transform

In this paper, we introduce the concept of linear canonical wave packet transform (LCWPT) based on the idea of linear canonical transform (LCT) and wave packet transform (WPT). Parseval’s identity and some properties of LCWPT are discussed. The inversion formula of LCWPT is formulated. Moreover, the composition of LCWPTs is defined and some properties are studied related to it. The LCWPTs of Mexican hat wavelet function are obtained.

Suicide cases in developed and emerging countries: an analysis using wavelets

ABSTRACT Objective The aim of this study was to use a wavelet technique to determine whether the number of suicides is similar between developed and emerging countries. Methods Annual data were obtained from World Health Organization (WHO) reports from 1986 to 2015. Discrete nondecimated wavelet transform was used for the analysis, and the Daubechies wavelet function was applied with five-level decomposition. Regarding clustering, energy (variance) was used to analyze the clusters and visualize the clustering process. We constructed a dendrogram using the Mahalanobis distance. The number of groups was set using a specific function in the R program. Results The cluster analysis verified the formation of four groups as follows: Japan, the United States and Brazil were distinct and isolated groups, and other countries (Austria, Belgium, Chile, Israel, Mexico, Italy and the Netherlands) constituted a single group. Conclusion The methods utilized in this paper enabled a detailed verification of countries with similar behaviors despite very distinct socioeconomic, geographic and climate characteristics.

An Improved Decision Tree Algorithm for Condition Monitoring on Storage Power Station of Internet Things

Power station is an important basic power generation organization, and its operation status is related to the continuous power generation capacity. At present, a large number of physical network equipment and intelligent equipment are used in pumped storage power station, which makes its data mass growth and its operation state become a difficult problem. Accurate operation monitoring results can provide decision support that power generation planners and government, but also reasonably dispatch corresponding resources. In the past, decision tree algorithm was used in operation condition monitoring, which has the problem of data distortion and affects the accuracy of monitoring results. Based on the above reasons, this paper combines the wavelet function and decision tree algorithm, proposes an improved decision tree algorithm to eliminate redundant data in order, and uses wavelet function to cluster distorted data, so as to improve the accuracy and computational efficiency of the algorithm. Matlab simulation results show that: decision tree algorithm can eliminate 90% of redundant data, reduce the impact of feature data extraction on decision tree. At the same time, the improved accuracy is 98%, the calculation time is less than 25s is better than that, the decision tree algorithm. Therefore, the improved algorithm can optimize the condition monitoring of pumped storage power station.

Wavelet-Based Elman Neural Network with the Modified Differential Evolution Algorithm for Forecasting Foreign Exchange Rates

It is challenging to forecast foreign exchange rates due to the non-linear characters of the data. This paper applied a wavelet-based Elman neural network with the modified differential evolution algorithm to forecast foreign exchange rates. Elman neural network has dynamic characters because of the context layer in the structure. It makes Elman neural network suit for time series problems. The main factors, which affect the accuracy of the Elman neural network, included the transfer functions of the hidden layer and the parameters of the neural network. We applied the wavelet function to replace the sigmoid function in the hidden layer of the Elman neural network, and we found there was a “disruption problem” caused by the non-linear performance of the wavelet function. It didn’t improve the performance of the Elman neural network, but made it get worse in reverse. Then, the modified differential evolution algorithm was applied to train the parameters of the Elman neural network. To improve the optimizing performance of the differential evolution algorithm, the crossover probability and crossover factor were modified with adaptive strategies, and the local enhanced operator was added to the algorithm. According to the experiment, the modified algorithm improved the performance of the Elman neural network, and it solved the “disruption problem” of applying the wavelet function. These results show that the performance of the Elman neural network would be improved if both of the wavelet function and the modified differential evolution algorithm were applied integratedly.

Evaluating Steady-State Visually Evoked Potentials-Based Brain-Computer Interface System Using Wavelet Features and Various Machine Learning Methods

Steady-state visual evoked potentials (SSVEPs) have been designated to be appropriate and are in use in many areas such as clinical neuroscience, cognitive science, and engineering. SSVEPs have become popular recently, due to their advantages including high bit rate, simple system structure and short training time. To design SSVEP-based BCI system, signal processing methods appropriate to the signal structure should be applied. One of the most appropriate signal processing methods of these non-stationary signals is the Wavelet Transform. In this study, we investigated both the effect of choosing a mother wavelet function and the most successful combination of classifier algorithm, wavelet features, and frequency pairs assigned to BCI commands. SSVEP signals that were recorded at seven different stimulus frequencies (6–6.5 – 7 – 7.5 – 8.2 – 9.3 – 10 Hz) were used in this study. A total of 115 features were extracted from time, frequency, and time-frequency domains. These features were classified by a total of seven different classification processes. Classification evaluation was presented with the 5-fold cross-validation method and accuracy values. According to the results, (I) the most successful wavelet function was Haar wavelet, (II) the most successful classifier was Ensemble Learning, (III) using the feature vector consisting of energy, entropy, and variance features yielded higher accuracy than using one of these features alone, and (IV) the highest performances were obtained in the frequency pairs with “6–10”, “6.5–10”, “7–10”, and “7.5–10” Hz.

Selection of a mother wavelet as identification pattern for the detection of cracks in shafts

Nowadays, there are many methods to detect and diagnose defects in mechanical components during operation. The newest methods that can be found in the literature are based on intelligent classification systems and evaluation of patterns to obtain a diagnosis; however, there is not any standard method to assess features. Wavelet packet transform allows to obtain interesting patterns for evaluating the condition of rotating elements. To perform this calculation, it is necessary to select a series of parameters that affect the resulting pattern. These parameters are the decomposition level and the mother wavelet function. A detailed methodology for the selection of the mother wavelet is proposed, which is the aim of this work, to obtain the most suitable patterns in the diagnostic task. This proposed methodology is applied to data obtained from a rotating shaft with a crack located at the change of section. These signals were measured at low rotation frequency (below the critical rotation frequency) and without eccentricity, where detection becomes more complex.