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In this paper, we study the connections between generalized mean operators and entropies, where the mean value operators are related to the strictly monotone logical operators of fuzzy theory. Here, we propose a new entropy measure based on the family of generalized Dombi operators. Namely, this measure is obtained by using the Dombi operator as a generator function in the general solution of the bisymmetric functional equation. We show how the proposed entropy can be used in a fuzzy system where the performance is consistent in choosing the best alternative in the Multiple Attribute Decision-Making Problem. This newly defined entropy was also applied to the problem of extracting useful information from time-frequency representations of noisy, nonstationary, and multicomponent signals. The denoising results were compared to Shannon and Rényi entropies. The proposed entropy measure is shown to significantly outperform the competing ones in terms of denoising classification accuracy and the F1-score due to its sensitivity to small changes in the probability distribution. [ABSTRACT FROM AUTHOR]

The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral form of the vertex–frequency analysis, and it will be considered in this paper since the spectral domain for signal localization is well ordered and thus simpler for application to the graph signals. The localized graph Fourier transform is defined based on its counterpart, the short-time Fourier transform, in classical signal analysis. We consider various spectral window forms based on which these transforms can tackle the localized signal behavior. Conditions for the signal reconstruction, known as the overlap-and-add (OLA) and weighted overlap-and-add (WOLA) methods, are also considered. Since the graphs can be very large, the realizations of vertex–frequency representations using polynomial form localization have a particular significance. These forms use only very localized vertex domains, and do not require either the graph Fourier transform or the inverse graph Fourier transform, are computationally efficient. These kinds of implementations are then applied to classical time–frequency analysis since their simplicity can be very attractive for the implementation in the case of large time-domain signals. Spectral varying forms of the localization functions are presented as well. These spectral varying forms are related to the wavelet transform. For completeness, the inversion and signal reconstruction are discussed as well. The presented theory is illustrated and demonstrated on numerical examples. [ABSTRACT FROM AUTHOR]

Electroencephalogram (EEG) signals are known to contain signatures of stimuli that induce brain activities. However, detecting these signatures to classify captured EEG waveforms is one of the most challenging tasks of EEG analysis. This paper proposes a novel time–frequency-based method for EEG analysis and characterization implemented in a computer-aided decision-support system that can be used to assist medical experts in interpreting EEG patterns. The computerized method utilizes EEG spectral non-stationarity, which is clearly revealed in the time–frequency distributions (TFDs) of multicomponent signals. The proposed algorithm, which is based on the modification of the Rényi entropy, called local or short-term Rényi entropy (STRE), was upgraded with a blind component separation procedure and instantaneous frequency (IF) estimation. The method was applied to EEGs of both forward and backward movements of the left and right hands, as well as to EEGs of imagined hand movements, which were captured by a 19-channel EEG recording system. The obtained results show that in a given virtual instrument, the proposed methods efficiently distinguish between real and imagined limb movements by considering their signatures in terms of the dominant EEG component's IFs at the specified subset of EEG channels (namely, F3, F4, F7, F8, T3, and T4). Furthermore, computing the number of EEG signal components, their extraction, and IF estimation provide important information that shows potential to enhance existing clinical diagnostic techniques for detecting the intensity, location, and type of brain function abnormalities in patients with neurological motor control disorders. [ABSTRACT FROM AUTHOR]

The rapid growth in the amount of data in the digital world leads to the need for data compression, and so forth, reducing the number of bits needed to represent a text file, an image, audio, or video content. Compressing data saves storage capacity and speeds up data transmission. In this paper, we focus on the text compression and provide a comparison of algorithms (in particular, entropy-based arithmetic and dictionary-based Lempel–Ziv–Welch (LZW) methods) for text compression in different languages (Croatian, Finnish, Hungarian, Czech, Italian, French, German, and English). The main goal is to answer a question: "How does the language of a text affect the compression ratio?" The results indicated that the compression ratio is affected by the size of the language alphabet, and size or type of the text. For example, The European Green Deal was compressed by 75.79%, 76.17%, 77.33%, 76.84%, 73.25%, 74.63%, 75.14%, and 74.51% using the LZW algorithm, and by 72.54%, 71.47%, 72.87%, 73.43%, 69.62%, 69.94%, 72.42% and 72% using the arithmetic algorithm for the English, German, French, Italian, Czech, Hungarian, Finnish, and Croatian versions, respectively. [ABSTRACT FROM AUTHOR]

Non-stationary signals are often analyzed using raw waveform data or spectrograms of those data; however, the possibility of alternative time–frequency representations being more informative than the original data or spectrograms is yet to be investigated. This paper tested whether alternative time–frequency representations could be more informative for machine learning classification of seismological data. The mentioned hypothesis was evaluated by training three well-established convolutional neural networks using nine time–frequency representations. The results were compared to the base model, which was trained on the raw waveform data. The signals that were used in the experiment are three-component seismogram instances from the Local Earthquakes and Noise DataBase (LEN-DB). The results demonstrate that Pseudo Wigner–Ville and Wigner–Ville time–frequency representations yield significantly better results than the base model, while spectrogram and Margenau–Hill perform significantly worse (p < 0.01). Interestingly, the spectrogram, which is often used in signal analysis, had inferior performance when compared to the base model. The findings presented in this research could have notable impacts in the fields of geophysics and seismology as the phenomena that were previously hidden in the seismic noise are now more easily identified. Furthermore, the results indicate that applying Pseudo Wigner–Ville or Wigner–Ville time–frequency representations could result in a large increase in earthquakes in the catalogs and lessen the need to add new stations with an overall reduction in the costs. Finally, the proposed approach of extracting valuable information through time–frequency representations could be applied in other domains as well, such as electroencephalogram and electrocardiogram signal analysis, speech recognition, gravitational waves investigation, and so on. [ABSTRACT FROM AUTHOR]

We present a signal decomposition procedure, which separates modes into individual components while preserving their integrity, in effort to tackle the challenges related to the characterization of modes in an acoustic dispersive environment. With this approach, each mode can be analyzed and processed individually, which carries opportunities for new insights into their characterization possibilities. The proposed methodology is based on the eigenanalysis of the autocorrelation matrix of the analyzed signal. When eigenvectors of this matrix are properly linearly combined, each signal component can be separately reconstructed. A proper linear combination is determined based on the minimization of concentration measures calculated exploiting time-frequency representations. In this paper, we engage a steepest-descent-like algorithm for the minimization process. Numerical results support the theory and indicate the applicability of the proposed methodology in the decomposition of acoustic signals in dispersive channels. [ABSTRACT FROM AUTHOR]

In clinical practice, fracture age estimation is commonly required, particularly in children with suspected non-accidental injuries. It is usually done by radiologically examining the injured body part and analyzing several indicators of fracture healing such as osteopenia, periosteal reaction, and fracture gap width. However, age-related changes in healing timeframes, inter-individual variabilities in bone density, and significant intra- and inter-operator subjectivity all limit the validity of these radiological clues. To address these issues, for the first time, we suggest an automated neural network-based system for determining the age of a pediatric wrist fracture. In this study, we propose and evaluate a deep learning approach for automatically estimating fracture age. Our dataset included 3570 medical cases with a skewed distribution toward initial consultations. Each medical case includes a lateral and anteroposterior projection of a wrist fracture, as well as patients' age, and gender. We propose a neural network-based system with Monte-Carlo dropout-based uncertainty estimation to address dataset skewness. Furthermore, this research examines how each component of the system contributes to the final forecast and provides an interpretation of different scenarios in system predictions in terms of their uncertainty. The examination of the proposed systems' components showed that the feature-fusion of all available data is necessary to obtain good results. Also, proposing uncertainty estimation in the system increased accuracy and F1-score to a final 0.906 ± 0.011 on a given task. [ABSTRACT FROM AUTHOR]

This paper proposes a new method, ConvGraph, to detect communities in highly cohesive and isolated weighted graphs, where the sum of the weights is significantly higher inside than outside the communities. The method starts by transforming the original graph into a line graph to apply a convolution, a common technique in the computer vision field. Although this technique was originally conceived to detect the optimum edge in images, it is used here to detect the optimum edges in communities identified by their weights rather than by their topology. The method includes a final refinement step applied to communities with a high vertex density that could not be detected in the first phase. The proposed algorithm was tested on a series of highly cohesive and isolated synthetic graphs and on a real-world export graph, performing well in both cases. [ABSTRACT FROM AUTHOR]