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Entropy and Information Theory in Machine Learning: Theoretical Insights and Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Signal and Data Analysis".

Deadline for manuscript submissions: closed (15 March 2024) | Viewed by 4455

Special Issue Editors


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Guest Editor
School of Engineering, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, USA
Interests: deep learning; machine learning; adaptive filters; signal processing; applications
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Guest Editor
Department of Electrical Engineering, Indian Institute of Technology, Gandhinagar, India
Interests: active noise control; adaptive signal processing; assistive listening devices; psychoacoustics
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Guest Editor
Department of Information Engineering, Electronics and Telecommunications (DIET), Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
Interests: deep learning; adaptive filters; machine learning; audio signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Entropy titled, “Entropy and Information Theory in Machine Learning: Theoretical Insights and Applications“, is a second-volume sequel to our first Special Issue titled, “Adaptive signal processing and Machine Learning Using Entropy and Information Theory“.

Adaptive signal processing, machine learning and deep learning, which rely on the paradigm of learning from data, have become indispensable tools for extracting information, making decisions and interacting with our environment. The information extraction process is a very critical step in this process. Many of the algorithms deployed for information extraction have largely been based on using the popular mean square error (MSE) criterion. They leverage the significant information contained in the data. The more accurate the process of extracting useful information from the data, the more precise and efficient the learning and signal processing will be.

It is well-known that information theoretic learning (ITL)-based cost measures can provide better nonlinear models in a range of problems from system identification and regression to classification. Information theoretic learning (ITL) has initially been applied for such supervised learning applications. ITL-based cost measures also perform better when the error distribution is non-Gaussian, such as in supervised learning.

Entropy and information theory have always represented useful tools to deal with information and the amount of information contained in a random variable. Information theory mainly relies on the basic intuition that learning that an unlikely event has occurred is more informative than learning that a likely event has occurred. Entropy gives a measure of the amount of information in an event drawn from a distribution. For this reason, they have been widely used in adaptive signal processing and machine learning to improve performance by designing and optimizing effective and specific models that fit the data, even in noisy and adverse scenario conditions.

The presence of strong disturbances in the error signal can severely deteriorate the convergence behavior of adaptive filters and, in some cases, cause the learning algorithms to diverge. Information theoretic learning (ITL) approaches have recently emerged as an effective solution to handle such scenarios.

Examples of several measures widely adopted include mutual information, cross-entropy, minimum error entropy (MEE) criterion, maximum correntropy criterion (MCC) and Kullback–Leibler divergence, among others. Moreover, a wide class of interesting tasks of adaptive signal processing, machine learning and deep learning take advantage of entropy and information theory, including: exploratory data analysis, feature and model selection, sampling and subset extraction, optimizing learning algorithms, clustering sensitivity analysis, representation learning, and data generation.

This Special Issue aims at providing an avenue for the publication of recent developments in the areas of entropy and information theoretic-based measures used in machine learning. We solicit papers expounding on theoretical insights as well as the latest applications of these techniques for solving various problems.

Prof. Dr. Tokunbo Ogunfunmi
Dr. Nithin V. George
Dr. Danilo Comminiello
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • adaptive signal processing and adaptive filters
  • machine listening and deep learning
  • information theoretic learning
  • generalized maximum correntropy criterion (GMCC)
  • maximum correntropy criterion (MCC) and cyclic correntropy
  • nonlinear adaptive filters
  • robust signal processing and robust learning
  • impulsive noise
  • model selection and feature extraction
  • Bayesian learning and representation learning

Published Papers (3 papers)

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Research

14 pages, 7993 KiB  
Article
An Improved Toeplitz Approximation Method for Coherent DOA Estimation in Impulsive Noise Environments
by Jiang’an Dai, Tianshuang Qiu, Shengyang Luan, Quan Tian and Jiacheng Zhang
Entropy 2023, 25(6), 960; https://doi.org/10.3390/e25060960 - 20 Jun 2023
Cited by 1 | Viewed by 1156
Abstract
Direction of arrival (DOA) estimation is an important research topic in array signal processing and widely applied in practical engineering. However, when signal sources are highly correlated or coherent, conventional subspace-based DOA estimation algorithms will perform poorly due to the rank deficiency in [...] Read more.
Direction of arrival (DOA) estimation is an important research topic in array signal processing and widely applied in practical engineering. However, when signal sources are highly correlated or coherent, conventional subspace-based DOA estimation algorithms will perform poorly due to the rank deficiency in the received data covariance matrix. Moreover, conventional DOA estimation algorithms are usually developed under Gaussian-distributed background noise, which will deteriorate significantly in impulsive noise environments. In this paper, a novel method is presented to estimate the DOA of coherent signals in impulsive noise environments. A novel correntropy-based generalized covariance (CEGC) operator is defined and proof of boundedness is given to ensure the effectiveness of the proposed method in impulsive noise environments. Furthermore, an improved Toeplitz approximation method combined CEGC operator is proposed to estimate the DOA of coherent sources. Compared to other existing algorithms, the proposed method can avoid array aperture loss and perform more effectively, even in cases of intense impulsive noise and low snapshot numbers. Finally, comprehensive Monte-Carlo simulations are performed to verify the superiority of the proposed method under various impulsive noise conditions. Full article
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17 pages, 3905 KiB  
Article
A Novel ECG Signal Denoising Algorithm Based on Sparrow Search Algorithm for Optimal Variational Modal Decomposition
by Jiandong Mao, Zhiyuan Li, Shun Li and Juan Li
Entropy 2023, 25(5), 775; https://doi.org/10.3390/e25050775 - 10 May 2023
Cited by 1 | Viewed by 1428
Abstract
ECG signal processing is an important basis for the prevention and diagnosis of cardiovascular diseases; however, the signal is susceptible to noise interference mixed with equipment, environmental influences, and transmission processes. In this paper, an efficient denoising method based on the variational modal [...] Read more.
ECG signal processing is an important basis for the prevention and diagnosis of cardiovascular diseases; however, the signal is susceptible to noise interference mixed with equipment, environmental influences, and transmission processes. In this paper, an efficient denoising method based on the variational modal decomposition (VMD) algorithm combined with and optimized by the sparrow search algorithm (SSA) and singular value decomposition (SVD) algorithm, named VMD–SSA–SVD, is proposed for the first time and applied to the noise reduction of ECG signals. SSA is used to find the optimal combination of parameters of VMD [K,α], VMD–SSA decomposes the signal to obtain finite modal components, and the components containing baseline drift are eliminated by the mean value criterion. Then, the effective modalities are obtained in the remaining components using the mutual relation number method, and each effective modal is processed by SVD noise reduction and reconstructed separately to finally obtain a clean ECG signal. In order to verify the effectiveness, the methods proposed are compared and analyzed with wavelet packet decomposition, empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm. The results show that the noise reduction effect of the VMD–SSA–SVD algorithm proposed is the most significant, and that it can suppress the noise and remove the baseline drift interference at the same time, and effectively retain the morphological characteristics of the ECG signals. Full article
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17 pages, 810 KiB  
Article
Knowledge-Enhanced Compressed Measurements for Detection of Frequency-Hopping Spread Spectrum Signals Based on Task-Specific Information and Deep Neural Networks
by Feng Liu and Yinghai Jiang
Entropy 2023, 25(1), 11; https://doi.org/10.3390/e25010011 - 21 Dec 2022
Cited by 2 | Viewed by 1172
Abstract
The frequency-hopping spread spectrum (FHSS) technique is widely used in secure communications. In this technique, the signal carrier frequency hops over a large band. The conventional non-compressed receiver must sample the signal at high rates to catch the entire frequency-hopping range, which is [...] Read more.
The frequency-hopping spread spectrum (FHSS) technique is widely used in secure communications. In this technique, the signal carrier frequency hops over a large band. The conventional non-compressed receiver must sample the signal at high rates to catch the entire frequency-hopping range, which is unfeasible for wide frequency-hopping ranges. In this paper, we propose an efficient adaptive compressed method to measure and detect the FHSS signals non-cooperatively. In contrast to the literature, the FHSS signal-detection method proposed in this paper is achieved directly with compressed sampling rates. The measurement kernels (the non-zero coefficients in the measurement matrix) are designed adaptively, using continuously updated knowledge from the compressed measurement. More importantly, in contrast to the iterative optimizations of the measurement matrices in the literature, the deep neural networks are trained once using task-specific information optimization and repeatedly implemented for measurement kernel design, enabling efficient adaptive detection of the FHSS signals. Simulations show that the proposed method provides stably low missing detection rates, compared to the compressed detection with random measurement kernels and the recently proposed method. Meanwhile, the measurement design in the proposed method is shown to provide improved efficiency, compared to the commonly used recursive method. Full article
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