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With the popularity of the Internet and the increase in the level of information technology, cyber attacks have become an increasingly serious problem. They pose a great threat to the security of individuals, enterprises, and the state. This has made network intrusion detection technology critically important. In this paper, a malicious traffic detection model is constructed based on a decision tree classifier of entropy and a proximal policy optimisation algorithm (PPO) of deep reinforcement learning. Firstly, the decision tree idea in machine learning is used to make a preliminary classification judgement on the dataset based on the information entropy. The importance score of each feature in the classification work is calculated and the features with lower contributions are removed. Then, it is handed over to the PPO algorithm model for detection. An entropy regularity term is introduced in the process of the PPO algorithm update. Finally, the deep reinforcement learning algorithm is used to continuously train and update the parameters during the detection process, and finally, the detection model with higher accuracy is obtained. Experiments show that the binary classification accuracy of the malicious traffic detection model based on the deep reinforcement learning PPO algorithm can reach 99.17% under the CIC-IDS2017 dataset used in this paper. [ABSTRACT FROM AUTHOR]

Addressing the issues of prolonged training times and low recognition rates in large model applications, this paper proposes a weight training method based on entropy gain for weight initialization and dynamic adjustment of the learning rate using the multilayer perceptron (MLP) model as an example. Initially, entropy gain was used to replace random initial values for weight initialization. Subsequently, an incremental learning rate strategy was employed for weight updates. The model was trained and validated using the MNIST handwritten digit dataset. The experimental results showed that, compared to random initialization, the proposed initialization method improves training effectiveness by 39.8% and increases the maximum recognition accuracy by 8.9%, demonstrating the feasibility of this method in large model applications. [ABSTRACT FROM AUTHOR]

Complex systems are prevalent in various disciplines encompassing the natural and social sciences, such as physics, biology, economics, and sociology. Leveraging data science techniques, particularly those rooted in artificial intelligence and machine learning, offers a promising avenue for comprehending the intricacies of complex systems without necessitating detailed knowledge of underlying dynamics. In this paper, we demonstrate that multiscale entropy (MSE) is pivotal in describing the steady state of complex systems. Introducing the multiscale entropy dynamics (MED) methodology, we provide a framework for dissecting system dynamics and uncovering the driving forces behind their evolution. Our investigation reveals that the MED methodology facilitates the expression of complex system dynamics through a Generalized Nonlinear Schrödinger Equation (GNSE) that thus demonstrates its potential applicability across diverse complex systems. By elucidating the entropic underpinnings of complexity, our study paves the way for a deeper understanding of dynamic phenomena. It offers insights into the behavior of complex systems across various domains. [ABSTRACT FROM AUTHOR]

Sleep apnea hypopnea syndrome (SAHS) is a common sleep disorder with a high prevalence. The apnea hypopnea index (AHI) is an important indicator used to diagnose the severity of SAHS disorders. The calculation of the AHI is based on the accurate identification of various types of sleep respiratory events. In this paper, we proposed an automatic detection algorithm for respiratory events during sleep. In addition to the accurate recognition of normal breathing, hypopnea and apnea events using heart rate variability (HRV), entropy and other manual features, we also presented a fusion of ribcage and abdomen movement data combined with the long short-term memory (LSTM) framework to achieve the distinction between obstructive and central apnea events. While only using electrocardiogram (ECG) features, the accuracy, precision, sensitivity, and F1 score of the XGBoost model are 0.877, 0.877, 0.876, and 0.876, respectively, demonstrating that it performs better than other models. Moreover, the accuracy, sensitivity, and F1 score of the LSTM model for detecting obstructive and central apnea events were 0.866, 0.867, and 0.866, respectively. The research results of this paper can be used for the automatic recognition of sleep respiratory events as well as AHI calculation of polysomnography (PSG), which provide a theoretical basis and algorithm references for out-of-hospital sleep monitoring. [ABSTRACT FROM AUTHOR]

The ability to learn continuously is crucial for a robot to achieve a high level of intelligence and autonomy. In this paper, we consider continual reinforcement learning (RL) for quadruped robots, which includes the ability to continuously learn sub-sequential tasks (plasticity) and maintain performance on previous tasks (stability). The policy obtained by the proposed method enables robots to learn multiple tasks sequentially, while overcoming both catastrophic forgetting and loss of plasticity. At the same time, it achieves the above goals with as little modification to the original RL learning process as possible. The proposed method uses the Piggyback algorithm to select protected parameters for each task, and reinitializes the unused parameters to increase plasticity. Meanwhile, we encourage the policy network exploring by encouraging the entropy of the soft network of the policy network. Our experiments show that traditional continual learning algorithms cannot perform well on robot locomotion problems, and our algorithm is more stable and less disruptive to the RL training progress. Several robot locomotion experiments validate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel fault diagnosis method for rolling bearing based on hierarchical refined composite multiscale fluctuation-based dispersion entropy (HRCMFDE) and particle swarm optimization-based extreme learning machine (PSO-ELM). First, HRCMFDE is used to extract fault features in the vibration signal at different time scales. By introducing the hierarchical theory algorithm into the vibration signal decomposition process, the problem of missing high-frequency signals in the coarse-grained process is solved. Fluctuation-based dispersion entropy (FDE) has the characteristics of insensitivity to noise interference and high computational efficiency based on the consideration of nonlinear time series fluctuations, which makes the extracted feature vectors more effective in describing the fault information embedded in each frequency band of the vibration signal. Then, PSO is used to optimize the input weights and hidden layer neuron thresholds of the ELM model to improve the fault identification capability of the ELM classifier. Finally, the performance of the proposed rolling bearing fault diagnosis method is verified and analyzed by using the CWRU dataset and MFPT dataset as experimental cases, respectively. The results show that the proposed method has high identification accuracy for the fault diagnosis of rolling bearings with varying loads and has a good load migration effect. [ABSTRACT FROM AUTHOR]

Frequency prediction after a disturbance has received increasing research attention given its substantial value in providing a decision-making foundation in power system emergency control. With the advancing development of machine learning, analysis power systems with machine-learning methods has become completely different from traditional approaches. In this paper, an ensemble algorithm using cross-entropy as a combination strategy is presented to address the trade-off between prediction accuracy and calculation speed. The prediction difficulty caused by inadequate numbers of severe disturbance samples is also overcome by the ensemble model. In the proposed ensemble algorithm, base learners are selected following the principle of diversity, which guarantees the ensemble algorithm's accuracy. Cross-entropy is applied to evaluate the fitting performance of the base learners and to set the weight coefficient in the ensemble algorithm. Subsequently, an online prediction model based on the algorithm is established that integrates training, prediction and updating. In theWestern System Coordinating Council 9-bus (WSCC 9) system and the Institute of Electrical and Electronics Engineers 39-bus (IEEE 39) system, the algorithm is shown to significantly improve the prediction accuracy in both sample-rich and sample-poor situations, verifying the effectiveness and superiority of the proposed ensemble algorithm. [ABSTRACT FROM AUTHOR]

Today's world faces a serious public health problem with cancer. One type of cancer that begins in the breast and spreads to other body areas is breast cancer (BC). Breast cancer is one of the most prevalent cancers that claim the lives of women. It is also becoming clearer that most cases of breast cancer are already advanced when they are brought to the doctor's attention by the patient. The patient may have the evident lesion removed, but the seeds have reached an advanced stage of development or the body's ability to resist them has weakened considerably, rendering them ineffective. Although it is still much more common in more developed nations, it is also quickly spreading to less developed countries. The motivation behind this study is to use an ensemble method for the prediction of BC, as an ensemble model aims to automatically manage the strengths and weaknesses of each of its separate models, resulting in the best decision being made overall. The main objective of this paper is to predict and classify breast cancer using Adaboost ensemble techniques. The weighted entropy is computed for the target column. Taking each attribute's weights results in the weighted entropy. Each class's likelihood is represented by the weights. The amount of information gained increases with a decrease in entropy. Both individual and homogeneous ensemble classifiers, created by mixing Adaboost with different single classifiers, have been used in this work. In order to deal with the class imbalance issue as well as noise, the synthetic minority over-sampling technique (SMOTE) was used as part of the data mining pre-processing. The suggested approach uses a decision tree (DT) and naive Bayes (NB), with Adaboost ensemble techniques. The experimental findings shown 97.95% accuracy for prediction using the Adaboost-random forest classifier. [ABSTRACT FROM AUTHOR]

As one of the entropy-based methods, the k-Star algorithm benefits from information theory in computing the distances between data instances during the classification task. k-Star is a machine learning method with a high classification performance and strong generalization ability. Nevertheless, as a standard supervised learning method, it performs learning only from labeled data. This paper proposes an improved method, called Semi-Supervised k-Star (SSS), which makes efficient predictions by considering unlabeled data in addition to labeled data. Moreover, it introduces a novel semi-supervised learning approach, called holo-training, against self-training. It has the advantage of enabling a powerful and robust model of data by combining multiple classifiers and using an entropy measure. The results of extensive experimental studies showed that the proposed holo-training approach outperformed the self-training approach on 13 out of the 18 datasets. Furthermore, the proposed SSS method achieved higher accuracy (95.25%) than the state-of-the-art semi-supervised methods (90.01%) on average. The significance of the experimental results was validated by using both the Binomial Sign test and the Friedman test. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of frequency stability prediction (FSP) following active power disturbances in power systems by proposing a vision transformer (ViT) method that predicts frequency stability in real time. The core idea of the FSP approach employing the ViT is to use the time-series data of power system operations as ViT inputs to perform FSP accurately and quickly so that operators can decide frequency control actions, minimizing the losses caused by incidents. Additionally, due to the high-dimensional and redundant input data of the power system and the O(N2) computational complexity of the transformer, feature selection based on copula entropy (CE) is used to construct image-like data with fixed dimensions from power system operation data and remove redundant information. Moreover, no previous FSP study has taken safety margins into consideration, which may threaten the secure operation of power systems. Therefore, a frequency security index (FSI) is used to form the sample labels, which are categorized as "insecurity", "relative security", and "absolute security". Finally, various case studies are carried out on a modified New England 39-bus system and a modified ACTIVSg500 system for projected 0% to 40% nonsynchronous system penetration levels. The simulation results demonstrate that the proposed method achieves state-of-the-art (SOTA) performance on normal, noisy, and incomplete datasets in comparison with eight machine-learning methods. [ABSTRACT FROM AUTHOR]

Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning (ML) methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable alphabet. The unboundedness of Shannon's entropy over the general class of all distributions on an alphabet prevents its potential utility from being fully realized. To fill the void in the foundation of information theory, Zhang (2020) proposed generalized Shannon's entropy, which is finitely defined everywhere. The plug-in estimator, adopted in almost all entropy-based ML method packages, is one of the most popular approaches to estimating Shannon's entropy. The asymptotic distribution for Shannon's entropy's plug-in estimator was well studied in the existing literature. This paper studies the asymptotic properties for the plug-in estimator of generalized Shannon's entropy on countable alphabets. The developed asymptotic properties require no assumptions on the original distribution. The proposed asymptotic properties allow for interval estimation and statistical tests with generalized Shannon's entropy. [ABSTRACT FROM AUTHOR]

As well-known machine learning methods, decision trees are widely applied in classification and recognition areas. In this paper, with the uncertainty of labels handled by belief functions, a new decision tree method based on belief entropy is proposed and then extended to random forest. With the Gaussian mixture model, this tree method is able to deal with continuous attribute values directly, without pretreatment of discretization. Specifically, the tree method adopts belief entropy, a kind of uncertainty measurement based on the basic belief assignment, as a new attribute selection tool. To improve the classification performance, we constructed a random forest based on the basic trees and discuss different prediction combination strategies. Some numerical experiments on UCI machine learning data set were conducted, which indicate the good classification accuracy of the proposed method in different situations, especially on data with huge uncertainty. [ABSTRACT FROM AUTHOR]

The spiking neural network (SNN) is regarded as a promising candidate to deal with the great challenges presented by current machine learning techniques, including the high energy consumption induced by deep neural networks. However, there is still a great gap between SNNs and the online meta-learning performance of artificial neural networks. Importantly, existing spike-based online meta-learning models do not target the robust learning based on spatio-temporal dynamics and superior machine learning theory. In this invited article, we propose a novel spike-based framework with minimum error entropy, called MeMEE, using the entropy theory to establish the gradient-based online meta-learning scheme in a recurrent SNN architecture. We examine the performance based on various types of tasks, including autonomous navigation and the working memory test. The experimental results show that the proposed MeMEE model can effectively improve the accuracy and the robustness of the spike-based meta-learning performance. More importantly, the proposed MeMEE model emphasizes the application of the modern information theoretic learning approach on the state-of-the-art spike-based learning algorithms. Therefore, in this invited paper, we provide new perspectives for further integration of advanced information theory in machine learning to improve the learning performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic systems. [ABSTRACT FROM AUTHOR]

Spectrum sensing is an important function in radio frequency spectrum management and cognitive radio networks. Spectrum sensing is used by one wireless system (e.g., a secondary user) to detect the presence of a wireless service with higher priority (e.g., a primary user) with which it has to coexist in the radio frequency spectrum. If the wireless signal is detected, the second user system releases the given frequency to maintain the principle of not interfering. This paper proposes a machine learning implementation of spectrum sensing using the entropy measure as a feature vector. In the training phase, the information about the activity of the wireless service with higher priority is gathered, and the model is formed. In the classification phase, the wireless system compares the current sensing report to the created model to calculate the posterior probability and classify the sensing report into either the presence or absence of wireless service with higher priority. This paper proposes the novel application of the Fluctuation Dispersion Entropy (FDE) measure recently introduced in the research community as a feature vector to build the model and implement the classification. An improved implementation of the FDE (IFDE) is used to enhance the robustness to noise. IFDE is further enhanced with an adaptive method (AIFDE) to automatically select the hyper-parameter introduced in IFDE. Then, this paper combines the machine learning approach with the entropy measure approach, which are both recent developments in spectrum sensing research. The approach is compared to similar approaches in literature and the classical energy detection method using a generated radar signal data set with different conditions of SNR(dB) and fading conditions. The results show that the proposed approach is able to outperform the approaches from literature based on other entropy measures or the Energy Detector (ED) in a consistent way across different levels of SNR and fading conditions. [ABSTRACT FROM AUTHOR]

Machine learning plays a vital role in several modern economic and industrial fields, and selecting an optimized machine learning method to improve time series' forecasting accuracy is challenging. Advanced machine learning methods, e.g., the support vector regression (SVR) model, are widely employed in forecasting fields, but the individual SVR pays no attention to the significance of data selection, signal processing and optimization, which cannot always satisfy the requirements of time series forecasting. By preprocessing and analyzing the original time series, in this paper, a hybrid SVR model is developed, considering periodicity, trend and randomness, and combined with data selection, signal processing and an optimization algorithm for short-term load forecasting. Case studies of electricity power data from New SouthWales and Singapore are regarded as exemplifications to estimate the performance of the developed novel model. The experimental results demonstrate that the proposed hybrid method is not only robust but also capable of achieving significant improvement compared with the traditional single models and can be an effective and efficient tool for power load forecasting. [ABSTRACT FROM AUTHOR]

In this paper, information entropy and ensemble learning based signal recognition theory and algorithms have been proposed. We have extracted 16 kinds of entropy features out of 9 types of modulated signals. The types of information entropy used are numerous, including Rényi entropy and energy entropy based on S Transform and Generalized S Transform. We have used three feature selection algorithms, including sequence forward selection (SFS), sequence forward floating selection (SFFS) and RELIEF-F to select the optimal feature subset from 16 entropy features. We use five classifiers, including k-nearest neighbor (KNN), support vector machine (SVM), Adaboost, Gradient Boosting Decision Tree (GBDT) and eXtreme Gradient Boosting (XGBoost) to classify the original feature set and the feature subsets selected by different feature selection algorithms. The simulation results show that the feature subsets selected by SFS and SFFS algorithms are the best, with a 48% increase in recognition rate over the original feature set when using KNN classifier and a 34% increase when using SVM classifier. For the other three classifiers, the original feature set can achieve the best recognition performance. The XGBoost classifier has the best recognition performance, the overall recognition rate is 97.74% and the recognition rate can reach 82% when the signal to noise ratio (SNR) is -10 dB. [ABSTRACT FROM AUTHOR]

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy ( S H p ) and a new approach based on Tsallis Spectral Permutation Entropy ( S q s ). Notably, our observations reveal the segregation of reaction terms in this S H p × S q s space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns. [ABSTRACT FROM AUTHOR]

Face detection is the first step of any automated face recognition system. One of the most popular approaches to detect faces in color images is using a skin color segmentation scheme, which in many cases needs a proper representation of color spaces to interpret image information. In this paper, we propose a fuzzy system for detecting skin in color images, so that each color tone is assumed to be a fuzzy set. The Red, Green, and Blue (RGB), the Hue, Saturation and Value (HSV), and the YCbCr (where Y is the luminance and Cb,Cr are the chroma components) color systems are used for the development of our fuzzy design. Thus, a fuzzy three-partition entropy approach is used to calculate all of the parameters needed for the fuzzy systems, and then, a face detection method is also developed to validate the segmentation results. The results of the experiments show a correct skin detection rate between 94% and 96% for our fuzzy segmentation methods, with a false positive rate of about 0.5% in all cases. Furthermore, the average correct face detection rate is above 93%, and even when working with heterogeneous backgrounds and different light conditions, it achieves almost 88% correct detections. Thus, our method leads to accurate face detection results with low false positive and false negative rates. [ABSTRACT FROM AUTHOR]

We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the resulting weight-adjusted empirical distribution. In this article, we substantially enhance the flexibility of such a methodology by introducing a nonparametrically imbued distributional constraint on the weights and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight-adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric, while allowing for subtle departures. The proposed scheme for the re-weighting of observations subject to constraints is reminiscent of the empirical likelihood and related ideas, but offers greater flexibility in applications where parametric distribution-guided constraints arise naturally. The versatility of the proposed framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task—namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms. [ABSTRACT FROM AUTHOR]

We have formulated a family of machine learning problems as the time evolution of parametric probabilistic models (PPMs), inherently rendering a thermodynamic process. Our primary motivation is to leverage the rich toolbox of thermodynamics of information to assess the information-theoretic content of learning a probabilistic model. We first introduce two information-theoretic metrics, memorized information (M-info) and learned information (L-info), which trace the flow of information during the learning process of PPMs. Then, we demonstrate that the accumulation of L-info during the learning process is associated with entropy production, and the parameters serve as a heat reservoir in this process, capturing learned information in the form of M-info. [ABSTRACT FROM AUTHOR]

Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relationships between multivariate entropy (joint or total marginal) and traditional measures of multivariate variability, such as total dispersion and generalized variance, are investigated. It is shown that for the jointly Gaussian case, the joint entropy (or entropy power) is equivalent to the generalized variance, while total marginal entropy is equivalent to the geometric mean of the marginal variances and total marginal entropy power is equivalent to the total dispersion. The smoothed multivariate entropy (joint or total marginal) and the kernel density estimation (KDE)-based entropy estimator (with finite samples) are also studied, which, under certain conditions, will be approximately equivalent to the total dispersion (or a total dispersion estimator), regardless of the data distribution. [ABSTRACT FROM AUTHOR]

Network security requires real-time monitoring of network traffic in order to detect new and unexpected attacks. Attack detection methods based on deep packet inspection are time consuming and costly, due to their high computational demands. This paper proposes a fast, lightweight method to distinguish different attack types observed in an IP darkspace monitor. The method is based on entropy measures of traffic-flow features and machine learning techniques. The explored data belongs to a portion of the Internet background radiation from a large IP darkspace, i.e., real traffic captures that exclusively contain unsolicited traffic, ongoing attacks, attack preparation activities and attack aftermaths. Results from an in-depth traffic analysis based on packet headers and content are used as a reference to label data and to evaluate the quality of the entropy-based classification. Full IP darkspace traffic captures from a three-week observation period in April, 2012, are used to compare the entropy-based classification with the in-depth traffic analysis. Results show that several traffic types present a high correlation to the respective traffic-flow entropy signals and can even fit polynomial regression models. Therefore, sudden changes in traffic types caused by new attacks or attack preparation activities can be identified based on entropy variations. [ABSTRACT FROM AUTHOR]

Measurement is a typical way of gathering information about an investigated object, generalized by a finite set of characteristic parameters. The result of each iteration of the measurement is an instance of the class of the investigated object in the form of a set of values of characteristic parameters. An ordered set of instances forms a collection whose dimensionality for a real object is a factor that cannot be ignored. Managing the dimensionality of data collections, as well as classification, regression, and clustering, are fundamental problems for machine learning. Compactification is the approximation of the original data collection by an equivalent collection (with a reduced dimension of characteristic parameters) with the control of accompanying information capacity losses. Related to compactification is the data completeness verifying procedure, which is characteristic of the data reliability assessment. If there are stochastic parameters among the initial data collection characteristic parameters, the compactification procedure becomes more complicated. To take this into account, this study proposes a model of a structured collection of stochastic data defined in terms of relative entropy. The compactification of such a data model is formalized by an iterative procedure aimed at maximizing the relative entropy of sequential implementation of direct and reverse projections of data collections, taking into account the estimates of the probability distribution densities of their attributes. The procedure for approximating the relative entropy function of compactification to reduce the computational complexity of the latter is proposed. To qualitatively assess compactification this study undertakes a formal analysis that uses data collection information capacity and the absolute and relative share of information losses due to compaction as its metrics. Taking into account the semantic connection of compactification and completeness, the proposed metric is also relevant for the task of assessing data reliability. Testing the proposed compactification procedure proved both its stability and efficiency in comparison with previously used analogues, such as the principal component analysis method and the random projection method. [ABSTRACT FROM AUTHOR]

The distance that compares the difference between two probability distributions plays a fundamental role in statistics and machine learning. Optimal transport (OT) theory provides a theoretical framework to study such distances. Recent advances in OT theory include a generalization of classical OT with an extra entropic constraint or regularization, called entropic OT. Despite its convenience in computation, entropic OT still lacks sufficient theoretical support. In this paper, we show that the quadratic cost in entropic OT can be upper-bounded using entropy power inequality (EPI)-type bounds. First, we prove an HWI-type inequality by making use of the infinitesimal displacement convexity of the OT map. Second, we derive two Talagrand-type inequalities using the saturation of EPI that corresponds to a numerical term in our expressions. These two new inequalities are shown to generalize two previous results obtained by Bolley et al. and Bai et al. Using the new Talagrand-type inequalities, we also show that the geometry observed by Sinkhorn distance is smoothed in the sense of measure concentration. Finally, we corroborate our results with various simulation studies. [ABSTRACT FROM AUTHOR]

A novelty signal processing method is proposed for a technical vision system (TVS). During data acquisition of an optoelectrical signal, part of this is random electrical fluctuation of voltages. Information theory (IT) is a well-known field that deals with random processes. A method based on using of the Shannon Entropy for feature extractions of optical patterns is presented. IT is implemented in structural health monitoring (SHM) to augment the accuracy of optoelectronic signal classifiers for a metrology subsystem of the TVS. To enhance the TVS spatial coordinate measurement performance at real operation conditions with electrical and optical noisy environments to estimate structural displacement better and evaluate its health for a better estimation of structural displacement and the evaluation of its health. Five different machine learning (ML) techniques are used in this work to classify optical patterns captured with the TVS. Linear predictive coding (LPC) and Autocorrelation function (ACC) are for extraction of optical patterns. The Shannon entropy segmentation (SH) method extracts relevant information from optical patterns, and the model's performance can be improved. The results reveal that segmentation with Shannon's entropy can achieve over 95.33%. Without Shannon's entropy, the worst accuracy was 33.33%. [ABSTRACT FROM AUTHOR]

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels' semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes' formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning. [ABSTRACT FROM AUTHOR]

In spite of great progress in recent years, deep learning (DNN) and transformers have strong limitations for supporting human–machine teams due to a lack of explainability, information on what exactly was generalized, and machinery to be integrated with various reasoning techniques, and weak defense against possible adversarial attacks of opponent team members. Due to these shortcomings, stand-alone DNNs have limited support for human–machine teams. We propose a Meta-learning/DNN → kNN architecture that overcomes these limitations by integrating deep learning with explainable nearest neighbor learning (kNN) to form the object level, having a deductive reasoning-based meta-level control learning process, and performing validation and correction of predictions in a way that is more interpretable by peer team members. We address our proposal from structural and maximum entropy production perspectives. [ABSTRACT FROM AUTHOR]

The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting. [ABSTRACT FROM AUTHOR]

Software aging is a phenomenon referring to the performance degradation of a long-running software system. This phenomenon is an accumulative process during execution, which will gradually lead the system from a normal state to a failure-prone state. It is a crucial challenge for system reliability to predict the Aging-Related Failures (ARFs) accurately. In this paper, permutation entropy (PE) is modified to Multidimensional Multi-scale Permutation Entropy (MMPE) as a novel aging indicator to detect performance anomalies, since MMPE is sensitive to dynamic state changes. An experiment is set on the distributed database system Voldemort, and MMPE is calculated based on the collected performance metrics during execution. Finally, based on MMPE, a failure prediction model using the machine learning method to reveal the anomalies is presented, which can predict failures with high accuracy. [ABSTRACT FROM AUTHOR]

Contextual bandits can solve a huge range of real-world problems. However, current popular algorithms to solve them either rely on linear models or unreliable uncertainty estimation in non-linear models, which are required to deal with the exploration–exploitation trade-off. Inspired by theories of human cognition, we introduce novel techniques that use maximum entropy exploration, relying on neural networks to find optimal policies in settings with both continuous and discrete action spaces. We present two classes of models, one with neural networks as reward estimators, and the other with energy based models, which model the probability of obtaining an optimal reward given an action. We evaluate the performance of these models in static and dynamic contextual bandit simulation environments. We show that both techniques outperform standard baseline algorithms, such as NN HMC, NN Discrete, Upper Confidence Bound, and Thompson Sampling, where energy based models have the best overall performance. This provides practitioners with new techniques that perform well in static and dynamic settings, and are particularly well suited to non-linear scenarios with continuous action spaces. [ABSTRACT FROM AUTHOR]

A restricted Boltzmann machine is a generative probabilistic graphic network. A probability of finding the network in a certain configuration is given by the Boltzmann distribution. Given training data, its learning is done by optimizing the parameters of the energy function of the network. In this paper, we analyze the training process of the restricted Boltzmann machine in the context of statistical physics. As an illustration, for small size bar-and-stripe patterns, we calculate thermodynamic quantities such as entropy, free energy, and internal energy as a function of the training epoch. We demonstrate the growth of the correlation between the visible and hidden layers via the subadditivity of entropies as the training proceeds. Using the Monte-Carlo simulation of trajectories of the visible and hidden vectors in the configuration space, we also calculate the distribution of the work done on the restricted Boltzmann machine by switching the parameters of the energy function. We discuss the Jarzynski equality which connects the path average of the exponential function of the work and the difference in free energies before and after training. [ABSTRACT FROM AUTHOR]

In this paper, we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated with Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle. [ABSTRACT FROM AUTHOR]

Recently, the concept of evaluating an unusually large learning effort of an adaptive system to detect novelties in the observed data was introduced. The present paper introduces a new measure of the learning effort of an adaptive system. The proposed method also uses adaptable parameters. Instead of a multi-scale enhanced approach, the generalized Pareto distribution is employed to estimate the probability of unusual updates, as well as for detecting novelties. This measure was successfully tested in various scenarios with (i) synthetic data, (ii) real time series datasets, and multiple adaptive filters and learning algorithms. The results of these experiments are presented. [ABSTRACT FROM AUTHOR]

Malaria is a severe public health problem worldwide, with some developing countries being most affected. Reliable remote diagnosis of malaria infection will benefit from efficient compression of high-resolution microscopic images. This paper addresses a lossless compression of malaria-infected red blood cell images using deep learning. Specifically, we investigate a practical approach where images are first classified before being compressed using stacked autoencoders. We provide probabilistic analysis on the impact of misclassification rates on compression performance in terms of the information-theoretic measure of entropy. We then use malaria infection image datasets to evaluate the relations between misclassification rates and actually obtainable compressed bit rates using Golomb–Rice codes. Simulation results show that the joint pattern classification/compression method provides more efficient compression than several mainstream lossless compression techniques, such as JPEG2000, JPEG-LS, CALIC, and WebP, by exploiting common features extracted by deep learning on large datasets. This study provides new insight into the interplay between classification accuracy and compression bitrates. The proposed compression method can find useful telemedicine applications where efficient storage and rapid transfer of large image datasets is desirable. [ABSTRACT FROM AUTHOR]

Recently, active learning is considered a promising approach for data acquisition due to the significant cost of the data labeling process in many real world applications, such as natural language processing and image processing. Most active learning methods are merely designed to enhance the learning model accuracy. However, the model accuracy may not be the primary goal and there could be other domain-specific objectives to be optimized. In this work, we develop a novel active learning framework that aims to solve a general class of optimization problems. The proposed framework mainly targets the optimization problems exposed to the exploration-exploitation trade-off. The active learning framework is comprehensive, it includes exploration-based, exploitation-based and balancing strategies that seek to achieve the balance between exploration and exploitation. The paper mainly considers regression tasks, as they are under-researched in the active learning field compared to classification tasks. Furthermore, in this work, we investigate the different active querying approaches—pool-based and the query synthesis—and compare them. We apply the proposed framework to the problem of learning the price-demand function, an application that is important in optimal product pricing and dynamic (or time-varying) pricing. In our experiments, we provide a comparative study including the proposed framework strategies and some other baselines. The accomplished results demonstrate a significant performance for the proposed methods. [ABSTRACT FROM AUTHOR]

The paper suggests a randomized model for dynamic migratory interaction of regional systems. The locally stationary states of migration flows in the basic and immigration systems are described by corresponding entropy operators. A soft randomization procedure that defines the optimal probability density functions of system parameters and measurement noises is developed. The advantages of soft randomization with approximate empirical data balance conditions are demonstrated, which considerably reduces algorithmic complexity and computational resources demand. An example of migratory interaction modeling and testing is given. [ABSTRACT FROM AUTHOR]

Uncertainty evaluation based on statistical probabilistic information entropy is a commonly used mechanism for a heuristic method construction of decision tree learning. The entropy kernel potentially links its deviation and decision tree classification performance. This paper presents a decision tree learning algorithm based on constrained gain and depth induction optimization. Firstly, the calculation and analysis of single- and multi-value event uncertainty distributions of information entropy is followed by an enhanced property of single-value event entropy kernel and multi-value event entropy peaks as well as a reciprocal relationship between peak location and the number of possible events. Secondly, this study proposed an estimated method for information entropy whose entropy kernel is replaced with a peak-shift sine function to establish a decision tree learning (CGDT) algorithm on the basis of constraint gain. Finally, by combining branch convergence and fan-out indices under an inductive depth of a decision tree, we built a constraint gained and depth inductive improved decision tree (CGDIDT) learning algorithm. Results show the benefits of the CGDT and CGDIDT algorithms. [ABSTRACT FROM AUTHOR]

The fault diagnosis classification method based on wavelet decomposition and weighted permutation entropy (WPE) by the extreme learning machine (ELM) is proposed to address the complexity and non-smoothness of rolling bearing vibration signals. The wavelet decomposition based on 'db3' is used to decompose the signal into four layers and extract the approximate and detailed components, respectively. Then, the WPE values of the approximate (CA) and detailed (CD) components of each layer are calculated and composed to be the feature vectors, which are finally fed into the extreme learning machine with optimal parameters for classification. The comparative study of the simulations based on WPE and permutation entropy (PE) shows that the classification method of seven kinds of signals of normal bearing signals and six types of fault states (7 mils and 14 mils) based on WPE (CA, CD) with the number of nodes in the hidden layers of ELM determined by the five-fold cross-validation has the best performances, the training accuracy can reach 100%, and the testing accuracy can reach 98.57% with 37 nodes of the hidden layer by ELM. The proposed method using WPE (CA, CD) by ELM provides guidance for the multi-classification of normal bearing signals. [ABSTRACT FROM AUTHOR]

In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of analyzing large amounts of data has been explored, such as machine learning (ML) algorithms. ML algorithms are being used to analyze and classify biological sequences, despite the intrinsic difficulty in extracting and finding representative biological sequence methods suitable for them. Thereby, extracting numerical features to represent sequences makes it statistically feasible to use universal concepts from Information Theory, such as Tsallis and Shannon entropy. In this study, we propose a novel Tsallis entropy-based feature extractor to provide useful information to classify biological sequences. To assess its relevance, we prepared five case studies: (1) an analysis of the entropic index q; (2) performance testing of the best entropic indices on new datasets; (3) a comparison made with Shannon entropy and (4) generalized entropies; (5) an investigation of the Tsallis entropy in the context of dimensionality reduction. As a result, our proposal proved to be effective, being superior to Shannon entropy and robust in terms of generalization, and also potentially representative for collecting information in fewer dimensions compared with methods such as Singular Value Decomposition and Uniform Manifold Approximation and Projection. [ABSTRACT FROM AUTHOR]

Despite the increasing applications, demands, and capabilities of drones, in practice they have only limited autonomy for accomplishing complex missions, resulting in slow and vulnerable operations and difficulty adapting to dynamic environments. To lessen these weaknesses, we present a computational framework for deducing the original intent of drone swarms by monitoring their movements. We focus on interference, a phenomenon that is not initially anticipated by drones but results in complicated operations due to its significant impact on performance and its challenging nature. We infer interference from predictability by first applying various machine learning methods, including deep learning, and then computing entropy to compare against interference. Our computational framework begins by building a set of computational models called double transition models from the drone movements and revealing reward distributions using inverse reinforcement learning. These reward distributions are then used to compute the entropy and interference across a variety of drone scenarios specified by combining multiple combat strategies and command styles. Our analysis confirmed that drone scenarios experienced more interference, higher performance, and higher entropy as they became more heterogeneous. However, the direction of interference (positive vs. negative) was more dependent on combinations of combat strategies and command styles than homogeneity. [ABSTRACT FROM AUTHOR]

Psychogenic non-epileptic seizures (PNES) may resemble epileptic seizures but are not caused by epileptic activity. However, the analysis of electroencephalogram (EEG) signals with entropy algorithms could help identify patterns that differentiate PNES and epilepsy. Furthermore, the use of machine learning could reduce the current diagnosis costs by automating classification. The current study extracted the approximate sample, spectral, singular value decomposition, and Renyi entropies from interictal EEGs and electrocardiograms (ECG)s of 48 PNES and 29 epilepsy subjects in the broad, delta, theta, alpha, beta, and gamma frequency bands. Each feature-band pair was classified by a support vector machine (SVM), k-nearest neighbour (kNN), random forest (RF), and gradient boosting machine (GBM). In most cases, the broad band returned higher accuracy, gamma returned the lowest, and combining the six bands together improved classifier performance. The Renyi entropy was the best feature and returned high accuracy in every band. The highest balanced accuracy, 95.03%, was obtained by the kNN with Renyi entropy and combining all bands except broad. This analysis showed that entropy measures can differentiate between interictal PNES and epilepsy with high accuracy, and improved performances indicate that combining bands is an effective improvement for diagnosing PNES from EEGs and ECGs. [ABSTRACT FROM AUTHOR]

This study examined the association between pressure injuries and complexity of abdominal temperature measured in residents of a nursing facility. The temperature served as a proxy measure for skin thermoregulation. Refined multiscale sample entropy and bubble entropy were used to measure the irregularity of the temperature time series measured over two days at 1-min intervals. Robust summary measures were derived for the multiscale entropies and used in predictive models for pressure injuries that were built with adaptive lasso regression and neural networks. Both types of entropies were lower in the group of participants with pressure injuries ( n = 11 ) relative to the group of non-injured participants ( n = 15 ). This was generally true at the longer temporal scales, with the effect peaking at scale τ = 22 min for sample entropy and τ = 23 min for bubble entropy. Predictive models for pressure injury on the basis of refined multiscale sample entropy and bubble entropy yielded 96% accuracy, outperforming predictions based on any single measure of entropy. Combining entropy measures with a widely used risk assessment score led to the best prediction accuracy. Complexity of the abdominal temperature series could therefore serve as an indicator of risk of pressure injury. [ABSTRACT FROM AUTHOR]

Purpose: In this work, we propose an implementation of the Bienenstock–Cooper–Munro (BCM) model, obtained by a combination of the classical framework and modern deep learning methodologies. The BCM model remains one of the most promising approaches to modeling the synaptic plasticity of neurons, but its application has remained mainly confined to neuroscience simulations and few applications in data science. Methods: To improve the convergence efficiency of the BCM model, we combine the original plasticity rule with the optimization tools of modern deep learning. By numerical simulation on standard benchmark datasets, we prove the efficiency of the BCM model in learning, memorization capacity, and feature extraction. Results: In all the numerical simulations, the visualization of neuronal synaptic weights confirms the memorization of human-interpretable subsets of patterns. We numerically prove that the selectivity obtained by BCM neurons is indicative of an internal feature extraction procedure, useful for patterns clustering and classification. The introduction of competitiveness between neurons in the same BCM network allows the network to modulate the memorization capacity of the model and the consequent model selectivity. Conclusions: The proposed improvements make the BCM model a suitable alternative to standard machine learning techniques for both feature selection and classification tasks. [ABSTRACT FROM AUTHOR]

Among neural disorders related to movement, essential tremor has the highest prevalence; in fact, it is twenty times more common than Parkinson’s disease. The drawing of the Archimedes’ spiral is the gold standard test to distinguish between both pathologies. The aim of this paper is to select non-linear biomarkers based on the analysis of digital drawings. It belongs to a larger cross study for early diagnosis of essential tremor that also includes genetic information. The proposed automatic analysis system consists in a hybrid solution: Machine Learning paradigms and automatic selection of features based on statistical tests using medical criteria. Moreover, the selected biomarkers comprise not only commonly used linear features (static and dynamic), but also other non-linear ones: Shannon entropy and Fractal Dimension. The results are hopeful, and the developed tool can easily be adapted to users; and taking into account social and economic points of view, it could be very helpful in real complex environments. [ABSTRACT FROM AUTHOR]

Artificial neural networks are currently one of the most commonly used classifiers and over the recent years they have been successfully used in many practical applications, including banking and finance, health and medicine, engineering and manufacturing. A large number of error functions have been proposed in the literature to achieve a better predictive power. However, only a few works employ Tsallis statistics, although the method itself has been successfully applied in other machine learning techniques. This paper undertakes the effort to examine the q -generalized function based on Tsallis statistics as an alternative error measure in neural networks. In order to validate different performance aspects of the proposed function and to enable identification of its strengths and weaknesses the extensive simulation was prepared based on the artificial benchmarking dataset. The results indicate that Tsallis entropy error function can be successfully introduced in the neural networks yielding satisfactory results and handling with class imbalance, noise in data or use of non-informative predictors. [ABSTRACT FROM AUTHOR]

Recently, Multi-Graph Learning was proposed as the extension of Multi-Instance Learning and has achieved some successes. However, to the best of our knowledge, currently, there is no study working on Multi-Graph Multi-Label Learning, where each object is represented as a bag containing a number of graphs and each bag is marked with multiple class labels. It is an interesting problem existing in many applications, such as image classification, medicinal analysis and so on. In this paper, we propose an innovate algorithm to address the problem. Firstly, it uses more precise structures, multiple Graphs, instead of Instances to represent an image so that the classification accuracy could be improved. Then, it uses multiple labels as the output to eliminate the semantic ambiguity of the image. Furthermore, it calculates the entropy to mine the informative subgraphs instead of just mining the frequent subgraphs, which enables selecting the more accurate features for the classification. Lastly, since the current algorithms cannot directly deal with graph-structures, we degenerate the Multi-Graph Multi-Label Learning into the Multi-Instance Multi-Label Learning in order to solve it by MIML-ELM (Improving Multi-Instance Multi-Label Learning by Extreme Learning Machine). The performance study shows that our algorithm outperforms the competitors in terms of both effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

We present a coupled variational autoencoder (VAE) method, which improves the accuracy and robustness of the model representation of handwritten numeral images. The improvement is measured in both increasing the likelihood of the reconstructed images and in reducing divergence between the posterior and a prior latent distribution. The new method weighs outlier samples with a higher penalty by generalizing the original evidence lower bound function using a coupled entropy function based on the principles of nonlinear statistical coupling. We evaluated the performance of the coupled VAE model using the Modified National Institute of Standards and Technology (MNIST) dataset and its corrupted modification C-MNIST. Histograms of the likelihood that the reconstruction matches the original image show that the coupled VAE improves the reconstruction and this improvement is more substantial when seeded with corrupted images. All five corruptions evaluated showed improvement. For instance, with the Gaussian corruption seed the accuracy improves by 10 14 (from 10 − 57.2 to 10 − 42.9 ) and robustness improves by 10 22 (from 10 − 109.2 to 10 − 87.0 ). Furthermore, the divergence between the posterior and prior distribution of the latent distribution is reduced. Thus, in contrast to the β -VAE design, the coupled VAE algorithm improves model representation, rather than trading off the performance of the reconstruction and latent distribution divergence. [ABSTRACT FROM AUTHOR]

Over the past two decades, the Bootstrap AGGregatING (bagging) method has been widely used for improving simulation. The computational cost of this method scales with the size of the ensemble, but excessively reducing the ensemble size comes at the cost of reduced predictive performance. The novel procedure proposed in this study is the Entropy Ensemble Filter (EEF), which uses the most informative training data sets in the ensemble rather than all ensemble members created by the bagging method. The results of this study indicate efficiency of the proposed method in application to synthetic data simulation on a sinusoidal signal, a sawtooth signal, and a composite signal. The EEF method can reduce the computational time of simulation by around 50% on average while maintaining predictive performance at the same level of the conventional method, where all of the ensemble models are used for simulation. The analysis of the error gradient (root mean square error of ensemble averages) shows that using the 40% most informative ensemble members of the set initially defined by the user appears to be most effective. [ABSTRACT FROM AUTHOR]

Data mining is an interdisciplinary subfield of computer science involving methods at the intersection of artificial intelligence, machine learning and statistics. One of the data mining tasks is anomaly detection which is the analysis of large quantities of data to identify items, events or observations which do not conform to an expected pattern. Anomaly detection is applicable in a variety of domains, e.g., fraud detection, fault detection, system health monitoring but this article focuses on application of anomaly detection in the field of network intrusion detection. The main goal of the article is to prove that an entropy-based approach is suitable to detect modern botnet-like malware based on anomalous patterns in network. This aim is achieved by realization of the following points: (i) preparation of a concept of original entropy-based network anomaly detection method, (ii) implementation of the method, (iii) preparation of original dataset, (iv) evaluation of the method. [ABSTRACT FROM AUTHOR]