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With the rapid development of computer technology, communication technology, and control technology, cyber-physical systems (CPSs) have been widely used and developed. However, there are massive information interactions in CPSs, which lead to an increase in the amount of data transmitted over the network. The data communication, once attacked by the network, will seriously affect the security and stability of the system. In this paper, for the data tampering attack existing in the linear system with multiple binary observations, in the case where the estimation algorithm of the defender is unknown, the optimization index is constructed based on information entropy from the attacker's point of view, and the problem is modeled. For the problem of the multi-parameter optimization with energy constraints, this paper uses particle swarm optimization (PSO) to obtain the optimal data tampering attack solution set, and gives the estimation method of unknown parameters in the case of unknown parameters. To implement the real-time improvement of online implementation, the BP neural network is designed. Finally, the validity of the conclusions is verified through numerical simulation. This means that the attacker can construct effective metrics based on information entropy without the knowledge of the defense's discrimination algorithm. In addition, the optimal attack strategy implementation based on PSO and BP is also effective. [ABSTRACT FROM AUTHOR]

We feature papers on recent developments in the areas of adaptive signal processing, machine learning, and deep learning using information theory and entropy to improve performance in widespread and popular problems, and also to provide effective solutions to emerging problems. Our goal is to publish recent developments in the areas of adaptive signal processing, machine learning, and deep learning using information theory and entropy to improve performance in widespread and popular problems, and also to provide effective solutions to emerging problems. This Special Issue on "Adaptive Signal Processing and Machine Learning Using Entropy and Information Theory" was birthed from observations of the recent trend in the literature. Entropy-based cost functions have replaced mean-square-error (MSE)-based ones and 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 conditions. [Extracted from the article]

The common channel attention mechanism maps feature statistics to feature weights. However, the effectiveness of this mechanism may not be assured in remotely sensing images due to statistical differences across multiple bands. This paper proposes a novel channel attention mechanism based on feature information called the feature information entropy attention mechanism (FEM). The FEM constructs a relationship between features based on feature information entropy and then maps this relationship to their importance. The Vaihingen dataset and OpenEarthMap dataset are selected for experiments. The proposed method was compared with the squeeze-and-excitation mechanism (SEM), the convolutional block attention mechanism (CBAM), and the frequency channel attention mechanism (FCA). Compared with these three channel attention mechanisms, the mIoU of the FEM in the Vaihingen dataset is improved by 0.90%, 1.10%, and 0.40%, and in the OpenEarthMap dataset, it is improved by 2.30%, 2.20%, and 2.10%, respectively. The proposed channel attention mechanism in this paper shows better performance in remote sensing land use classification. [ABSTRACT FROM AUTHOR]

Medical image diagnosis using deep learning has shown significant promise in clinical medicine. However, it often encounters two major difficulties in real-world applications: (1) domain shift, which invalidates the trained model on new datasets, and (2) class imbalance problems leading to model biases towards majority classes. To address these challenges, this paper proposes a transfer learning solution, named Dynamic Weighting Translation Transfer Learning (DTTL), for imbalanced medical image classification. The approach is grounded in information and entropy theory and comprises three modules: Cross-domain Discriminability Adaptation (CDA), Dynamic Domain Translation (DDT), and Balanced Target Learning (BTL). CDA connects discriminative feature learning between source and target domains using a synthetic discriminability loss and a domain-invariant feature learning loss. The DDT unit develops a dynamic translation process for imbalanced classes between two domains, utilizing a confidence-based selection approach to select the most useful synthesized images to create a pseudo-labeled balanced target domain. Finally, the BTL unit performs supervised learning on the reassembled target set to obtain the final diagnostic model. This paper delves into maximizing the entropy of class distributions, while simultaneously minimizing the cross-entropy between the source and target domains to reduce domain discrepancies. By incorporating entropy concepts into our framework, our method not only significantly enhances medical image classification in practical settings but also innovates the application of entropy and information theory within deep learning and medical image processing realms. Extensive experiments demonstrate that DTTL achieves the best performance compared to existing state-of-the-art methods for imbalanced medical image classification tasks. [ABSTRACT FROM AUTHOR]

Underwriters play a pivotal role in the IPO process. Information entropy, a tool for measuring the uncertainty and complexity of information, has been widely applied to various issues in complex networks. Information entropy can quantify the uncertainty and complexity of nodes in the network, providing a unique analytical perspective and methodological support for this study. This paper employs a bipartite network analysis method to construct the relationship network between underwriters and accounting firms, using the centrality of underwriters in the network as a measure of their influence to explore the impact of underwriters' influence on the distribution of interests and audit outcomes. The findings indicate that a more pronounced influence of underwriters significantly increases the ratio of underwriting fees to audit fees. Higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals that companies underwritten by more influential underwriters experience a decline in audit quality. Finally, the study reveals that a well-structured audit committee governance and the rationalization of market sentiments can mitigate the negative impacts of underwriters' influence. The innovation of this paper is that it enriches the content related to underwriters by constructing the relationship network between underwriters and accounting firms for the first time using a bipartite network through the lens of information entropy. This conclusion provides new directions for thinking about the motives and possibilities behind financial institutions' cooperation, offering insights for market regulation and policy formulation. [ABSTRACT FROM AUTHOR]

Traffic state classification and relevance calculation at intersections are both difficult problems in traffic control. In this paper, we propose an intersection relevance model based on a temporal graph attention network, which can solve the above two problems at the same time. First, the intersection features and interaction time of the intersections are regarded as input quantities together with the initial labels of the traffic data. Then, they are inputted into the temporal graph attention (TGAT) model to obtain the classification accuracy of the target intersections in four states—free, stable, slow moving, and congested—and the obtained neighbouring intersection weights are used as the correlation between the intersections. Finally, it is validated by VISSIM simulation experiments. In terms of classification accuracy, the TGAT model has a higher classification accuracy than the three traditional classification models and can cope well with the uneven distribution of the number of samples. The information gain algorithm from the information entropy theory was used to derive the average delay as the most influential factor on intersection status. The correlation from the TGAT model positively correlates with traffic flow, making it interpretable. Using this correlation to control the division of subareas improves the road network's operational efficiency more than the traditional correlation model does. This demonstrates the effectiveness of the TGAT model's correlation. [ABSTRACT FROM AUTHOR]

Microwave hyperspectral instruments represent one of the main atmospheric sounders of China's next-generation Fengyun meteorological satellites. In order to better apply microwave hyperspectral observations in the fields of atmospheric parameter retrieval and data assimilation, this paper analyzes the sensitivity of trace gases to five selected bandwidth channels using a radiative transfer model based on the simulated data of microwave hyperspectral radiances at 50–60 GHz. This method uses information entropy and a weighting function to select channels and analyze the impact of this on the retrieval accuracy of atmospheric profiles before and after channel selection. The experimental results show that channel selection can reduce the number of channels by approximately 74.05% while maintaining a large amount of information content, and this retrieval effect is significantly better than that of MWTS-III. After channel selection, the 10 MHz, 30 MHz, and 50 MHz bandwidths have the best retrieval results in the stratosphere, whole atmosphere, and troposphere, respectively. When considering the number of channels, computational scale, and retrieval results comprehensively, the channel selection method is effective. [ABSTRACT FROM AUTHOR]

In this paper, a multi-point geostatistical (MPS) method based on variational function partition simulation is proposed to solve the key problem of MPS 3D modeling using 2D training images. The new method uses the FILTERSIM algorithm framework, and the variational function is used to construct simulation partitions and training image sequences, and only a small number of training images close to the unknown nodes are used in the partition simulation to participate in the MPS simulation. To enhance the reliability, a new covariance filter is also designed to capture the diverse features of the training patterns and allow the filter to downsize the training patterns from any direction; in addition, an information entropy method is used to reconstruct the whole 3D space by selecting the global optimal solution from several locally similar training patterns. The stability and applicability of the new method in complex geological modeling are demonstrated by analyzing the parameter sensitivity and algorithm performance. A geological model of a uranium deposit is simulated to test the pumping of five reserved drill holes, and the results show that the accuracy of the simulation results of the new method is improved by 11.36% compared with the traditional MPS method. [ABSTRACT FROM AUTHOR]

Bridge structures are susceptible to environmental and operational variations (EOVs). Improperly handling these influences may result in incorrect assessments of the bridge's health condition. Blind source separation (BSS) techniques show promising potential in suppressing the effects of EOVs. However, major challenges such as high data variability, difficulty in parameter selection, lack of reliable decision thresholds, and practical engineering validation have seriously hindered the application of such techniques in bridge health monitoring. Consequently, this paper proposes a new method for bridge damage detection that combines complexity pursuit (CP) and extreme value theory (EVT). This method first uses the exponentially weighted moving average (EWMA) technique to preprocess the measured modal frequencies. The CP algorithm and information entropy are then used to extract structural damage sources from the preprocessed data automatically. Based on the extracted structural damage sources, the damage index (DI) is defined using k-means clustering and Euclidean distance. Following that, the generalized extreme value (GEV) distribution is used to fit the DI data under the normal condition of the bridge, and the damage detection threshold is given according to the fitted distribution. Benchmark data of the KW51 railway bridge are considered to verify the effectiveness of the proposed method along with several comparative studies. The results show that even under strong EOV influences, the proposed method still maintains good damage detection accuracy and robustness, and its effectiveness is superior to some well-known damage detection methods. [ABSTRACT FROM AUTHOR]

To better meet communication needs, 6G proposes Integrated Satellite-Terrestrial Networks. Integrated Sensing and Communication (ISAC) is one of the key technologies of Integrated Satellite-Terrestrial Networks, which can reduce the energy consumption of the system, improve communication efficiency, and increase the utilization rate of spectrum resources. In the existing technology, the Modulated Wideband Converter (MWC) system can provide support for the miniaturization and intelligence of wireless device sensing and communication systems. Therefore, the MWC system can be used as a preliminary application of ISAC technology. However, the reconstruction effect of the conventional MWC system under the influence of noise is not stable. Therefore, we propose a signal processing optimization scheme for the MWC system based on spatial information entropy. First, the subsequent reconstruction algorithm is considered to require the dynamic and flexible processing of the sampled signals to reduce the influence of noise. Second, for the shortcomings of the original Orthogonal Matching Pursuit (OMP) algorithm, the concept of the genetic algorithm is used to optimize the algorithm by constructing the feature factor through spatial information gain and spatial information features. According to the simulation results, compared with the traditional MWC system, the scheme proposed in this paper is improved in all indicators. [ABSTRACT FROM AUTHOR]

To improve the performance of roller bearing fault diagnosis, this paper proposes an algorithm based on subtraction average-based optimizer (SABO), variational mode decomposition (VMD), and weighted Manhattan-K nearest neighbor (WMH–KNN). Initially, the SABO algorithm uses a composite objective function, including permutation entropy and mutual information entropy, to optimize the input parameters of VMD. Subsequently, the optimized VMD is used to decompose the signal to obtain the optimal decomposition characteristics and the corresponding intrinsic mode function (IMF). Finally, the weighted Manhattan function (WMH) is used to enhance the classification distance of the KNN algorithm, and WMH–KNN is used for fault diagnosis based on the optimized IMF features. The performance of the SABO–VMD and WMH–KNN models is verified through two experimental cases and compared with traditional methods. The results show that the accuracy of motor-bearing fault diagnosis is significantly improved, reaching 97.22% in Dataset 1, 98.33% in Dataset 2, and 99.2% in Dataset 3. Compared with traditional methods, the proposed method significantly reduces the false positive rate. [ABSTRACT FROM AUTHOR]

This paper highlights that metrics from the machine learning field (e.g., entropy and information gain) used to qualify a classifier model can be used to evaluate the effectiveness of separation systems. To evaluate the efficiency of separation systems and their operation units, entropy- and information gain-based metrics were developed. The receiver operating characteristic (ROC) curve is used to determine the optimal cut point in a separation system. The proposed metrics are verified by simulation experiments conducted on the stochastic model of a waste-sorting system. [ABSTRACT FROM AUTHOR]

Flower classification is of great significance to the fields of plants, food, and medicine. However, due to the inherent inter-class similarity and intra-class differences of flowers, it is a difficult task to accurately classify them. To this end, this paper proposes a novel flower classification method that combines enhanced VGG16 (E-VGG16) with decision fusion. Firstly, facing the shortcomings of the VGG16, an enhanced E-VGG16 is proposed. E-VGG16 introduces a parallel convolution block designed in this paper on VGG16 combined with several other optimizations to improve the quality of extracted features. Secondly, considering the limited decision-making ability of a single E-VGG16 variant, parallel convolutional blocks are embedded in different positions of E-VGG16 to obtain multiple E-VGG16 variants. By introducing information entropy to fuse multiple E-VGG16 variants for decision-making, the classification accuracy is further improved. The experimental results on the Oxford Flower102 and Oxford Flower17 public datasets show that the classification accuracy of our method reaches 97.69% and 98.38%, respectively, which significantly outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

During routine bridge maintenance, edge detection allows the partial condition of the bridge to be viewed. However, many edge detection methods often have unsatisfactory performances when dealing with images with complex backgrounds. Moreover, the processing often involves the manual selection of thresholds, which can result in repeated testing and comparisons. To address these problems in this paper, the wavelet transform modulus maxima method is used to detect the target image, and then the threshold value of the image can be determined automatically according to the OTSU method to remove the pseudo-edges. Thus, the real image edges can be detected. The results show that the information entropy and SSIM of the detection results are the highest when compared with the commonly used Canny and Laplace algorithms, which means that the detection quality is optimal. To more fully illustrate the advantages of the algorithms, images with more complex backgrounds were detected and the processing results of the algorithms in this paper are still optimal. In addition, the automatic selection of thresholds saves the operator's effort and improves the detection efficiency. Thanks to the combined use of the above two methods, detection quality and efficiency are significantly improved, which has a good application in engineering practice. [ABSTRACT FROM AUTHOR]

The quality of pipeline leakage fault feature extractions deteriorates due to the influence of fluid pipeline running state and signal acquisition equipment. The pressure signal is characterized by high complexity, nonlinear and strong correlation. Therefore, traditional denoising methods have difficulty dealing with this kind of signal. In order to realize accurate leakage fault alarm and leak location, a denoising method based on variational mode decomposition (VMD) technology is proposed in this paper. Firstly, the intrinsic mode functions are screened out using the correlation coefficient. Secondly, information entropy is used to optimize the VMD decomposition layers k. Finally, based on the denoising signal, the inflection point of the negative pressure wave is extracted, and the position of the leakage point is calculated according to the time difference between the two inflection points. To verify the effectiveness of the algorithm, both laboratory experiments and real pipeline tests are conducted. Experimental results show that the method proposed by this paper can be used to effectively denoise the pressure signal. Furthermore, from the perspective of positioning accuracy, compared other methods, the proposed method can achieve a better positioning effect, as the positioning accuracy of the laboratory experiment reaches up to 0.9%, and that of the real pipeline test leakage point reaches up to 0.41%. [ABSTRACT FROM AUTHOR]

This paper presents a multivariate textual analysis of more than 1300 papers on entropy in ecology. There are six main insights that emerged. First, there is a large body of literature that has addressed some aspect of entropy in ecology, most of which has been published in the last 5–10 years. Second, the vast majority of these papers focus on species distribution, species richness, relative abundance or trophic structure and not landscape-scale patterns or processes, pe se. Third, there have been few papers addressing landscape-level questions related to entropy. Fourth, the quantitative analysis with hierarchical clustering identified a strongly nested structure among papers that addressed entropy in ecology. Fifth, there is clear differentiation of papers focused on landscape-level applications of entropy from other papers, with landscape focused papers clustered together at each level of the hierarchy in a relatively small and closely associated group. Sixth, this group of landscape-focused papers was substructured between papers that explicitly adopted entropy measures to quantify the spatial pattern of landscape mosaics, often using variations on Boltzmann entropy, versus those that utilize Shannon entropy measures from information theory, which are not generally explicit in their assessment of spatial configuration. This review provides a comprehensive, quantitative assessment of the scope, trends and relationships among a large body of literature related to entropy in ecology and for the first time puts landscape ecological research on entropy into that context. [ABSTRACT FROM AUTHOR]

This article presents a statistical approach using entropy and classification-based analysis to detect anomalies in industrial control systems traffic. Several statistical techniques have been proposed to create baselines and measure deviation to detect intrusion in enterprise networks with a centralized intrusion detection approach in mind. Looking at traffic volume alone to find anomalous deviation may not be enough—it may result in increased false positives. The near real-time communication requirements, coupled with the lack of centralized infrastructure in operations technology and limited resources of the sensor motes, require an efficient anomaly detection system characterized by these limitations. This paper presents extended results from our previous work by presenting a detailed cluster-based entropy analysis on selected network traffic features. It further extends the analysis using a classification-based approach. Our detailed entropy analysis corroborates with our earlier findings that, although some degree of anomaly may be detected using univariate and bivariate entropy analysis for Denial of Service (DOS) and Man-in-the-Middle (MITM) attacks, not much information may be obtained for the initial reconnaissance, thus preventing early stages of attack detection in the Cyber Kill Chain. Our classification-based analysis shows that, overall, the classification results of the DOS attacks were much higher than the MITM attacks using two Modbus features in addition to the three TCP/IP features. In terms of classifiers, J48 and random forest had the best classification results and can be considered comparable. For the DOS attack, no resampling with the 60–40 (training/testing split) had the best results (average accuracy of 97.87%), but for the MITM attack, the 80–20 non-attack vs. attack data with the 75–25 split (average accuracy of 82.81%) had the best results. [ABSTRACT FROM AUTHOR]

This paper introduces the complex Rayleigh–van-der- Pol–Duffing oscillators (RVDOs), which are hyperchaotic and can be autonomous or nonautonomous. The fundamental dynamics of the autonomous and nonautonomous complex RVDOs, including dissipation, symmetry, fixed points, and stability, are studied. These oscillators are found in various necessary fields of physics and engineering. The paper proposes a scheme to achieve phase synchronization (PS) and antiphase synchronization (APS) for different dimensional models. These kinds of synchronization are considered a generalization of several other types of synchronization. We use the active control method based on Lyapunov's stability theory for this scheme. By analytically determining the control functions, the scheme achieved PS and APS. Our scheme is applied to study the PS of hyperchaotic behaviors for two distinct hyperchaotic nonautonomous and autonomous complex RVDOs. Additionally, the scheme is employed to achieve the APS of a chaotic real nonautonomous RVDO and a hyperchaotic complex autonomous RVDO, including those with different dimensions. Our work presents numerical results that plot the amplitudes and phases of these hyperchaotic behaviors, demonstrating the achievement of the PS and APS. The encryption and decryption of grayscale images are researched based on APS. The experimental results of image encryption and decryption are computed with information entropy, visual analysis, and histograms. [ABSTRACT FROM AUTHOR]

The reliability of the machining process is a vital indicator in the manufacturing process of mechanical parts, and directly related to the machining quality of mechanical products. In order to effectively utilize machining process information and machining quality inspection data to evaluate the reliability of the machining process, this paper extends the relevant concepts of information theory to the field of mechanical manufacturing error analysis and establishes a reliability analysis model of the machining process. The model introduces information entropy into the analysis of machining process reliability by defining vertex entropy to measure the uncertainty of the machining quality of each process, and thus realizing the determination of critical processes using a fully quantitative method. Meanwhile, the transfer coefficient defined by mutual information is used to measure the transfer of machining error between two processes. Through combining vertex entropy and the transfer coefficient, the quantitative analysis of machining process reliability is achieved. The model proposed in this paper addresses the issue that the subjective factors of researchers in other related studies have an impact on the analysis results. Finally, the correctness of the proposed model is verified using Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

With the development of image recovery models, especially those based on adversarial and perceptual losses, the detailed texture portions of images are being recovered more naturally. However, these restored images are similar but not identical in detail texture to their reference images. With traditional image quality assessment methods, results with better subjective perceived quality often score lower in objective scoring. Assessment methods suffer from subjective and objective inconsistencies. This paper proposes a regional differential information entropy (RDIE) method for image quality assessment to address this problem. This approach allows better assessment of similar but not identical textural details and achieves good agreement with perceived quality. Neural networks are used to reshape the process of calculating information entropy, improving the speed and efficiency of the operation. Experiments conducted with this study's image quality assessment dataset and the PIPAL dataset show that the proposed RDIE method yields a high degree of agreement with people's average opinion scores compared with other image quality assessment metrics, proving that RDIE can better quantify the perceived quality of images. [ABSTRACT FROM AUTHOR]

The pulse-coupled neural network (PCNN), due to its effectiveness in simulating the mammalian visual system to perceive and understand visual information, has been widely applied in the fields of image segmentation and image fusion. To address the issues of low contrast and the loss of detail information in infrared and visible light image fusion, this paper proposes a novel image fusion method based on an improved adaptive dual-channel PCNN model in the non-subsampled shearlet transform (NSST) domain. Firstly, NSST is used to decompose the infrared and visible light images into a series of high-pass sub-bands and a low-pass sub-band, respectively. Next, the PCNN models are stimulated using the weighted sum of the eight-neighborhood Laplacian of the high-pass sub-bands and the energy activity of the low-pass sub-band. The high-pass sub-bands are fused using local structural information as the basis for the linking strength for the PCNN, while the low-pass sub-band is fused using a linking strength based on multiscale morphological gradients. Finally, the fused high-pass and low-pass sub-bands are reconstructed to obtain the fused image. Comparative experiments demonstrate that, subjectively, this method effectively enhances the contrast of scenes and targets while preserving the detail information of the source images. Compared to the best mean values of the objective evaluation metrics of the compared methods, the proposed method shows improvements of 2.35%, 3.49%, and 11.60% in information entropy, mutual information, and standard deviation, respectively. [ABSTRACT FROM AUTHOR]

Most trajectory compression methods primarily focus on geometric similarity between compressed and original trajectories, lacking explainability of compression results due to ignoring semantic information. This paper proposes a spatio-temporal semantic constrained trajectory compression method. It constructs a new trajectory distance measurement model integrating both semantic and spatio-temporal features. This model quantifies semantic features using information entropy and measures spatio-temporal features with synchronous Euclidean distance. The compression principle is to retain feature points with maximum spatio-temporal semantic distance from the original trajectory until the compression rate is satisfied. Experimental results show these methods closely resemble each other in maintaining geometric similarity of trajectories, but our method significantly outperforms DP, TD-TR, and CascadeSync methods in preserving semantic similarity of trajectories. This indicates that our method considers both geometric and semantic features during compression, resulting in the compressed trajectory becoming more interpretable. [ABSTRACT FROM AUTHOR]

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences: notably, lifetime, medical, and financial sciences. This paper introduces a heavy-tailed Nadarajah Haghighi model by compounding the heavy-tailed family and Nadarajah Haghighi distribution. The model obtained has three parameters that account for the scale and shape of the distribution. The proposed distribution's fundamental characteristics, such as the probability density, cumulative distribution, hazard rate, and survival functions, are provided, several key statistical properties are established, and several entropy information measures are proposed. Estimation of model parameters is performed via a maximum likelihood estimator procedure. Further, different simulation experiments are conducted to demonstrate the proposed estimator's performance using measures like the average estimate, the average bias, and the associated mean square error. Finally, we apply our proposed model to analyze three different real datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing models. [ABSTRACT FROM AUTHOR]

The accurate identification of target imagery in the presence of sea fog is essential for the precise detection and comprehension of targets situated at sea. To overcome the issues encountered when applying traditional polarimetric dehazing methods to sea fog imagery, this paper proposes an improved polarimetric dehazing method. Initially, the methodology employs quartile-based selection on polarization difference images to ascertain atmospheric light at an infinite distance. Subsequently, the study describes a segmentation approach for sea–sky background images based on the degree of polarization. The results show that the image information entropy of the segmentation process improves by more than 6% compared to that of alternative methodologies, and the local contrast of the image is increased by more than 30% compared to that of the original foggy image. These outcomes confirm the effectiveness of the proposed dehazing methodology in addressing the challenges associated with sea fog imagery. [ABSTRACT FROM AUTHOR]

Top-coal structure detection is an important basis for realizing effective mining in fully mechanized cave faces. However, the top-coal structure is very complex and often contains multi-layer gangues, which seriously influence the level of effective mining. For these reasons, this paper proposes a novel multi-frequency ground-penetrating radar (GPR) data-fusing method through a joint sliding window and wavelet transform weighting method to accurately detect the top-coal structure. It possesses the advantages of both high resolution and great detection depth, and it can also integrate multi-frequency GPR data into one composite profile to interpret the internal structure information of top coal in detail. The detection procedure is implemented following several steps: First of all, the multi-frequency GPR data are preprocessed and aligned through a band-pass filter and a zero offset elimination method to establish their spatial correspondences. Secondly, the proposed method is used to determine the time-varying weight values of each frequency GPR signal according to the wavelet energy proportion within the sliding window; also, the edge detection algorithm is introduced to improve the fusion efficiency of the wavelet transform so as to realize the effective fusion of the multi-frequency GPR data. Thirdly, a reflection intensity model of multi-frequency GPR signals traveling in the top-coal is established by using the stratified identification method, and then, the detailed top-coal structure can be inversely interpreted. Finally, the quantitative evaluation criteria, information entropy (IE), space–frequency (SF) and Laplacian gradient (LG), are used to evaluate the multi-frequency GPR data fusion's effectiveness in laboratory and field environments. The experimental results show that, compared with the genetic, time-varying and wavelet transform fusion method, the fusion performance of the presented method possesses higher values in the IE, SF and LG evaluation criteria, and it also has both the merits of high resolution and great detection depth. [ABSTRACT FROM AUTHOR]

In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. The potential energy of a body is actually stored in the form of rest mass, the interaction energy too, but temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence, the "mass–energy–information equivalence principle" that has been recently proposed. In this paper, it is first recalled that for a thermodynamic system made of non-interacting entities at constant temperature, the internal energy is also constant. So, the energy involved in a variation in entropy ( T Δ S ) differs from a change in the potential energy stored or released and cannot be associated to a corresponding variation in mass of the system, even if it is expressed in terms of the quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state-dependent property) and thermodynamical irreversibility (a path-dependent property), and to return to the nature of the link between energy and information that is dynamical. [ABSTRACT FROM AUTHOR]

Mobile robot olfaction of toxic and hazardous odor sources is of great significance in anti-terrorism, disaster prevention, and control scenarios. Aiming at the problems of low search efficiency and easily falling into a local optimum of the current odor source localization strategies, the paper proposes the adaptive space-aware Infotaxis II algorithm. To improve the tracking efficiency of robots, a new reward function is designed by considering the space information and emphasizing the exploration behavior of robots. Considering the enhancement in exploratory behavior, an adaptive navigation-updated mechanism is proposed to adjust the movement range of robots in real time through information entropy to avoid an excessive exploration behavior during the search process, which may lead the robot to fall into a local optimum. Subsequently, an improved adaptive cosine salp swarm algorithm is applied to confirm the optimal information adaptive parameter. Comparative simulation experiments between ASAInfotaxis II and the classical search strategies are carried out in 2D and 3D scenarios regarding the search efficiency and search behavior, which show that ASAInfotaxis II is competent to improve the search efficiency to a larger extent and achieves a better balance between exploration and exploitation behaviors. [ABSTRACT FROM AUTHOR]

On social media platforms, users can not only unfollow others whose opinion excessively opposes their own, but they can also add new connections. To better reflect the evolution of opinions on social media, this paper proposes an opinion asymmetry evolution model based on a dynamic network structure, where the trusts between two individuals are not mutual and dynamic. First, the paper analyzes the general properties of the model. We prove that group opinion can converge to a steady state even if the connection is unidirectional. Second, we compare the evolution process of static and dynamic network structures. Computer simulation results show that a higher probability of new connections leads to less aggregation of group opinion, higher information entropy, lower HHI, and lower degrees of polarization. [ABSTRACT FROM AUTHOR]

In this paper, we provide geometric insights with visualization into the multivariate Gaussian distribution and its entropy and mutual information. In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion, supported by illustrations, both technically and statistically. The paper examines broad measurements of structure for the Gaussian distributions, which show that they can be described in terms of the information theory between the given covariance matrix and correlated random variables (in terms of relative entropy). The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic's science and implementations. It also helps readers grasp the themes' fundamental concepts to study the application of multivariate sets of data in Gaussian distribution. The simulation results also convey the behavior of different elliptical interpretations based on the multivariate Gaussian distribution with entropy for real-world applications in our daily lives, including information coding, nonlinear signal detection, etc. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis, a wide range of information is addressed, including basic application concerns as well as clinical diagnostics to detect the multi-disease effects. [ABSTRACT FROM AUTHOR]

Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue "Entropy in Landscape Ecology" in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics. [ABSTRACT FROM AUTHOR]

Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. Recognizing the high sensitivity of Deep Neural Networks (DNNs) to small perturbations, we propose HAG-NET, a method based on image carriers, which is jointly trained by the encoder, decoder, and attacker. In this paper, the encoder generates Adversarial Steganographic Examples (ASEs) that are adversarial to the target classification network, thereby providing protection for the carrier data. Additionally, the decoder can recover secret data from ASEs. The experimental results demonstrate that ASEs produced by HAG-NET achieve an average success rate of over 99% on both the MNIST and CIFAR-10 datasets. ASEs generated with the attacker exhibit greater robustness in terms of attack ability, with an average increase of about 3.32%. Furthermore, our method, when compared with other generative stego examples under similar perturbation strength, contains significantly more information according to image information entropy measurements. [ABSTRACT FROM AUTHOR]

Synthetic Aperture Radar (SAR) images are widely utilized in the field of remote sensing. However, there is a limited body of literature specifically addressing the compression of SAR learning images. To address the escalating volume of SAR image data for storage and transmission, which necessitates more effective compression algorithms, this paper proposes a novel framework for compressing SAR images. Experimental validation is performed using a representative low-resolution Sentinel-1 dataset and the high-resolution QiLu-1 dataset. Initially, we introduce a novel two-stage transformation-based approach aimed at suppressing the low-frequency components of the input data, thereby achieving a high information entropy and minimizing quantization losses. Subsequently, a quality map guidance image compression algorithm is introduced, involving the fusion of the input SAR images with a target-aware map. This fusion involves convolutional transformations to generate a compact latent representation, effectively exploring redundancies between focused and non-focused areas. To assess the algorithm's performance, experiments are carried out on both the low-resolution Sentinel-1 dataset and the high-resolution QiLu-1 dataset. The results indicate that the low-frequency suppression algorithm significantly outperforms traditional processing algorithms by 3–8 dB when quantifying the input data, effectively preserving image features and improving image performance metrics. Furthermore, the quality map guidance image compression algorithm demonstrates a superior performance compared to the baseline model. [ABSTRACT FROM AUTHOR]

Few-shot learning aims to solve the difficulty in obtaining training samples, leading to high variance, high bias, and over-fitting. Recently, graph-based transductive few-shot learning approaches supplement the deficiency of label information via unlabeled data to make a joint prediction, which has become a new research hotspot. Therefore, in this paper, we propose a novel ensemble semi-supervised few-shot learning strategy via transductive network and Dempster–Shafer (D-S) evidence fusion, named ensemble transductive propagation networks (ETPN). First, we present homogeneity and heterogeneity ensemble transductive propagation networks to better use the unlabeled data, which introduce a preset weight coefficient and provide the process of iterative inferences during transductive propagation learning. Then, we combine the information entropy to improve the D-S evidence fusion method, which improves the stability of multi-model results fusion from the pre-processing of the evidence source. Third, we combine the L2 norm to improve an ensemble pruning approach to select individual learners with higher accuracy to participate in the integration of the few-shot model results. Moreover, interference sets are introduced to semi-supervised training to improve the anti-disturbance ability of the mode. Eventually, experiments indicate that the proposed approaches outperform the state-of-the-art few-shot model. The best accuracy of ETPN increases by 0.3% and 0.28% in the 5-way 5-shot, and by 3.43% and 7.6% in the 5-way 1-shot on miniImagNet and tieredImageNet, respectively. [ABSTRACT FROM AUTHOR]

In the context of autonomous driving, sensing systems play a crucial role, and their accuracy and reliability can significantly impact the overall safety of autonomous vehicles. Despite this, fault diagnosis for sensing systems has not received widespread attention, and existing research has limitations. This paper focuses on the unique characteristics of autonomous driving sensing systems and proposes a fault diagnosis method that combines hardware redundancy and analytical redundancy. Firstly, to ensure the authenticity of the study, we define 12 common real-world faults and inject them into the nuScenes dataset, creating an extended dataset. Then, employing heterogeneous hardware redundancy, we fuse MMW radar, LiDAR, and camera data, projecting them into pixel space. We utilize the "ground truth" obtained from the MMW radar to detect faults on the LiDAR and camera data. Finally, we use multidimensional temporal entropy to assess the information complexity fluctuations of LiDAR and the camera during faults. Simultaneously, we construct a CNN-based time-series data multi-classification model to identify fault types. Through experiments, our proposed method achieves 95.33% accuracy in detecting faults and 82.89% accuracy in fault diagnosis on real vehicles. The average response times for fault detection and diagnosis are 0.87 s and 1.36 s, respectively. The results demonstrate that the proposed method can effectively detect and diagnose faults in sensing systems and respond rapidly, providing enhanced reliability for autonomous driving systems. [ABSTRACT FROM AUTHOR]

Standard training via empirical risk minimization may result in making predictions that overly rely on spurious correlations. This can degrade the generalization to out-of-distribution settings where these correlations no longer hold. Invariant learning has been shown to be a promising approach for identifying predictors that ignore spurious correlations. However, an important limitation of this approach is that it assumes access to different "environments" (also known as domains), which may not always be available. This paper proposes a simple yet effective strategy for discovering maximally informative environments from a single dataset. Our frustratingly easy environment discovery (FEED) approach trains a biased reference classifier using a generalized cross-entropy loss function and partitions the dataset based on its performance. These environments can be used with various invariant learning algorithms, including Invariant Risk Minimization, Risk Extrapolation, and Group Distributionally Robust Optimization. The results indicate that FEED can discover environments with a higher group sufficiency gap compared to the state-of-the-art environment inference baseline and leads to improved test accuracy on CMNIST, Waterbirds, and CelebA datasets. [ABSTRACT FROM AUTHOR]

To further reduce the size of the neural network model and enable the network to be deployed on mobile devices, a novel fusion pruning algorithm based on information entropy stratification is proposed in this paper. Firstly, the method finds similar filters and removes redundant parts by Affinity Propagation Clustering, then secondly further prunes the channels by using information entropy stratification and batch normalization (BN) layer scaling factor, and finally restores the accuracy training by fine-tuning to achieve a reduced network model size without losing network accuracy. Experiments are conducted on the vgg16 and Resnet56 network using the cifar10 dataset. On vgg16, the results show that, compared with the original model, the parametric amount of the algorithm proposed in this paper is reduced by 90.69% and the computation is reduced to 24.46% of the original one. In ResNet56, we achieve a 63.82%-FLOPs reduction by removing 63.53% parameters. The memory occupation and computation speed of the new model are better than the baseline model while maintaining a high network accuracy. Compared with similar algorithms, the algorithm has obvious advantages in the dimensions of computational speed and model size. The pruned model is also deployed to the Internet of Things (IoT) as a target detection system. In addition, experiments show that the proposed model is able to detect targets accurately with low reasoning time and memory. It takes only 252.84 ms on embedded devices, thus matching the limited resources of IoT. [ABSTRACT FROM AUTHOR]

In this paper, based on the information entropy and spatio-temporal correlation of sensing nodes in the Internet of Things (IoT), a Spatio-temporal Scope Information Model (SSIM) is proposed to quantify the scope of the valuable information of sensor data. Specifically, the valuable information of sensor data decays with space and time, which can be used to guide the system to make efficient sensor activation scheduling decisions for regional sensing accuracy. A simple sensing and monitoring system with three sensor nodes is investigated in this paper, and a single-step scheduling decision mechanism is proposed for the optimization problem of maximizing valuable information acquisition and efficient sensor activation scheduling in the sensed region. Regarding the above mechanism, the scheduling results and approximate numerical bounds on the node layout between different scheduling results are obtained through theoretical analyses, which are consistent with simulation. In addition, a long-term decision mechanism is also proposed for the aforementioned optimization issues, where the scheduling results with different node layouts are derived by modeling as a Markov decision process and utilizing the Q-learning algorithm. Concerning the above two mechanisms, the performance of both is verified by conducting experiments using the relative humidity dataset; furthermore, the differences in performance and limitations of the model are discussed and summarized. [ABSTRACT FROM AUTHOR]

Identifying influential nodes is a key research topic in complex networks, and there have been many studies based on complex networks to explore the influence of nodes. Graph neural networks (GNNs) have emerged as a prominent deep learning architecture, capable of efficiently aggregating node information and discerning node influence. However, existing graph neural networks often ignore the strength of the relationships between nodes when aggregating information about neighboring nodes. In complex networks, neighboring nodes often do not have the same influence on the target node, so the existing graph neural network methods are not effective. In addition, the diversity of complex networks also makes it difficult to adapt node features with a single attribute to different types of networks. To address the above problems, the paper constructs node input features using information entropy combined with the node degree value and the average degree of the neighbor, and proposes a simple and effective graph neural network model. The model obtains the strength of the relationships between nodes by considering the degree of neighborhood overlap, and uses this as the basis for message passing, thereby effectively aggregating information about nodes and their neighborhoods. Experiments are conducted on 12 real networks, using the SIR model to verify the effectiveness of the model with the benchmark method. The experimental results show that the model can identify the influence of nodes in complex networks more effectively. [ABSTRACT FROM AUTHOR]

The problem that the randomly generated random projection matrix will lead to unstable classification results is addressed in this paper. To this end, a Tighter Random Projection-oriented entropy-weighted ensemble algorithm is proposed for classifying hyperspectral remote sensing images. In particular, this paper presents a random projection matrix selection strategy based on the separable information of a single class able to project the features of a certain class of objects. The projection result is measured by the degree of separability, thereby obtaining the low-dimensional image with optimal separability of the class. After projecting samples with the same random projection matrix, to calculate the distance matrix, the Minimum Distance classifier is devised, repeating for all classes. Finally, the weight of the distance matrix is considered in ensemble classification by using the information entropy. The proposed algorithm is tested on real hyperspectral remote sensing images. The experiments show an increase in both stability and performance. [ABSTRACT FROM AUTHOR]

Image dehazing has always been one of the main areas of research in image processing. The traditional dark channel prior algorithm (DCP) has some shortcomings, such as incomplete fog removal and excessively dark images. In order to obtain haze-free images with high quality, a hybrid dark channel prior (HDCP) algorithm is proposed in this paper. HDCP first employs Retinex to remove the interference of the illumination component. The variant genetic algorithm (VGA) is then used to obtain the guidance image required by the guided filter to optimize the atmospheric transmittance. Finally, the modified dark channel prior algorithm is used to obtain the dehazed image. Compared with three other modified DCP algorithms, HDCP has the best subjective visual effects of haze removal and color fidelity. HDCP also shows superior objective indexes in the mean square error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and information entropy (E) for different haze degrees. [ABSTRACT FROM AUTHOR]

The safe and comfortable operation of high-speed trains has attracted extensive attention. With the operation of the train, the performance of high-speed train bogie components inevitably degrades and eventually leads to failures. At present, it is a common method to achieve performance degradation estimation of bogie components by processing high-speed train vibration signals and analyzing the information contained in the signals. In the face of complex signals, the usage of information theory, such as information entropy, to achieve performance degradation estimations is not satisfactory, and recent studies have more often used deep learning methods instead of traditional methods, such as information theory or signal processing, to obtain higher estimation accuracy. However, current research is more focused on the estimation for a certain component of the bogie and does not consider the bogie as a whole system to accomplish the performance degradation estimation task for several key components at the same time. In this paper, based on soft parameter sharing multi-task deep learning, a multi-task and multi-scale convolutional neural network is proposed to realize performance degradation state estimations of key components of a high-speed train bogie. Firstly, the structure takes into account the multi-scale characteristics of high-speed train vibration signals and uses a multi-scale convolution structure to better extract the key features of the signal. Secondly, considering that the vibration signal of high-speed trains contains the information of all components, the soft parameter sharing method is adopted to realize feature sharing in the depth structure and improve the utilization of information. The effectiveness and superiority of the structure proposed by the experiment is a feasible scheme for improving the performance degradation estimation of a high-speed train bogie. [ABSTRACT FROM AUTHOR]

Tea is one of the most popular drinks in the world. The rapid and accurate recognition of tea diseases is of great significance for taking targeted preventive measures. In this paper, an information entropy masked vision transformation (IEM-ViT) model was proposed for the rapid and accurate recognition of tea diseases. The information entropy weighting (IEW) method was used to calculate the IE of each segment of the image, so that the model could learn the maximum amount of knowledge and information more quickly and accurately. An asymmetric encoder–decoder architecture was used in the masked autoencoder (MAE), where the encoder operated on only a subset of visible patches and the decoder recovered the labeled masked patches, reconstructing the missing pixels for parameter sharing and data augmentation. The experimental results showed that the proposed IEM-ViT had an accuracy of 93.78% for recognizing the seven types of tea diseases. In comparison to the currently common image recognition algorithms including the ResNet18, VGG16, and VGG19, the recognition accuracy was improved by nearly 20%. Additionally, in comparison to the other six published tea disease recognition methods, the proposed IEM-ViT model could recognize more types of tea diseases and the accuracy was improved simultaneously. [ABSTRACT FROM AUTHOR]

This paper studies the remaining useful life (RUL) of lubricating oil based on condition monitoring (CM). Firstly, the element composition and content of the lubricating oil in use were quantitatively analyzed by atomic emission spectrometry (AES). Considering the large variety of oil data obtained through AES, the accuracy and efficiency of the RUL prediction model may be reduced. To solve this problem, a comprehensive parameter selection method based on information entropy, correlation analysis, and lubricant deterioration analysis is proposed to screen oil data. Then, based on a support vector machine (SVM), the RUL prediction model of lubricant was established. By comparing the experimental results with the output data of the prediction model, it is shown that the accuracy and efficiency of the SVM prediction model established after parameter screening have been significantly improved. [ABSTRACT FROM AUTHOR]

This paper proposes an encryption scheme for high pixel density images. Based on the application of the quantum random walk algorithm, the long short-term memory (LSTM) can effectively solve the problem of low efficiency of the quantum random walk algorithm in generating large-scale pseudorandom matrices, and further improve the statistical properties of the pseudorandom matrices required for encryption. The LSTM is then divided into columns and fed into the LSTM in order for training. Due to the randomness of the input matrix, the LSTM cannot be trained effectively, so the output matrix is predicted to be highly random. The LSTM prediction matrix of the same size as the key matrix is generated based on the pixel density of the image to be encrypted, which can effectively complete the encryption of the image. In the statistical performance test, the proposed encryption scheme achieves an average information entropy of 7.9992, an average number of pixels changed rate (NPCR) of 99.6231%, an average uniform average change intensity (UACI) of 33.6029%, and an average correlation of 0.0032. Finally, various noise simulation tests are also conducted to verify its robustness in real-world applications where common noise and attack interference are encountered. [ABSTRACT FROM AUTHOR]

This paper proposes a new string transformation technique called Move with Interleaving (MwI). Four possible ways of rearranging 2D raster images into 1D sequences of values are applied, including scan-line, left-right, strip-based, and Hilbert arrangements. Experiments on 32 benchmark greyscale raster images of various resolutions demonstrated that the proposed transformation reduces information entropy to a similar extent as the combination of the Burrows–Wheeler transform followed by the Move-To-Front or the Inversion Frequencies. The proposed transformation MwI yields the best result among all the considered transformations when the Hilbert arrangement is applied. [ABSTRACT FROM AUTHOR]

Aerial TDI cameras can obtain images with a high sensitivity, high resolution, and wide dynamic range under low-illumination conditions. Under the condition of low illumination, exposure is an important parameter that affects the image quality of the camera. Auto-exposure aims to obtain the information of target scene in advance and uses it as the basis for determining exposure parameters, which can avoid the loss of image information caused by overexposure or underexposure. The auto-exposure of TDI CCD is usually difficult, as the shooting mode of TDI CCD is a push and sweep mode, which can only take one image of the target scene, and the output image is not repetitive, so it is difficult to obtain an image of the target scene in advance. At present, the common method is to add an additional sensor to collect the feature information of the target scene in advance; however, this increases the complexity of the system. Therefore, this paper proposes that the camera uses TDI CCD to collect the first N rows of data of the target scene in advance as the basis, and then adjusts and determines the exposure parameters with the median gray value as the target; thus, without adding additional sensors, the auto-exposure of TDI CCD can be realized. To evaluate the effect of auto-exposure, three methods of image power spectrum variance, image histogram, and image information entropy are used. The test results show that, after auto-exposure, the variance in the image power spectrum increased by 0.4362, the entropy of image information increased by 1.7064, and the distribution of the image histogram was more uniform than that before auto-exposure. This shows that the effect of auto-exposure is good, and it has better scene adaptation, allowing for it to meet the requirements of auto-exposure imaging under low-illumination conditions in aerial TDI cameras. [ABSTRACT FROM AUTHOR]

Nowadays, the utilization of memristors to enhance the dynamical properties of chaotic systems has become a popular research topic. In this paper, we present the design of a novel 2D memristor-enhanced polynomial hyper-chaotic map (2D-MPHM) by utilizing the cross-coupling of two TiO 2 memristors. The dynamical properties of the 2D-MPHM were investigated using Lyapunov exponents, bifurcation diagrams, and trajectory diagrams. Additionally, Kolmogorov entropy and sample entropy were also employed to evaluate the complexity of the 2D-MPHM. Numerical analysis has demonstrated the superiority of the 2D-MPHM. Subsequently, the proposed 2D-MPHM was applied to a multi-channel image encryption algorithm (MIEA-MPHM) whose excellent security was demonstrated by key space, key sensitivity, plaintext sensitivity, information entropy, pixel distribution, correlation analysis, and robustness analysis. Finally, the encryption efficiency of the MIEA-MPHM was evaluated via numerous encryption efficiency tests. These tests demonstrate that the MIEA-MPHM not only possesses excellent security but also offers significant efficiency advantages, boasting an average encryption rate of up to 87.2798 Mbps. [ABSTRACT FROM AUTHOR]

The main application scenario for wearable sensors involves the generation of data and monitoring metrics. fNIRS (functional near-infrared spectroscopy) allows the nonintrusive monitoring of human visual perception. The quantification of visual perception by fNIRS facilitates applications in engineering-related fields. This study designed a set of experimental procedures to effectively induce visible alterations and to quantify visual perception in conjunction with the acquisition of Hbt (total hemoglobin), Hb (hemoglobin), and HbO2 (oxygenated hemoglobin) data obtained from HfNIRS (high-density functional near-infrared spectroscopy). Volunteers completed the visual task separately in response to different visible changes in the simulated scene. HfNIRS recorded the changes in Hbt, Hb, and HbO2 during the study, the time point of the visual difference, and the time point of the task change. This study consisted of one simulated scene, two visual variations, and four visual tasks. The simulation scene featured a car driving location. The visible change suggested that the brightness and saturation of the car operator interface would change. The visual task represented the completion of the layout, color, design, and information questions answered in response to the visible change. This study collected data from 29 volunteers. The volunteers completed the visual task separately in response to different visual changes in the same simulated scene. HfNIRS recorded the changes in Hbt, Hb, and HbO2 during the study, the time point of the visible difference, and the time point of the task change. The data analysis methods in this study comprised a combination of channel dimensionality reduction, feature extraction, task classification, and score correlation. Channel downscaling: This study used the data of 15 channels in HfNIRS to calculate the mutual information between different channels to set a threshold, and to retain the data of the channels that were higher than those of the mutual information. Feature extraction: The statistics derived from the visual task, including time, mean, median, variance, extreme variance, kurtosis, bias, information entropy, and approximate entropy were computed. Task classification: This study used the KNN (K-Nearest Neighbors) algorithm to classify different visual tasks and to calculate the accuracy, precision, recall, and F1 scores. Scoring correlation: This study matched the visual task scores with the fluctuations of Hbt, Hb, and HbO2 and observed the changes in Hbt, Hb, and HbO2 under different scoring levels. Mutual information was used to downscale the channels, and seven channels were retained for analysis under each visual task. The average accuracy was 96.3% ± 1.99%; the samples that correctly classified the visual task accounted for 96.3% of the total; and the classification accuracy was high. By analyzing the correlation between the scores on different visual tasks and the fluctuations of Hbt, Hb, and HbO2, it was found that the higher the score, the more obvious, significant, and higher the fluctuations of Hbt, Hb, and HbO2. Experiments found that changes in visual perception triggered changes in Hbt, Hb, and HbO2. HfNIRS combined with Hbt, Hb, and HbO2 recorded by machine learning algorithms can effectively quantify visual perception. However, the related research in this paper still needs to be further refined, and the mathematical relationship between HfNIRS and visual perception needs to be further explored to realize the quantitative study of subjective and objective visual perception supported by the mathematical relationship. [ABSTRACT FROM AUTHOR]