Information Entropy Research Articles

ENTROPY BASED EVALUATION OF THE IMPACT OF EDUCATION ON ECONOMIC DEVELOPMENT

In contemporary economic landscapes, effective managerial decision-making requires serious justifications often facilitated by information technologies. The article proposes the application of the foundational principles from information theory and entropy to determine the correlation between education and economic development. This research employs entropy methodology to explore the correlations and implications of these multifaceted domains, drawing insights from a range of global indices. By analyzing data from indices such as the Human Development Index, we investigate the relationship between average years of education and entropy values, shedding light on the diversity and standardization of human capital systems across nations. Moreover, economic indexes, encapsulating factors such as economic freedom and innovation, provide critical insights into the vibrancy and resilience of national economies. Through the lens of the Global Innovation Index, we explore how countries with higher levels of economic freedom and innovation efficiency exhibit less diversity in economic approaches and innovation strategies, leading to a reduction in entropy values. By examining entropy values in conjunction with innovation indicators, such as research and development expenditure and patent applications, we uncover patterns and trends indicative of the diversity or standardization of innovation strategies across countries. Additionally, cybersecurity emerges as a critical dimension of national security and resilience, with implications for economic well-being and societal trust. Through the National Cybersecurity Index, we assess the level of diversity and uncertainty in cybersecurity landscapes, highlighting the importance of robust cybersecurity measures in safeguarding against emerging threats and reducing entropy values. Ultimately, this research contributes to the discourse on sustainable development and resilience in an interconnected world. By identifying specific challenges and opportunities within education, economy, innovation, and cybersecurity domains, it facilitates informed decision-making and strategic interventions to promote inclusive growth and societal well-being on a global scale.

Research on Housing Market Risk Management Based on Multidimensional Evaluation

The housing market is a high-risk industry with too many factors influenced by the outside world, and if these risks are not effectively managed, it will bring serious impacts on the stability of the economy and society. This paper takes the risk management of housing market as the research object, utilizes the information entropy model and ANP combined method to combine and assign the risk indicators, and constructs the cloud model of housing market risk evaluation. And the cloud model is applied to the GJ housing case for practical evaluation, and it is found that the cloud droplets of the comprehensive risk of the GJ housing market are mainly distributed in the medium-risk interval from 31 to 54, focusing on 41, and a small number of risk cloud droplets appear in the higher-risk cloud map, which is in line with the actual evaluation results, and further verifies the feasibility and validity of the method. Finally, based on the evaluation results, the risk control strategy of the relevant housing market is proposed, which can be used as a reference in the development process of subsequent housing projects.

IIS-FVIQA: Finger Vein Image Quality Assessment with intra-class and inter-class similarity

In recent years, Finger Vein Image Quality Assessment (FVIQA) has been recognized as an effective solution to the problem of erroneous recognition resulting from low image quality due to false and missing information in finger vein images, and has become an important part of finger vein recognition systems. Compared to traditional FVIQA methods that rely on domain knowledge, newer methods that reject low-quality images have been favored for their independence from human interference. However, these methods only consider intra-class similarity information and ignore valuable information from inter-class distribution, which is also an important factor in evaluating the performance of recognition systems. In this work, we propose a novel FVIQA approach, named IIS-FVIQA, which concurrently takes into account the intra-class similarity density and inter-class similarity distribution distance within recognition systems. Specifically, our method generates quality scores for finger vein images by combining the information entropy of intra-class similarity distribution and Wasserstein distance of inter-class distribution. Then, we train a regression network for quality prediction using training images and corresponding quality scores. When a new image enters the recognition system, the trained regression network directly predicts the quality score of the image, making it easier for the system to select the corresponding operation based on the quality score of the image. Extensive experiments conducted on benchmark datasets demonstrate that the IIS-FVIQA method proposed in this paper consistently achieves top performance across multiple public datasets. After filtering out 10% of low-quality images predicted by the quality regression network, the recognition system’s performance improves by 43.96% (SDUMLA), 32.23% (MMCBNU_6000), and 21.20% (FV-USM), respectively. Furthermore, the method exhibits strong generalizability across different recognition algorithms (e.g., LBP, MC, and Inception V3) and datasets (e.g., SDUMLA, MMCBNU_6000, and FV-USM).

Multiple-perspective consumer segmentation using improved weighted Fuzzy k-prototypes clustering and swarm intelligence algorithm for fresh apricot market

Leveraging clustering technology for consumer segmentation is crucial for discerning the nuanced differences among fresh apricot consumer groups and subsequently executing precise marketing strategies. To achieve a more comprehensive and lucid consumer segmentation and identify typical characteristics of apricot consumers in different clusters, this research constructs a novel multiple-perspective segmentation indicator system for fresh apricot consumers. Given the diverse degrees of importance and types of consumer segmentation variables, and the inherent sensitivity of the original Fuzzy k-prototypes (FKP) algorithm to clustering centers, we proposed the weighted Fuzzy k-prototypes (WFKP) algorithms for mixed data (MD) optimized by the particle swarm optimization (PSO) algorithm (MDPSO-WFKP) and mixed data sparrow search algorithm (SSA) (MDSSA-WFKP), both incorporating information entropy weighting for mixed attributes. We test the proposed algorithms on four University of California Irvine machine learning repository (UCI) datasets and the consumer segmentation dataset, and the performance of all selected evaluation indexes shows significant improvement. These findings unequivocally validate the efficacy of the proposed methodologies. Since the MDSSA-WFKP algorithm has the best comprehensive effect on the evaluation indexes, we use it to conduct in-depth apricot consumer segmentation research and find that the apricot consumers can be subdivided into three groups with differentiation: ‘Buddhist-like youths’, ‘Upscale attribute enthusiasts’, and ‘Quality-oriented consumers’. Finally, this paper gives the corresponding marketing suggestions based on the characteristics of the segmented groups.

Elucidating the link between binding statistics and Shannon information in biological networks.

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding.

Fault Diagnosis for Motor Bearings via an Intelligent Strategy Combined with Signal Reconstruction and Deep Learning

To overcome the incomplete decomposition of vibration signals in traditional motor-bearing fault diagnosis algorithms and improve the ability to characterize fault characteristics and anti-interference, a diagnostic strategy combining dual signal reconstruction and deep learning architecture is proposed. In this study, an improved complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD)-based signal reconstruction method is first introduced to extract features representing motor bearing faults. A feature matrix construction method based on improved information entropy is then proposed to quantify these fault features. Finally, a fault diagnosis algorithm architecture integrating a multi-scale convolutional neural network (MSCNN) with attention mechanisms and a bidirectional long short-term memory network (BiLSTM) is developed. The experimental results for four fault states show that this model can effectively extract fault features from original vibration signals and, compared to other fault diagnosis models, offer high diagnostic accuracy and strong generalization, maintaining high accuracy even under varying speeds and noise interference.

Traditional landscape painting and art image restoration methods based on structural information guidance

Abstract In the field of traditional landscape painting and art image restoration, traditional restoration methods have gradually revealed limitations with the development of society and technological progress. In order to enhance the restoration effects of Chinese landscape paintings, an innovative image restoration algorithm is designed in this research, combining edge restoration with generative adversarial networks (GANs). Simultaneously, a novel image restoration model with embedded multi-scale attention dilated convolution is proposed to enhance the modeling capability for details and textures in landscape paintings. To better preserve the structural features of artistic images, a structural information-guided art image restoration model is introduced. The introduction of adversarial networks into the repair model can improve the repair effect. The art image repair model adds a multi-scale attention mechanism to handle more complex works of art. The research results show that the image detection model improves by 0.20, 0.07, and 0.06 in the Spearman rank correlation coefficient, Pearson correlation coefficient, and peak signal-to-noise ratio (PSNR), respectively, compared to other models. The proposed method outperforms mean filtering, wavelet denoising, and median filtering algorithms by 6.3, 9.1, and 15.8 dB in PSNR and by 0.06, 0.12, and 0.11 in structural similarity index. In the image restoration task, the structural similarity and information entropy indicators of the research model increase by approximately 9.3 and 3%, respectively. The image restoration method proposed in this study is beneficial for preserving and restoring precious cultural heritage, especially traditional Chinese landscape paintings, providing new technological means for cultural relic restoration.

Novel discretized gravitational search algorithm for effective medical hyperspectral band selection

Medical hyperspectral imaging present a promising avenue for non-invasive diagnostic methods for diseases. Nonetheless, the sparsity of medical hyperspectral data within high-dimensional spaces introduces the “curse of dimensionality”, which diminishes the efficiency and accuracy of data processing efforts. Therefore, spectral dimensionality reduction emerges as an essential process in the analysis and utilization of MHSIs data. To retain the intrinsic properties of the spectral bands, an effective unsupervised band selection algorithm is proposed leveraging the gravitational search algorithm (GSA-UBS) to identify the optimal band subset. Taking into account the informational content and redundancy among candidate bands, a comprehensive evaluation criterion is established that incorporates a band distance matrix and an information entropy vector. Additionally, a straightforward discrete search strategy is developed that enables gravitational search algorithm to directly retrieve the original sequence numbers of the selected bands, bypassing the conventional 0–1 band weighting approach. The extensive evaluation of GSA-UBS on three publicly available invivo brain cancer MHSIs datasets and a remote sensing hyperspectral image demonstrates its superior performance compared to various state-of-the-art methods. The source code for GSA-UBS can be accessed at https://github.com/zhangchenglong1116/GSA_UBS.

A practical scheme for enhancing consistency and independence in wireless key generation for Wi-Fi networks

Wi-Fi networks benefit from physical layer wireless key generation, a theoretically secure method for improving information transmission security. This paper introduces the Consistent Independent Key Generation (CIKG) scheme based on the Wi-Fi signal transmission model. It addresses the dual challenges of channel noise and virtual carrier low-pass effects. The scheme begins with extracting the channel frequency response (CFR) from the entire signal preamble, including both long and short symbols, followed by applying cubic spline interpolation to the short symbol-derived CFR to achieve fine-grained frequency fading corresponding to the long symbols. This refined CFR is averaged to bolster noise resistance, improving key consistency. Subsequently, the inverse Fourier transform is used to obtain the channel impulse response (CIR), and a deconvolution strategy reduces the impact of virtual carrier low-pass filtering on the multipath information of CIR, thus improving key independence. Implemented within Wi-Fi networks, the effectiveness of the CIKG scheme is rigorously tested across diverse scenarios. Quantitative evaluations indicate that the scheme substantially improves key consistency, achieving a 5 dB enhancement in signal-to-noise ratio over traditional CFR-based schemes and elevates information entropy by 20%, significantly boosting key independence. These advances affirm the potential of the CIKG scheme as a formidable solution for developing robust and secure wireless communication networks.

Electroencephalography Emotion Recognition Based on Rhythm Information Entropy Extraction

Electroencephalography (EEG) is a physiological signal directly generated by the central nervous system. Brain rhythm is closely related to a person’s emotional state and is widely used for EEG emotion recognition. In previous studies, the rhythm specificity between different brain channels was seldom explored. In this paper, the rhythm specificity of brain channels is studied to improve the accuracy of EEG emotion recognition. Variational mode decomposition is used to decompose rhythm signals and enhance features, and two kinds of information entropy, i.e., differential entropy (DE) and dispersion entropy (DispEn) are extracted. The rhythm being used to get the best result of single channel emotion recognition is selected as the representative rhythm, and the remove one method is employed to obtain rhythm information entropy feature. In the experiment, the DEAP database was used for EEG emotion recognition in valence-arousal space. The results showed that the best result of rhythm DE feature classification in the valence dimension is 77.04%, and the best result of rhythm DispEn feature classification in the arousal dimension is 79.25%.

Phases and coherence of strongly interacting finite bosonic systems in shallow optical lattice

We explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function. Two new many-body phases: fragmented or quasi superfluid (QSF) and incomplete fragmented Mott or quasi Mott insulator (QMI) are emerged due to the strong interplay between short-range contact interaction and lattice depth. Fragmentation is utilized as a figure of merit to distinguish these two new phases. We utilize the eigenvalues of the reduced one-body density matrix and define an order parameter that characterizes the pathway from a very weak lattice to a deep lattice. We provide a detailed investigation through the measures of one- and two-body correlations and information entropy. We find that the structures in one- and two-body coherence are good markers to understand the gradual built-up of intra-well correlation and decay of inter-well correlation with increase in lattice depth. For the dipolar interaction, the many-body features become more distinct and true Mott state can appear even in a shallow lattice. Whereas, for incommensurate fraction of particles, incomplete localization happens that exhibits distinct features in the measure of two-body coherence.

Case-Based Deduction for Entailment Tree Generation

Maintaining logical consistency in structured explanations is critical for understanding and troubleshooting the reasoning behind a system’s decisions. However, existing methods for entailment tree generation often struggle with logical consistency, resulting in erroneous intermediate conclusions and reducing the overall accuracy of the explanations. To address this issue, we propose case-based deduction (CBD), a novel approach that retrieves cases with similar logical structures from a case base and uses them as demonstrations for logical deduction. This method guides the model toward logically sound conclusions without the need for manually constructing logical rule bases. By leveraging a prototypical network for case retrieval and reranking them using information entropy, CBD introduces diversity to improve in-context learning. Our experimental results on the EntailmentBank dataset show that CBD significantly improves entailment tree generation, achieving performance improvements of 1.7% in Task 1, 0.6% in Task 2, and 0.8% in Task 3 under the strictest Overall AllCorrect metric. These findings confirm that CBD enhances the logical consistency and overall accuracy of AI systems in structured explanation tasks.

Research on Critical Quality Feature Recognition and Quality Prediction Method of Machining Based on Information Entropy and XGBoost Hyperparameter Optimization

To address the problem of predicting machining quality for critical features in the manufacturing process of mechanical products, a method that combines information entropy and XGBoost (version 2.1.1) hyperparameter optimization is proposed. Initially, machining data of mechanical products are analyzed based on information entropy theory to identify critical quality characteristics. Subsequently, a quality prediction model for these critical features is established using the XGBoost machine learning framework. The model’s hyperparameters are then optimized through Bayesian optimization. This method is applied as a case study to a medium-speed marine diesel engine piston. After the critical quality characteristics in the machining process are identified, the machining quality of these vital characteristics is predicted, and the results are compared with those obtained from a machine learning model without hyperparameter optimization. The findings demonstrate that the proposed method effectively predicts the machining quality of mechanical products.

Investigating the Satisfaction of Residents in the Historic Center of Macau and the Characteristics of the Townscape: A Decision Tree Approach to Machine Learning

The historic city of Macau is China’s 31st world heritage site, and its residents have actively contributed to preserving its heritage and will continue to reside there for the foreseeable future. Residents’ satisfaction with the current urban environment is closely related to the landscape characteristics of the towns surrounding the historic center of Macau. This study aims to analyze the relationship between landscape characteristics and residents’ satisfaction, determine the key factors affecting their satisfaction and how they are combined, and provide a scientific basis for urban planning. This study used a decision tree machine learning model to analyze 524 questionnaire survey responses that addressed five aspects of the historic town’s landscape: the architectural, Largo Square, street, mountain and sea, and commercial landscapes. The data-driven approach helped find the best decision path. The results indicate that (1) the layout of Largo Square, the commercial colors and materials, the location of the former humanities and religion center, and the commercial signage system are the primary factors influencing residents’ satisfaction. (2) Incorporating decision tree parameters with information entropy as the splitting criterion and a minimum sample split number of two (with no maximum depth) led to the best performance when investigating residents’ satisfaction with Macau’s historic town landscape characteristics. (3) A reasonable layout for Largo Square (satisfaction > 3.50), prominent and harmonious commercial colors and materials (satisfaction > 3.50), rich cultural and religious elements (satisfaction > 4.50), and an excellent commercial signage system (satisfaction > 4.00) can significantly improve residents’ satisfaction. This provides important empirical support and a reference for urban planning and landscape design in Macau and other historical and cultural cities.

An adaptive cycle framework for navigating sustainability of oasis socio-ecological system: The case of Hotan region in Xinjiang, China

Assessing the sustainability of socio-ecological system (SES) is the basis for ensuring human well-being and achieving Sustainable Development Goals (SDG) worldwide, especially in arid regions. However, the oasis as a typical socio-ecological system is still lacking a proper approach to examine its evolutionary direction and the sustainability of suitable scale. This study proposes an adaptive cycle framework assessing the sustainability of oasis socio-ecological system to quantify the relationships between the evolution of oasis socio-ecological system and its scale suitability. The framework is constructed by coordination degree, order degree, and oasis suitability metrics of the oasis socio-ecological system to apply in the oases of Tarim basin, Northwest China. The results show that the adaptive cycle evolution of various oases subsystems in study area does not go through four stages successively, but proceeds in a hopping way. The most of them are in the conservation (K) −recognition (α), or recognition (α) − conservation (K) stage. The information entropy of oasis socio-ecological system is inversely proportional to the order degree. The overall oasis information entropy is high ranging from 0.64 to 1.06, but the order degree is at a low level ranging from 0.04 to 0.41. The higher the degree of coordination between subsystems, the higher the degree of oasis suitability. The overall oasis suitability in study area shows a barely appropriate- appropriate-barely appropriate fluctuation state. The main factors affecting the oasis evolution of socio-economic, eco-environment and water resources subsystem are the distribution of industrial structure, green ratio, water consumption per unit grain output, and per capita daily living water consumption, respectively. This study provides support for guiding the sustainable evolution of desert oasis system to adapt to the development scale and the management of oasis socio-ecological system.

Complexity measures of electric screening effect in interstellar medium

Using the screening potential, we explore probability density properties in interstellar mediums (ISM) in information theory. With the eigenfunctions obtained for the screening potential using the Schrodinger equation, we studied the probability distribution for Shannon entropy, Fisher information, and their complexity measures for the values of n and l. From our numerical result, for Shannon entropy, we observed a more localized probability distribution in position and a decreasing localization in the momentum space as the values of n and l increases. For Fisher information, localization increases in the position space and, consequently, delocalization in their momentum spaces. The uncertainty relations of Shannon entropy and Fisher information were computed and satisfied the relations. For interstellar mediums, our findings align with Heinsberg’s uncertainty principle. Complexity measure was also studied for the interstellar mediums and our findings showed increasing disorder in the position space for increasing values of n and l. Furthermore, we extended the Debye-Hückel length to other regimes particularly, Magnetosphere (D=102) and Intergalactic Mediums (D=105)

Securing blockchain-enabled smart health care image encryption framework using Tinkerbell Map

IoT enables the emergence and implementation of smart devices to address real-world problems and challenges. Today we are surrounded by various smart devices, such as smart phones, smart homes, smart cars, smart televisions, and smartwatches that assist us in making our lives easier and smoother. IoT is a conglomeration of multiple technologies at various layers to impart the best of ubiquitous and pervasive computing to deliver several benefits in a variety of application sectors such as medicine, agriculture, and industry. In an IoT setting, blockchain technology is used for addressing security challenges and eradicating third-party participation. Utilizing public networks for storing or transmitting health care images poses risks of eavesdropping, data breaches, and unauthorized access. Before uploading medical data to the decentralized network, encryption is required to prevent unauthorized access. The aim of this study is to integrate technologies to ensure transactions are conducted safely and securely. We proposed an IoT-Blockchain system based on chaos encryption scheme using Tinkerbell mapping to ensure medical data integrity and authenticity. The suggested approach is examined to assess performance parameters such as, key space analysis, key sensitivity analysis, Information Entropy (IE), histogram, correlation of adjacent pixels, Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI), Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE) and Structural Similarity Index (SSIM). These findings demonstrated that the suggested method is extremely efficient in avoiding security breaches and guaranteeing information integrity.

A new 2D cross hyperchaotic Sine-modulation-Logistic map and its application in bit-level image encryption

Chaotic theory is being increasingly researched for application in image encryption scheme (IES). This paper presents a novel two-dimensional cross hyperchaotic Sine-modulation-Logistic map (2D-CHSLM) based on the famous Sine and Logistic maps. The hyperchaotic behaviors of 2D-CHSLM are demonstrated through bifurcation diagrams, trajectory plots, Lyapunov exponents, histogram, correlation dimension, sensitivity to initial conditions, sample entropy, 0–1 test, and NIST 800–22 test. A new bit-level IES with traditional an encryption structure is proposed utilizing 2D-CHSLM. The 2D-CHSLM-IES performs 2D-CHSLM-based bit-level confusion using a zigzag transform and 2D-CHSLM-based cross coupled diffusion operations to generate a highly secure cipher-image. Simulations and security analyses, including key space, key sensitivity, histogram, correlation, information entropy, encryption quality, known-plain and chosen-plain attacks, floating Frequency, differential attack, noise and data loss attacks, demonstrate the robust security of the proposed 2D-CHSLM-IES.

A threefold chaotic image encryption technique for efficacious image data protection

With the profound use of digital contents in education and social media, multimedia content have become a prevalent means of communication and with such rapid increase, information security is still a major concern. This paper provides a summary of the techniques of securing image data focusing primarily on encryption. This paper additionally also explores the contribution of chaos theory in the domain of image encryption and applies a threefold chaotic map sequence to design an image encryption technique. This chaos-based encryption technique renders characteristics like sensitivity, determinacy, and ergodicity, and hence provides a better trade-off between security and computational speed. The efficacy of proposed algorithm is also evaluated based on well-known statistical metrics like Number of Changing Pixel Rate (NPCR), Unified Average Changing Intensity (UACI), Information Entropy, local Entropy, Correlation analysis, key sensitivity analysis, and NIST Randomness test. Furthermore, the key sensitivity analysis is also discussed which is a major part of any encryption algorithm analysis.

An accurate and efficient forecast framework for fine PM2.5 maps using spatiotemporal recurrent neural networks

Commonly used numerical prediction models for PM2.5 maps suffer from low accuracy and high computation cost, which cannot meet the requirements for fine-scale air pollution control. In this study, we propose a framework based on the spatiotemporal recurrent neural network (PredRNN) to efficiently generate accurate 3-h and 6-km PM2.5 maps with a lead time of 5 days. In this framework, two PredRNN networks are initially utilized to forecast PM2.5 concentration at ground monitoring sites and the spatial distribution of aerosol optical depth (AOD) by assimilating the output of numerical prediction model. Subsequently, the 3-h and 6-km PM2.5 forecasted maps with a lead time of 5 days can be inferred by establishing the regression links between the forecasted results of PM2.5 concentration at ground sites and AOD maps. We evaluate the proposed framework in the Beijing-Tianjin-Hebei urban agglomeration region during 2017–2020. Compared with the numerical prediction products of the Copernicus Atmosphere Monitoring Service, the proposed framework achieves higher accuracy, with R2 of 0.83 at the forecast base time and 0.70 at the fifth day. The spatial information richness is also enhanced by approximately 15.67% according to the information entropy metrics. Notably, the proposed framework only requires 1 min for forecasting 5-days PM2.5 maps. These results demonstrate that our framework can efficiently generate accurate and fine PM2.5 maps with a lead time of 5 days.