Chebyshev Distance Research Articles

Synchronization of directly coupled complex networks with multiweights and multiple delays

This paper investigates the synchronization of directed and multiweighted dynamic networks (DMDNs) with different delay couplings. Time delays in this paper are assumed to exist between the communication process, so communication between different nodes can generate time delays, while communications between the same nodes do not need time delays. Using the normalized left eigenvectors (NLEigs) corresponding to the zero eigenvalue of the coupling matrix, we prove that if both the time delay and the Chebyshev distance between NLEigs are small enough, all coupling matrices can accelerate the synchronization. Moreover, we also investigate the consensus for directed and multiweighted multi-agents with arbitrary bounded/unbounded time delays. Furthermore, the corresponding pinning control synchronization and consensus problem are also investigated, and sufficient synchronization criteria are also obtained. Numerical simulations are presented to show the validity of obtained theoretical results.

Improved indoor localization using k‐medoids and k‐nearest neighbour algorithms with context similarity coefficient‐based fingerprint similarity metric

AbstractFingerprint database clustering and localization using k‐medoids and k‐nearest neighbour (k‐NN) algorithms respectively typically use distance‐based fingerprint similarity metrics, with their performances dependent on the type of distance metric used. This paper proposes employing a pattern‐based metric, the context similarity coefficient (CSC), for both algorithms instead of traditional distance‐based metrics. The CSC accounts for fingerprint behaviour and the non‐linear relationships among fingerprints during the similarity measurement. The performance of both algorithms with the CSC as the similarity metric is evaluated on four publicly available fingerprint databases, using position root mean square error (RMSE) and silhouette score as performance metrics. These results are compared to those of the same algorithms using five distance‐based metrics: Euclidean, square Euclidean, Manhattan, cosine, and Chebyshev distances. The k‐medoids algorithm with CSC shows moderate clustering performance compared to the five distance‐based metrics considered. However, when combined with the k‐NN algorithm also using CSC, it achieves the highest localization accuracy, with at least a 29% improvement in position RMSE across all four databases. The results indicate that while k‐medoids with CSC may not create well‐separated clusters, combining it with the k‐NN algorithm with CSC as its similarity metric significantly enhances localization accuracy compared to distance‐based metrics.

Generative Models for Grid-Based and Image-Based Pathfinding

Pathfinding is a challenging problem which generally asks to find a sequence of valid moves for an agent provided with a representation of the environment, i.e. a map, in which it operates. In this work, we consider pathfinding on binary grids and on image representations of the digital elevation models. In the former case, the transition costs are known, while in latter scenario, they are not. A widespread method to solve the first problem is to utilize a search algorithm that systematically explores the search space to obtain a solution. Ideally, the search should also be complemented with an informative heuristic to focus on the goal and prune the unpromising regions of the search space, thus decreasing the number of search iterations. Unfortunately, the widespread heuristic functions for grid-based pathfinding, such as Manhattan distance or Chebyshev distance, do not take the obstacles into account and in obstacle-rich environments demonstrate inefficient performance. As for pathfinding with image inputs, the heuristic search cannot be applied straightforwardly as the transition costs, i.e. the costs of moving from one pixel to the other, are not known. To tackle both challenges, we suggest utilizing modern deep neural networks to infer the instance-dependent heuristic functions at the pre-processing step and further use them for pathfinding with standard heuristic search algorithms. The principal heuristic function that we suggest learning is the path probability, which indicates how likely the grid cell (pixel) is lying on the shortest path (for binary grids with known transition costs, we also suggest another variant of the heuristic function that can speed up the search). Learning is performed in a supervised fashion (while we have also explored the possibilities of end-to-end learning that includes a planner in the learning pipeline). At the test time, path probability is used as the secondary heuristic for the Focal Search, a specific heuristic search algorithm that provides the theoretical guarantees on the cost bound of the resultant solution. Empirically, we show that the suggested approach significantly outperforms state-of-the-art competitors in a variety of different tasks (including out-of-the distribution instances).

Data-Driven Dynamic Security Partition Assessment of Power Systems Based on Symmetric Electrical Distance Matrix and Chebyshev Distance

A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a dynamic security partition assessment method, aiming to develop accurate and incrementally updated DSA models with simple structures. Firstly, the power grid is self-adaptively partitioned into several local regions based on the mean shift algorithm. The input of the mean shift algorithm is a symmetric electrical distance matrix, and the distance metric is the Chebyshev distance. Secondly, high-level features of operating conditions are extracted based on the stacked denoising autoencoder. The symmetric electrical distance matrix is modified to represent fault locations in local regions. Finally, DSA models are constructed for fault locations in each region based on the radial basis function neural network (RBFNN) and Chebyshev distance. An online incremental updating strategy is designed to enhance the model adaptability. With the simulation software PSS/E 33.4.0, the proposed dynamic security partition assessment method is verified in a simplified provincial system and a large-scale practical system in China. Test results demonstrate that the Chebyshev distance can improve the partition quality of the mean shift algorithm by approximately 50%. The RBFNN-based partition assessment model achieves an accuracy of 98.96%, which is higher than the unified assessment with complex models. The proposed incremental updating strategy achieves an accuracy of over 98% and shortens the updating time to 30 s, which can meet the efficiency of online application.

Discrete Homogeneous and Non-Homogeneous Markov Chains Enhance Predictive Modelling for Dairy Cow Diseases.

Modelling and predicting dairy cow diseases empowers farmers with valuable information for herd health management, thereby decreasing costs and increasing profits. For this purpose, predictive models were developed based on machine learning algorithms. However, machine-learning based approaches require the development of a specific model for each disease, and their consistency is limited by low farm data availability. To overcome this lack of complete and accurate data, we developed a predictive model based on discrete Homogeneous and Non-homogeneous Markov chains. After aggregating data into categories, we developed a method for defining the adequate number of Markov chain states. Subsequently, we selected the best prediction model through Chebyshev distance minimization. For 14 of 19 diseases, less than 15% maximum differences were measured between the last month of actual and predicted disease data. This model can be easily implemented in low-tech dairy farms to project costs with antibiotics and other treatments. Furthermore, the model's adaptability allows it to be extended to other disease types or conditions with minimal adjustments. Therefore, including this predictive model for dairy cow diseases in decision support systems may enhance herd health management and streamline the design of evidence-based farming strategies.

Comparative Analysis of Leak Detection Methods Using Hydraulic Modelling and Sensitivity Analysis in Rural and Urban–Rural Areas

Water scarcity is a significant global challenge, exacerbated by leakages in water distribution networks. This paper addresses the challenge of detecting leakages in rural and urban–rural water supply systems through hydraulic modelling and a sensitivity analysis. Two distinct real-world network models were studied to assess real and simulated leakage scenarios varying in location and magnitude. A distinct leakage detection approach utilizing outflow measurements from hydrants was tested. Additionally, the effectiveness of various statistical measures—such as correlation, angular closeness, Euclidean distance, Manhattan distance, Chebyshev distance, cosine similarity, and Spearman correlation—were evaluated to determine their efficacy in leakage detection. Different methods for identifying leak candidates were explored and compared, either by selecting a single leak candidate based on similarity measures or by identifying a group of candidates to mark leak hotspots. Density-based spatial clustering of applications with noise was used to assess the number of potential leak candidate groups. The study’s findings contribute to the optimization of leak detection strategies in water supply networks, particularly in rural settings, where detection is challenging due to scarce measurement datasets, budget restrictions, and operational constraints.

Identification of generator coherency in power systems with wind farm

In the context of the "dual carbon" goal, the penetration rate of new energy represented by wind power is gradually increasing. The large-scale grid connection of wind power makes the power system more complex and uncertain. The output of wind farms changes the system flow, indirectly affecting the power angle characteristics of synchronous generators, and thereby changing the coherence between generators. Affects synchronous generator homology identification. This paper proposes a generator homology identification method for power systems containing wind farms, in response to the problem that the existing methods for identifying unit homology have not taken into account the adverse effects of wind farms on identification results. Translate the influence of wind farms on the homology of synchronous generators into the contraction admittance matrix as a static electrical distance indicator; Select dynamic data reflecting the homology of synchronous generators after disturbance, and form four dynamic indicators to measure the power angle increment curve between each generator: Euclidean distance, Chebyshev distance, grey correlation, and correlation coefficient; By using the combination weighting method to determine the weights of each indicator, a comprehensive similarity matrix is formed, and the optimal clustering results are determined using fuzzy system clustering and F-statistical values. Finally, the effectiveness of the proposed method was verified using EPRI-9 node system, EPRI-36 node system, and IEEE68 node system as examples.© 2017 Elsevier Inc. All rights reserved.

Secure computation protocol of Chebyshev distance under the malicious model

Secure multi-party computation of Chebyshev distance represents a crucial method for confidential distance measurement, holding significant theoretical and practical implications. Especially within electronic archival management systems, secure computation of Chebyshev distance is employed for similarity measurement, classification, and clustering of sensitive archival information, thereby enhancing the security of sensitive archival queries and sharing. This paper proposes a secure protocol for computing Chebyshev distance under a semi-honest model, leveraging the additive homomorphic properties of the NTRU cryptosystem and a vector encoding method. This protocol transforms the confidential computation of Chebyshev distance into the inner product of confidential computation vectors, as demonstrated through the model paradigm validating its security under the semi-honest model. Addressing potential malicious participant scenarios, a secure protocol for computing Chebyshev distance under a malicious model is introduced, utilizing cryptographic tools such as digital commitments and mutual decryption methods. The security of this protocol under the malicious model is affirmed using the real/ideal model paradigm. Theoretical analysis and experimental simulations demonstrate the efficiency and practical applicability of the proposed schemes.

Centroidous Method for Determining Objective Weights

When using multi-criteria decision-making methods in applied problems, an important aspect is the determination of the criteria weights. These weights represent the degree of each criterion’s importance in a certain group. The process of determining weight coefficients from a dataset is described as an objective weighting method. The dataset considered here contains quantitative data representing measurements of the alternatives being compared, according to a previously determined system of criteria. The purpose of this study is to suggest a new method for determining objective criteria weights and estimating the proximity of the studied criteria to the centres of their groups. It is assumed that the closer a criterion is to the centre of the group, the more accurately it describes the entire group. The accuracy of the description of the entire group’s priorities is interpreted as the importance, and the higher the value, the more significant the weight of the criterion. The Centroidous method suggested here evaluates the importance of each criterion in relation to the centre of the entire group of criteria. The stability of the Centroidous method is examined in relation to the measures of Euclidean, Manhattan, and Chebyshev distances. By slightly modifying the data in the original normalised data matrix by 5% and 10% 100 and 10,000 times, stability is examined. A comparative analysis of the proposed Centroidous method obtained from the entropy, CRITIC, standard deviation, mean, and MEREC methods was performed. Three sets of data were generated for the comparative study of the methods, as follows: the mean value for alternatives with weak and strong differences and criteria with linear dependence. Additionally, an actual dataset from mobile phones was also used for the comparison.

ANALYZING THE EFFECT OF SIMILARITY FUNCTIONS ON PARTITIONING AROUND MEDOIDS ALGORITHM FOR MAPPING DHF DISEASE IN NORTH SUMATRA

Dengue hemorrhagic fever (DHF) is an acute febrile illness caused by a virus through the Aedes mosquito. North Sumatra is among the three provinces with the highest incidence and mortality rates in Indonesia. Mapping of DHF cases is very important in efforts to control and prevent the disease. The Partitioning Around Medoid (PAM) algorithm is commonly used to cluster DHF cases. The idea of PAM is a clustering algorithm with a similarity-based approach to grouping objects in one cluster. There are two main focuses in the research: mapping regencies/cities based on dengue case information and analyzing the performance of several similarity functions. The dataset includes variables of incidence rate (IR), case fatality rate (CFR), larva-free rate (ABJ), and population, obtained from the North Sumatra Provincial Health Office and the Central Statistics Agency (BPS). The analysis showed that three clusters were formed in North Sumatra Province. The first cluster includes regencies/cities such as Langkat, Deli Serdang, Karo, Simalungun, Dairi, Samosir, Humbahas, North Labuhan Batu, North Padang Lawas, South Labuhan Batu, Padang Sidempuan, Nias, South Nias, North Nias, and Sibolga. The second cluster consists of regencies/cities such as Medan, Binjai, Sedang Berdagai, Tebing Tinggi, Batubara, Asahan, Tanjung Balai, Labuhan Batu, Toba, North Tapanuli, Central Tapanuli, Gunungsitoli, and West Nias. The third cluster includes the regencies of South Tapanuli and Mandailing Natal. In addition, an evaluation was conducted using the Silhouette Index to measure the quality of the clustering. Based on the comparison using distance methods (Euclidean distance, Manhattan distance, Minkowski distance, and Chebyshev distance), the highest Silhouette Index value was obtained using Chebyshev distance, which amounted to 0.527554. This value indicates reasonable cluster quality. Thus, this study contributes to the mapping of DHF cases in North Sumatra Province and can be the basis for decision-making in overcoming the disease.

An Improved Dempster–Shafer Evidence Theory Based on the Chebyshev Distance and Its Application in Rock Burst Prewarnings

An Improved Dempster–Shafer Evidence Theory Based on the Chebyshev Distance and Its Application in Rock Burst Prewarnings

A Methodological Approach for Gap Filling of WFV Gaofen-1 Images from Spatial Autocorrelation and Enhanced Weighting

Clouds and cloud shadow cover cause missing data in some images captured by the Gaofen-1 Wide Field of View (GF-1 WFV) cameras, limiting the extraction and analysis of the image information and further applications. Therefore, this study proposes a methodology to fill GF-1 WFV images using the spatial autocorrelation and improved weighting (SAIW) method. Specifically, the search window size is adaptively determined using Getis-Ord Gi* as a metric. The spatial and spectral weights of the pixels are computed using the Chebyshev distance and spectral angle mapper to better filter the suitable similar pixels. Each missing pixel is predicted using linear regression with similar pixels on the reference image and the corresponding similar pixel located in the non-missing region of the cloudy image. Simulation experiments showed that the average correlation coefficient of the proposed method in this study is 0.966 in heterogeneous areas, 0.983 in homogeneous farmland, and 0.948 in complex urban areas. It suggests that SAIW can reduce the spread of errors in the gap-filling process to significantly improve the accuracy of the filling results and can produce satisfactory qualitative and quantitative fill results in a wide range of typical land cover types and has extensive application potential.

Formula omitted]-adic distance and [formula omitted]-Nearest Neighbor classification

The k-Nearest Neighbor (k-NN) is a well-known supervised learning algorithm. The effect of the distance used in the analysis on the k-NN performance is very important. According to Ostrowski’s theorem, there are only two nontrivial absolute values on the field of rational numbers, Q, which are the usual absolute value and the p-adic absolute value for a prime p. In view of this theorem, the p-adic absolute value motivates us to calculate the p-adic distance between two samples for the k-NN algorithm. In this study, the p-adic distance on Q was coupled with the k-NN algorithm and was applied to 10 well-known public datasets containing categorical, numerical, and mixed (both categorical and numerical) type predictive attributes. Moreover, the p-adic distance performance was compared with Euclidean, Manhattan, Chebyshev, and Cosine distances. It was seen that the average accuracy obtained from the p-adic distance ranks first in 5 out of 10 datasets. Especially, in mixed datasets, the p-adic distance gave better results than other distances. For r=1,2,3, the effect of the r-decimal values of the number for the p-adic calculation was examined on numerical and mixed datasets. In addition, the p parameter of the p-adic distance was tested with prime numbers less than 29, and it was found that the average accuracy obtained for each p was very close to each other, especially in categorical and mixed datasets. Also, it can be concluded that k-NN with the p-adic distance may be more suitable for binary classification than multi-class classification.

On the handling of inconsistent systems of max-min fuzzy relational equations

In this article, we study the inconsistency of systems of max-min fuzzy relational equations. We first compute by an explicit analytical formula the Chebyshev distance (defined by the L-infinity norm) between the second member of an inconsistent system and the set of second members of consistent systems defined with the same matrix: that of the inconsistent system. Then we study the set of Chebyshev approximations of the second member of the inconsistent system, which are the second members of the consistent systems defined with the same matrix as the inconsistent system, whose distance to the second member of the inconsistent system is equal to the computed Chebyshev distance. This set is non-empty and associated to the approximate solutions set of the inconsistent system in the following sense: an approximate solution is a solution vector of a consistent system defined with the same matrix as the inconsistent system, whose second member is a Chebyshev approximation of the second member of the inconsistent system. As main results, we describe both the structure of the approximate solutions set and that of the set of the Chebyshev approximations of the second member of the inconsistent system. As an application of our results, we show that our work can help to find approximate values for the rule parameters of a possibilistic rule-based system.

A new spectral distance based on adaptive selection algorithm for non-stationary time series

We propose a distance metric to quantify the dissimilarity between time series from the perspective of the frequency domain, especially non-stationary time series, called the Wasserstein Hilbert marginal spectral distance (WHMS). It calculates the Wasserstein distance between the Hilbert marginal spectral (HMS) of the time series, where HMS is the integral of Hilbert spectrum. Hilbert spectrum is obtained by the Hilbert transform performed on the intrinsic mode functions (IMFs) generated after the Empirical Mode Decomposition (EMD) operation. On this basis, we propose an IMF adaptive selection algorithm to improve the feature extraction accuracy of the HMS, free from a large number of prior experiments to set the threshold. We demonstrate that WHMS distance can be used as a general measure of time series from both theoretical and practical aspects. Combined with multidimensional scaling (MDS), we comprehensively evaluate the proposed method through simulation experiments and empirical data. The results confirm the good applicability of the WHMS distance combined with the IMF adaptive selection algorithm, which can distinguish different types of complex systems, is robust to noise, and is superior to Wasserstein–Fourier (WF) distance, Wasserstein–Fourier distance with short time Fourier transform (STFT), Euclidean distance and Chebyshev distance.

An edge detection method of colony image based on mediocrity ant colony algorithm

The colony is one of the important research objects in microbial technology, which can realize the evaluation of food safety level, environmental pollution degree, therapeutic effect of medical drugs, and characteristics of agricultural fungicides. Traditional colony image research requires human visual observation and statistics, which will result in low work efficiency and high work intensity. Colony image edge detection is an important basis for colony image research. Traditional edge detection operators cannot meet the accuracy requirements of the detection results. This paper proposes a Mediocrity Ant Colony Algorithm (MACA) to achieve edge detection of colony images. MACA combines the mediocrity rule, uses empirical functions to establish a pheromone database that can be used as a pheromone update reference table, adopts the Chebyshev distance as a weight that affects pheromone update, and combines heuristic information acquisition with maximum variance classification method and local path weights. The method that jointly affects the ant transition probability incorporates feedback rules for obtaining path weights to improve the edge detection effect. By performing edge detection simulation experiments on six colonies of three types of bacteria, and comparing with the classic edge detection operators and two classic ant colony edge detection algorithms, the detection performance, detection results and running time are proposed. The stability and accuracy of MACA algorithm is better than other methods, and the ideal results of the colony image edge detection by the ant colony algorithm are obtained.

3D inversion of magnetic gradient data based on equivalent source weighting method

3D magnetic inversion is an important method for detecting underwater or underground magnetic objects, which can obtain the physical parameters and geometric features of the target. In order to solve the problem of smooth inversion results of L2 norm regularization, this paper proposes a three-dimensional inversion method of magnetic gradient data based on equivalent source weighting. First, the center position of the magnetic object is estimated using the correlation imaging method, and then the equivalent source weighting function is constructed based on the acquired center position. The weights are calculated according to the distance from the grid to the center of the magnetic object. The further away the grid is, the higher weight will be given. The Euclidean distance and Chebyshev distance are used for calculating the weights of grids. Finally, the equivalent source weighting function is added to the total objective function and solved by conjugate gradient method. Simulation experiments show that the equivalent source weighting function can reduce the root-mean-square error of the inversion results and improve the structural similarity. Compared with the Euclidean distance, the inversion result of the edges and corners of cubic magnetic body model is better when weighted with the Chebyshev distance. The proposed method does not require iterative solving and can avoid generating too smooth results, which improves the inversion accuracy.

A sophisticated Drowsiness Detection System via Deep Transfer Learning for real time scenarios

<abstract> <p>Driver drowsiness is one of the leading causes of road accidents resulting in serious physical injuries, fatalities, and substantial economic losses. A sophisticated Driver Drowsiness Detection (DDD) system can alert the driver in case of abnormal behavior and avoid catastrophes. Several studies have already addressed driver drowsiness through behavioral measures and facial features. In this paper, we propose a hybrid real-time DDD system based on the Eyes Closure Ratio and Mouth Opening Ratio using simple camera and deep learning techniques. This system seeks to model the driver's behavior in order to alert him/her in case of drowsiness states to avoid potential accidents. The main contribution of the proposed approach is to build a reliable system able to avoid false detected drowsiness situations and to alert only the real ones. To this end, our research procedure is divided into two processes. The offline process performs a classification module using pretrained Convolutional Neural Networks (CNNs) to detect the drowsiness of the driver. In the online process, we calculate the percentage of the eyes' closure and yawning frequency of the driver online from real-time video using the Chebyshev distance instead of the classic Euclidean distance. The accurate drowsiness state of the driver is evaluated with the aid of the pretrained CNNs based on an ensemble learning paradigm. In order to improve models' performances, we applied data augmentation techniques for the generated dataset. The accuracies achieved are 97 % for the VGG16 model, 96% for VGG19 model and 98% for ResNet50 model. This system can assess the driver's dynamics with a precision rate of 98%.</p> </abstract>

Toward the Believability of Non-Player Characters (NPC) Movement in Video Games

In video games, artificial intelligence is the effort of going beyond scripted interactions, however complex into the arena of truly interactive systems. To make a game world appear more real, these video games must be responsive, adaptive, and intelligent. For example, in real time strategy games, if there is an enemy seekinghunting the player, it will be moving in paths, turning around and even maybe jumping in order to find the player. In this case, if the enemy actsmoves more real like human, it will be a benefit for making the game more attractive and exciting. This paper aims to develop a fast, intelligent, and realistic pathfinding approach that makes a user feel that heshe is playing with a human being instead of a machine. To achieve this, this paper presents a Heap Heuristic A* Algorithm as an enhancement of A* algorithm, in which the Chebyshev distance is used to control the smoothness of the resulted path and heapsort algorithm to sort the nodes easily without a lot of memory consumption. Compared to the pervious improved A* algorithms, the proposed algorithm produces a smoother path while consuming less memory to get a final result of human like movement. The experiments results showed that the proposed algorithm reduced the computing time by 66.6% using a grid size of 200*200 compared with A*MOD algorithm. Also, they showed that the proposed work takes almost 91ms to find the path compared to 363 ms and 116 ms when Native A* and A*MOD algorithms are used, respectively, Furthermore, the proposed algorithm performance remains stable in the case of increasing the number of visited nodes, despite the changing order of obstacles.

Clustering Performance Analysis of the K-Medoids Algorithm for Improved Fingerprint-Based Localization

Fingerprint-based localization, which uses received signal strength (RSS) measurements from spatially deployed wireless access points (APs), is a popular technique for indoor positioning. The size of the fingerprint database has a significant impact on the accuracy of localization. The higher the density of the fingerprint database, the more accurate the localization, but the longer the localization time. Clustering is one of the techniques used such systems to improve localization accuracy and reduce localization time. To cluster fingerprints, the majority of clustering techniques employ a distance-based fingerprint similarity metric. However, the choice of distance metric has a significant impact on the performance of the clustering algorithm. Using four publicly available RSS-based fingerprint databases, this paper investigates the clustering performance of the k-medoids algorithm using six distance metrics, namely Euclidean, Manhattan, cosine, Mahalanobis, Chebyshev, and Canberra distance. Using the silhouette score as a performance metric, the cosine and Euclidean distance metrics outperform the others, with the highest silhouette score values of about 0.38, 0.43, 0.34, and 0.31 on the SEUG_IndoorLoc, IIRC_IndoorLoc, MSI_IndoorLoc, and IPIN_2019_PIEP_UM databases, respectively. It demonstrates that on these four databases, using Euclidean distance as well as the angle between fingerprint measurement vectors is the best option for generating efficient clusters that will result in high localization accuracy and low localization time.