Weighted Graph Research Articles

A dynamic evaluation of an underground transportation system using image processing and centrality index computation

ABSTRACT The study of transportation networks covers a wide range of topics related to managing services and maintaining structures. In order to represent the topological structure of such a network, we associated a graph to a network. Then some different properties or attributes of the network can be managed as weights to be applied to the graph itself. In addition, different centrality indices can be computed in order to identify nodes or edges that are more important or more exposed to capacity changes (such as, for example, disruptive events). The purpose of this research is to provide a methodology for dynamically evaluating the significance of stations in a transportation network. This is accomplished through two distinct phases of activity. Firstly, we propose a dynamic analysis of the underground transportation system of the city of Milan, Italy. This transportation system is the mobility backbone of the city and counts four lines with 110 links and 107 stations, including 21 junctions (the transfer stations that connect the lines). Two data sets about passenger flows (both entering and leaving stations) are used to calculate the flows on links with a resolution of 1 min. The data sets refer to a week in 2018, without the changes in demand due to the pandemic scenario. Data are processed through an ad hoc written assignment procedure. Secondly, a centrality index is calculated by using passenger flows (entering, exiting, and on-segments) as weights of the underground graph. After maps reporting the outcomes of those calculations are drawn, an image comparison is carried out by using image processing tools and different aggregation intervals, in order to investigate how the importance or exposure of each station changes over time. The findings demonstrate that over time, indices vary by station, with junction stations naturally having the highest values. By increasing the observation interval from 1 min up to 30 min, index changes become progressively smoother, like an application of a low pass filter, suggesting that for certain applications (e.g. those concerning security), aggregating data could lead to misleading conclusions.

Distance-reconstructed dependency enhanced aspect-based sentiment analysis with sentiment strength

Aspect-based sentiment analysis (ABSA) is a fine-grained sentiment analysis task that requires the detection of sentiment polarity towards specific aspects. Dependency tree-based graph convolutional network models (GCN) have been widely applied in ABSA. These studies utilize syntactic analysis tools to derive syntactic dependency graphs, which are then inputted into GCN. It enables iterative learning of sentiment dependency information from contextual words to aspect terms. However, directly using syntactic dependency graphs can lead to two shortcomings. First, the long-distance sentiment information in long sentences will be weakened during GCN iterative computations. Second, the syntactic dependency graphs of short sentences lack sentiment strength information. To address these two shortcomings, we propose a Distance-Reconstructed Dependency Enhanced Sentiment analysis approach with Sentiment Strength based on GCN (DRD-SE-GCN) approach, in which the syntactic dependency graph of long sentences is reconstructed based on distance, thus narrowing the gap between sentiment words and target aspect words. It ensures that the sentiment dependency information carried by the long-distance sentiment words will not be weakened or lost during the GCN iteration. Additionally, the weights of the syntactic dependency graph for short sentences are reassigned so as to carry the strength information of sentiment words. Experimental results on four standard datasets show that our proposed model can effectively improve the accuracy of aspect-level sentiment analysis.

Research on metal surface specular removal algorithm based on unsupervised learning

The highlights on the surface of metal materials can seriously destroy the continuity of the image, produce certain false edges, and cause the texture details in the highlights area to weaken or even disappear, which interferes with the subsequent operations such as surface region segmentation and defect detection. Aiming at the low efficiency, high loss, easy distortion and difficult calibration of metal highlight data, an unsupervised perceptual enhancement network model based on the convolutional neural network (CNN) is proposed. Firstly, the method of generating antagonism is used to generate a large number of metal images with high-light feature information, which is used to increase the number of high-light metal image data sets in the training set. Secondly, a detail enhance model(DEM) and a color enhance model(CEM) are introduced into the context aggregation network to improve the feature detail retention rate in the low resolution weight graphs. Finally, the multi-scale structural similarity function is used to replace the original structural similarity function to solve the insensitive detail when the image size is too large. Experiments show that comparing with other multi-exposure image fusion models, the present model can improve the evaluation index of mutual information and average gradient of fused images by about 10%, and can retain more texture feature information.

Interpretable multi-graph convolution network integrating spatio-temporal attention and dynamic combination for wind power forecasting

Graph neural networks (GNN) can effectively improve wind power forecasting accuracy due to their ability to capture spatial correlations between wind farms. However, conventional GNN-based forecasting models constructing the graphs from only one specific perspective fail to characterize the spatial correlation patterns comprehensively and accurately. Furthermore, their black-box structure leads to deficient interpretability of the forecasting results, which hampers the quantification of forecasting uncertainty and reduces the credibility of applying these forecasting models in practice. To address the above problems, an interpretable ultra-short-term wind power forecasting method is proposed based on multi-graph convolution network integrating spatio-temporal attention and dynamic graph combination. Four undirected weight graphs are constructed to form a multi-graph scheme by considering various geographical and statistical aspects, and then graph convolution network (GCN) and temporal convolution network (TCN) are used to enhance the forecasting performance by leveraging information in both space and time dimensions. Meanwhile, it consists of temporal attention that deeply mines the temporal dependencies and spatial attention that interprets the influence of wind farms on the forecasts. Additionally, to boost the adaptability and generalization capability of the proposed method, an improved reinforcement learning is elaborately designed to combine the results of different graphs by dynamically optimizing their weights to obtain the final forecasts. Experiment results suggest that the proposed method exhibits superior forecasting accuracy and reasonable interpretability compared with other benchmark methods.

Generating functions of non-backtracking walks on weighted digraphs: Radius of convergence and Ihara's theorem

It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results such as Ihara's theorem and the zeta function on graphs. In Grindrod et al. [13], the radius of convergence of the generating function was studied for simple (i.e., undirected, unweighted and with no loops) graphs, and shown to depend on the number of cycles in the graph. In this paper, we use technologies from the theory of polynomial and rational matrices to greatly extend these results by studying the radius of convergence of the corresponding generating function for general, possibly directed and/or weighted, graphs. We give an analogous characterization of the radius of convergence for directed (unweighted or weighted) graphs, showing that it depends on the number of cycles in the undirectization of the graph. We also consider backtrack-downweighted walks on unweighted digraphs, and we prove a version of Ihara's theorem in that case. Finally, for weighted directed graphs, we provide for the first time an exact formula for the radius of convergence, improving a previous result that exhibited a lower bound, and we also prove a version of Ihara's theorem.

A faster deep graph clustering network based on dynamic graph weight update mechanism

A faster deep graph clustering network based on dynamic graph weight update mechanism

Probabilistic Nearest Neighbors Based Locality Preserving Projections for Unsupervised Metric Learning

Dimensionality reduction based unsupervised metric learning consists in finding meaningful compact data representations previously to clustering and classification problems. One of the major aspects of these algorithms is the approximation of the underlying manifold by a weighted graph. A limitation with most manifold learning algorithms is that edge weights in the proximity graph rely heavily on the Euclidean distance, which is known to be quite sensitive to the presence of outliers. In this paper, we propose to improve the Locality Preserving Projections (LPP) algorithm by incorporating a recently proposed graph inference method called Probabilistic Nearest Neighbors (PNN), an extension of the Clustering with Adaptive Neighbors (CAN) approach, used with success in graph-based semi-supervised learning. The proposed PNN-LPP algorithm is able to achieve better classification results than regular LPP, showing competitive performance against state-of-the-art approaches for dimensionality reduction, such as the UMAP algorithm, especially in datasets with a limited number of samples.

Segmentation in Measure Spaces

We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces.

Application graph theory to evaluate the stability of landslide slopes

Evaluation of the stability of slopes is a complex and important engineering task, the solution of which requires the analysis of a significant number of factors. Many different methods of slope stability calculation have been developed to solve this type of problem. However, two groups of methods - limit equilibrium methods and the finite element method (FEM) - have become the most widely used. However, these methods have certain disadvantages. Limit equilibrium methods are limited by the assumptions used during the calculation, including the hypothesis of a solid compartment, which does not allow analyzing the stress-strain state. The FEM of the elements does not make it possible to unambiguously localize the sliding surface of the slope, and the determination of the stability coefficient using the method of reducing the strength of the soil requires a large number of complex iterative calculations. The methods and approaches of graph theory can be used precisely to combat the shortcomings of FEM. The paper examines the basics of graph theory. The main methods of specifying graphs, as well as certain types of graphs with an indication of their key features, are presented. The concept of isomorphism of graphs and some features of their graphical representation are revealed. The article presents the basic idea of using graph theory to calculate the stability of slopes. The main questions that must be solved when applying graph theory to the given type of problem are outlined. Two methods of converting a mesh of finite elements into a graph are considered in detail. The advantages and disadvantages of the proposed methods are analyzed. The transformation of the calculation scheme of an imaginary slope with a given geometry, which was simulated in the LIRA-SAPR software complex, into graphs using the above methods is demonstrated. An overview of the approaches that can be used to create a graph weight function is given.

User tendency-based rating scaling in online trading networks.

Social networks often involve the users rating each other based on their beliefs, abilities, and other characteristics. This is particularly common in e-commerce platforms where buyers rate sellers based on their trustworthiness. However, the rating tends to vary between users due to differences in their individual scoring criteria. For example, in a transaction network, a positive user may give a high rating unless the transaction was unsatisfactory while a neutral user may give a mid-rating, consequently giving the same numeric score to different levels of satisfaction. In this paper, we propose a novel method called user tendency-based rating scaling, which adjusts the current rating (its score) based on the pattern of past ratings. We investigate whether this rating scaling method can classify between "good users" and "bad users" in online trade social networks better when compared with using the original rating scores without scaling. Classifying between good users and bad users is especially important for anonymous rating networks like Bitcoin transaction networks, where users' reputations must be recorded to preclude fraudulent and risky users. We evaluate the proposed rating scaling method by performing user classification, link prediction, and clustering tasks, using three real-world online rating network datasets. We use both the original ratings and the scaled ratings as weights of graphs and use a weighted graph embedding method to find node representations that reflect users' positive and negative information. The experimental results showed that using the proposed rating scaling method outperformed using the original (i.e., unscaled) ratings by up to 17% in classification accuracy, and by up to 2.5% in link prediction based on the AUC ROC measure, and by up to 21% in the clustering tasks based on the Dunn-index.

Evaluation of Eye-Blinking Dynamics in Human Emotion Recognition Using Weighted Visibility Graph

Purpose: Designing an automated emotion recognition system using biosignals has become a hot and challenging issue in many fields, including human-computer interferences, robotics, and affective computing. Several algorithms have been proposed to characterize the internal and external behaviors of the subjects in confronting emotional events/stimuli. Eye movements, as an external behavior, are habitually analyzed in a multi-modality system using classic statistical measures, and the evaluation of its dynamics has been neglected so far.
 Materials and Methods: This experiment intended to provide an innovative single-modality scheme for emotion classification using eye-blinking data. The dynamics of eye-blinking data have been characterized by weighted visibility graph-based indices. The extracted measures were then fed to the different classifiers, including support vector machine, decision tree, k-Nearest neighbor, Adaptive Boosting, and random subset to complete the process of classifying sad, happy, neutral, and fearful affective states. The scheme has been evaluated utilizing the available signals in the SEED-IV database.
 Results: The proposed framework provided significant performance in terms of recognition rates. The highest average recognition rates of > 90% were achieved using the decision tree.
 Conclusion: In brief, our results showed that eye-blinking data has the potential for emotion recognition. The present system can be extended for designing future affect recognition systems.

Online Multi-Agent Forecasting With Interpretable Collaborative Graph Neural Networks.

This article considers predicting future statuses of multiple agents in an online fashion by exploiting dynamic interactions in the system. We propose a novel collaborative prediction unit (CoPU), which aggregates the predictions from multiple collaborative predictors according to a collaborative graph. Each collaborative predictor is trained to predict the agent status by integrating the impact of another agent. The edge weights of the collaborative graph reflect the importance of each predictor. The collaborative graph is adjusted online by multiplicative update, which can be motivated by minimizing an explicit objective. With this objective, we also conduct regret analysis to indicate that, along with training, our CoPU achieves similar performance with the best individual collaborative predictor in hindsight. This theoretical interpretability distinguishes our method from many other graph networks. To progressively refine predictions, multiple CoPUs are stacked to form a collaborative graph neural network. Extensive experiments are conducted on three tasks: online simulated trajectory prediction, online human motion prediction, and online traffic speed prediction, and our methods outperform state-of-the-art works on the three tasks by 28.6%, 17.4%, and 21.0% on average, respectively; in addition, the proposed CoGNNs have lower average time costs in one online training/testing iteration than most previous methods.

Alon–Boppana-Type Bounds for Weighted Graphs

The unraveled ball of radius $r$ centered at a vertex $v$ in a weighted graph $G$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We present a general bound on the maximum spectral radius of unraveled balls of fixed radius in a weighted graph.
 The weighted degree of a vertex in a weighted graph is the sum of weights of edges incident to the vertex. A weighted graph is called regular if the weighted degrees of its vertices are the same. Using the result on unraveled balls, we prove a variation of the Alon–Boppana theorem for regular weighted graphs.

Deterministic remote state preparation with weight graph states in quantum networks

The weight graph states (WGS) usually serve as the imperfect generation of the graph states due to the limitation in experiments. In this paper, we study the deterministic remote state preparation (RSP) protocol by leveraging multiple WGS. First, we introduce the quantum circuit of the entanglement concentration based on the theory of majorization, calculating the entanglement coefficients by applying the Schmidt decomposition onto the bipartite WGS. Then, we establish the positive operator-valued measurement (POVM) that helps to extract available entanglement for the RSP protocol. In three-particle 1D WGS, we demonstrate that the bipartite entanglement between the sender and the receiver depends on the measurement basis selected by the repeater node. Here we find a set of orthogonal bases that retains the entanglement unchanged, which guarantees the robustness of the RSP scheme. In the end, we discuss the performance of our protocol and extend the channel to the multi-particle 1D WGS, illustrating the relationship between the entanglements and the different weights of edges. Our scheme provides a viable method to reuse the imperfect graph states, hoping to contribute to the future study of graph states in quantum networks.

Computation of Wiener and Wiener Polarity Indices of a Class of Nanostar Dendrimer Using Vertex Weighted Graphs

Nanostar dendrimers are tree-like nanostructures with a well-defined, symmetrical architecture. They are built in a step-by-step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell. A weighted graph is a type of graph in which vertices or edges are assigned weights that represent cost, distance, and a variety of other relative measuring units. The weighted graphs have many applications and properties in a mathematical context. The topological indices are numerical values that represent the symmetry of a molecular structure. They have rich applications in theoretical chemistry. Various topological indices can be used to investigate a wide range of properties of chemical compounds with a molecular structure. They are very important in mathematical chemistry, especially in quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies. In this paper, we examine the topological properties of the molecular graphs of nanostar dendrimers. For this purpose, the topological indices, namely, the Wiener index and the Wiener polarity index are computed for a class of nanostar dendrimers.

Fermatean Shortest Route Problem with Interval Fermatean Neutrosophic Fuzzy Arc Length: Formulation and a Modified Dijkstra’s Algorithm

Dijkstra’s algorithm (DA) is a very popular approach for finding the shortest route (SR) in the shortest route problem (SRP). The SRP becomes a challenging and complex problem in real life scenarios. The Fermatean neutrosophic set is a mathematical model that combines Fermatean sets with neutrosophic sets. It can handle the unclear, ambiguous, inconsistent, confusing, and uncertain information that comes from real-world problems. Decision-makers face difficulty accurately determining the precise membership (MG) and non membership levels due to the lack of appropriate data available. The FNS can handle this problem. In this study, we consider the interval FNS to describe the arc weight of a neutrosophic graph (NG). This SRP is called an interval Fermatean neutrosophic shortest route problem (IFNSRP). A modified DA is presented to solve this IFNSRP in an uncertain environment. The effectiveness of the presented method is illustrated with a numerical instance of a neutrosophic network.

Extraction of Representative Scenarios for Photovoltaic Power With Shared Weight Graph Clustering

Extraction of Representative Scenarios for Photovoltaic Power With Shared Weight Graph Clustering

Quafu-Qcover: Explore combinatorial optimization problems on cloud-based quantum computers

We introduce Quafu-Qcover, an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends. Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm (QAOA). It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization (QUBO) model and its corresponding Ising model, which can be subsequently transformed into a weight graph. The core of Qcover relies on a graph decomposition-based classical algorithm, which efficiently derives the optimal parameters for the shallow QAOA circuit. Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers. Compared to a general-purpose compiler, our compiler demonstrates the ability to generate shorter circuit depths, while also exhibiting superior speed performance. Additionally, the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time, utilizing the most recent calibration data from the superconducting quantum devices. This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity. The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time, enabling asynchronous processing. Moreover, it incorporates modules for results preprocessing and visualization, facilitating an intuitive display of solutions for combinatorial optimization problems. We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.

EPAN-SERec: Expertise preference-aware networks for software expert recommendations with knowledge graph

The software knowledge community provides software developers with valuable knowledge of technologies, activities, tools and project management related to software development. However, a large number of unresolved questions and the lack of expert participation have become evident and critical challenges for the software knowledge community. To address the problems of label dependence, interactive data’s sparsity and unassociated knowledge in community-based software expert recommendation, we propose an Expertise Preference-Aware Network model for Software Expert Recommendation (EPAN-SERec) with knowledge graph. Firstly, the software knowledge graph is utilized as an auxiliary resource to provide domain knowledge representation. Secondly, we devise an expertise preference-learning framework by means of deep reinforcement learning that models the historical interactive information of experts and generate the expertise preference weight graph. To better learn expertise preference features, a graph convolutional network (GCN) model with integrated graph self-supervised learning is proposed to optimize the features representation. Finally, software knowledge entity embeddings with semantic information are obtained by exploiting the graph-embedding model, and the final features of question to be answered are obtained by fusing the expertise preference of experts. Extensive experiments on the dataset based on StackOverflow demonstrate that our approach achieves a better outcome than baseline models.

PRUNING MINIMUM SPANNING TREES AND CUTTING LONGEST EDGES TO CONNECT A GIVEN NUMBER OF NODES BY MINIMIZING TOTAL EDGE LENGTH

Background. Whereas in many tasks of designing efficient telecommunication networks, the number of network nodes is limited, the initial choice of nodes is wider. There are more possible locations than factually active tools to be settled to those locations to further satisfy consumers. This induces an available node constraint problem.
 Objective. Given an initial set of planar nodes, the problem is to build a minimum spanning tree connecting a given number of the nodes, which is less than the cardinality of the initial set. Therefore, the available node constraint problem aims at building an optimally minimum spanning tree to connect a given number of planar nodes being less than an initial number of nodes by minimizing the tree length.
 Methods. The initial set of nodes is triangulated. This gives a set of edges, whose lengths are calculated and used as graph weights. A minimum spanning tree is built over this graph. The desired number of nodes is reached by pruning the minimum spanning tree connecting the initial number of nodes, where free edges whose weights are the largest are iteratively removed from the tree. The other approach, the cutting method, removes longest edges off the initial minimum spanning tree, regardless of whether they are free or not.
 Results. Unlike the pruning method, the method of cutting longest edges may result in a minimum spanning tree connecting fewer nodes than the desired number. However, the cutting method often outputs a shorter tree, especially when the edge length varies much. Besides, the cutting method is slower due to it iteratively rebuilds a minimum spanning tree.
 Conclusions. The problem is initially solved by the pruning method. Then the cutting method is used and its solution is compared to the solution by the pruning method. The best tree is shorter. A tradeoff for the nodes and tree length is possible.