Weighted Graph Research Articles

DiffSeer: Difference-Based Dynamic Weighted Graph Visualization.

Existing dynamic weighted graph visualization approaches rely on users' mental comparison to perceive temporal evolution of dynamic weighted graphs, hindering users from effectively analyzing changes across multiple timeslices. We propose DiffSeer, a novel approach for dynamic weighted graph visualization by explicitly visualizing the differences of graph structures (e.g., edge weight differences) between adjacent timeslices. Specifically, we present a novel nested matrix design that overviews the graph structure differences over a time period as well as shows graph structure details in the timeslices of user interest. By collectively considering the overall temporal evolution and structure details in each timeslice, an optimization-based node reordering strategy is developed to group nodes with similar evolution patterns and highlight interesting graph structure details in each timeslice. We conducted two case studies on real-world graph datasets and in-depth interviews with 12 target users to evaluate DiffSeer. The results demonstrate its effectiveness in visualizing dynamic weighted graphs.

Intensifying graph diffusion-based salient object detection with sparse graph weighting

Intensifying graph diffusion-based salient object detection with sparse graph weighting

Graph Laplacian for Heterogeneous Data Clustering in Sensor-Based Internet of Things

Traditional clustering algorithms are not suited for the heterogeneous data of the sensor-based Internet of Things. The accuracy of real-time data processing, in such applications, is further compromised because of the noise and missing values in the data. Considering the need for accurate clustering, a graph Laplacian-based heterogeneous data clustering is proposed in this work. Exploiting the correlation structure of the data, weight graphs are used to generate a graph Laplacian matrix to obtain co-related data points. Eigenvalues are further used to obtain distance-based, accurate clusters. The proposed algorithm is validated on five different real-world data sets and is able to outperform most of the existing algorithms. A detailed mathematical analysis followed by extensive simulation on real-world data sets proves the dexterity of the proposed method, as the performance gap, with respect to the state-of-the-art methods, in terms of accuracy and purity is as high as 30%.

An MMSE graph spectral magnitude estimator for speech signals residing on an undirected multiple graph

The paper uses the K-graphs learning method to construct weighted, connected, undirected multiple graphs, aiming to reveal intrinsic relationships of speech samples in the inter-frame and intra-frame. To benefit from the learned multiple graphs’ property and enhance interpretability, we study the spectral property of speech samples in the joint vertex-frequency domain by using the new graph weight matrix. Moreover, we propose the representation of minimum mean-square error (MMSE) graph spectral magnitude estimator for speech signals residing on undirected multiple graphs. We use the MMSE graph spectral magnitude estimator to improve speech enhancement performance. The numerical simulation results show that the proposed method outperforms the existing methods in graph signal processing (GSP) and the baseline methods for speech enhancement in discrete signal processing (DSP) in terms of PESQ, LLR, output SNR, and STOI results. These results also demonstrate the validity of the learned multiple graphs.

Test-data generation and integration for long-distance e-vehicle routing

Advanced route planning algorithms are one of the key enabling technologies for emerging electric and autonomous mobility. Large realistic data sets are needed to test such algorithms under conditions that capture natural time-varying traffic patterns and corresponding travel-time and energy-use predictions. Further, the time-varying availability of charging infrastructure and vehicle-specific charging-power curves may be necessary to support advanced planning. While some data sets and synthetic data generators capture some of the aspects mentioned above, no integrated testbeds include all of them. We contribute with a modular testbed architecture. First, it includes a semi-synthetic data generator that uses a state-of-the-art traffic simulator, real traffic volume distribution patterns, EV-specific data, and elevation data. These elements support the generation of time-dependent travel-time and energy-use weights in a road-network graph. The generator ensures that the data satisfies the FIFO property, which is essential for time-dependent routing. Next, the testbed provides a thin layer of services that can serve as building blocks for future advanced routing algorithms. The experimental study demonstrates that the testbed can reproduce travel-time and energy-use patterns for long-distance trips similar to commercially available services.

Social Media Recommendation System

Abstract-Social networking sites always have a unique idea to make the connection between two people compact and fast. Famous social networking sites like Facebook, Twitter, LinkedIn, etc. show recommendations of the people and pages to follow, by comparing and connecting various other mutual connections. The recommendations are based on the number of mutual connections and mutual interests between one and the other person, more the number of mutual friends and interests, more the chances of recommendation. Each social media network has a unique set of technical elements, intricate logic, and usage analytics that make up the algorithm that delivers content to its users. Various optimization algorithms and logics are the base of this technology. Our project is based on the graphs and matrix data structures, which will be used to compare the interests of people which are one hop away from adjacent nodes and recommend them as friends suggestions based on their interests. This will be achieved by optimization and maximum weight algorithm. Keywords:Mutual Connection, Optimization Algorithms, Maximum weight graphs.

Peer-to-peer energy trading in energy local area network considering decentralized energy routing

Peer-to-peer (P2P) energy trading is perceived as a promising energy management mechanism for decentralized renewable energy sources. The concept of energy local area network (e-LAN) is proposed as a new system framework for future microgrids to facilitate P2P trading where the end-to-end power delivery is achieved by energy routing. Decentralized P2P trading in e-LAN requires a perfectly competitive market and flexible end-to-end power delivery. In this paper, a new P2P trading model incorporating decentralized energy routing is proposed for e-LAN. The proposed model is composed of a P2P energy market and a loss compensation market. In the P2P energy market, a tripartite graph model is proposed to represent transactions where trading decisions and energy routing are jointly considered for each participant to pursue its optimal benefit. Considering the size problem and nonlinear weights of the tripartite graph, an extended depth-first branch-and-bound algorithm is proposed to prune low-efficiency paths. Based on the pruned tripartite graph, the competitive P2P market is captured by a multi-leader multi-follower Stackelberg game model. A loss compensation market is established to coordinate energy routing paths planned in a decentralized manner. By means of setting the price for utilizing each transmission line, the loss compensation market avoids network congestion and ensure a normal operation of e-LAN. Simulation results show that the proposed model can bring higher utilities for P2P participants compared with the existing P2P trading models in e-LAN. Additionally, the effectiveness of the proposed model in resolving path conflicts in a decentralized fashion and improving computation efficiency, are verified.

The distance backbone of directed networks.

In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We have previously developed a parameter-free, algebraically-principled methodology to uncover such redundancy and reveal the distance backbone of weighted graphs, which has been shown to be important in transmission dynamics, inference of important paths, and quantifying the robustness of networks. However, the method was developed for undirected graphs. Here we expand this methodology to weighted directed graphs and study the redundancy and robustness found in nine networks ranging from social, biomedical, and technical systems. We found that similarly to undirected graphs, directed graphs in general also contain a large amount of redundancy, as measured by the size of their (directed) distance backbone. Our methodology adds an additional tool to the principled sparsification of complex networks and the measure of their robustness.

Mathematical modelling of abnormal account detection on social media platform based on improved edge weight

In order to overcome the problems of traditional methods such as large time consumption, high missed detection rate and low recall rate of detection results, a mathematical modelling method of abnormal account detection on social media platform based on improved edge weight was proposed. The social media platform is regarded as a directed social graph, the node states in the social graph are judged, and the edge weight of the social graph is used to calculate the edge potential. First, take the improved edge weight processing results as the operation constraints of the model. Then, build the abnormal account detection mathematical model. Finally, input the user account information into the model, and output the abnormal account detection results. The experimental results show that the maximum detection time consumption of the proposed method is only 0.88 min, the highest missed detection rate is only 2.9%, and the lowest recall rate can reach 98.49%.

A graph neural network-enhanced knowledge graph framework for intelligent analysis of policing cases.

In this paper, we model a knowledge graph based on graph neural networks, conduct an in-depth study on building knowledge graph embeddings for policing cases, and design a graph neural network-enhanced knowledge graph framework. In detail, we use the label propagation algorithm (LPA) to assist the convolutional graph network (GCN) in training the edge weights of the knowledge graph to construct a policing case prediction method. This improves the traditional convolutional neural network from a single-channel network to a multichannel network to accommodate the multiple feature factors of policing cases. In addition, this expands the perceptual field of the convolutional neural network to improve prediction accuracy. The experimental results show that the multichannel convolutional neural network's prediction accuracy can reach 87.7%. To ensure the efficiency of the security case analysis network, an efficient pairwise feature extraction base module is added to enhance the backbone network, which reduces the number of parameters of the whole network and decreases the complexity of operations. We experimentally demonstrate that this method achieves a better balance of efficiency and performance by obtaining approximate results with 53.5% fewer floating-point operations and 70.2% fewer number parameters than its contemporary work.

Multi-View Diffusion Process for Spectral Clustering and Image Retrieval.

This paper presents a novel approach to multi-view graph learning that combines weight learning and graph learning in an alternating optimization framework. Multi-view graph learning refers to the problem of constructing a unified affinity graph using heterogeneous sources of data representation, which is a popular technique in many learning systems where no prior knowledge of data distribution is available. Our approach is based on a fusion-and-diffusion strategy, in which multiple affinity graphs are fused together via a weight learning scheme based on the unsupervised graph smoothness and utilised as a consensus prior to the diffusion. We propose a novel multi-view diffusion process that learns a manifold-aware affinity graph by propagating affinities on tensor product graphs, leveraging high-order contextual information to enhance pairwise affinities. In contrast to existing multi-view graph learning approaches, our approach is not limited by the quality of initial graphs or the assumption of a latent common subspace among multiple views. Instead, our approach is able to identify the consistency among views and fuse multiple graphs adaptively. We formulate both weight learning and diffusion-based affinity learning in a unified framework and propose an alternating optimization solver that is guaranteed to converge. The proposed approach is applied to image retrieval and clustering tasks on 16 real-world datasets. Extensive experimental results demonstrate that our approach outperforms state-of-the-art methods for both retrieval and clustering on 13 out of 16 datasets.

Absence of backward infinite paths for first-passage percolation in arbitrary dimension

In first-passage percolation (FPP), one places nonnegative random variables (weights) (te) on the edges of a graph and studies the induced weighted graph metric. We consider FPP on Zd for d≥2 and analyze the geometric properties of geodesics, which are optimizing paths for the metric. Specifically, we address the question of existence of bigeodesics, which are doubly-infinite paths whose subpaths are geodesics. It is a famous conjecture originating from a question of Furstenberg and most strongly supported for d=2 that, for continuously distributed i.i.d. weights, there a.s. are no bigeodesics. We provide the first progress on this question in general dimensions under no unproven assumptions. Our main result is that geodesic graphs, introduced in a previous paper of two of the authors, constructed in any deterministic direction a.s. do not contain doubly-infinite paths. As a consequence, one can construct random graphs of subsequential limits of point-to-hyperplane geodesics, which contain no bigeodesics. This gives evidence that bigeodesics, if they exist, cannot be constructed in a translation-invariant manner as limits of point-to-hyperplane geodesics.

Generative Boltzmann Adversarial Network in Manet Attack Detection and QOS Enhancement with Latency

Mobile Ad-Hoc Network (MANET) are considered as self-configured network those does not have any centralized base station for the network monitoring and control. MANET environment does not control architecture for routing for the frequent maintenance of topology. The drastic development of Internet leads to adverse effect of development in MANET for different multimedia application those are sensitive to latency. Upon the effective maintenance of the QoS routing route discovery is performed to calculate queue and contention delay. However, the MANET requirement comprises of the complex procedure to withstand the Quality of Service (QoS) with Artificial Intelligence (AI). In MANET it is necessary to compute the MANET attacks with improved QoS with the reduced latency as existing model leads to higher routing and increased latency. In this paper proposed a Generative Boltzmann Networking Weighted Graph (GBNWG) model for the QoS improvement in MANET to reduce latency. With GBNWG model the MANET model network performance are computed with the weighted graph model. The developed weighted graph computes the routes in the MANET network for the estimation of the available path in the routing metrices. The proposed GBNWG model is comparatively estimated with the conventional QOD technique. Simulation analysis stated that GBNWG scheme exhibits the improved performance in the QoS parameters. The GBNWG scheme improves the PDR value by 12%, 41% reduced control packets and 45% improved throughput value.

Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph

An edge labeling of graph G is a function g from the edge set of graph G to the first natural numbers up to the number of the edge set. Graph G admits a rainbow vertex antimagic coloring if, for any two vertices, there is a path with different colors of all internal vertices. The vertex color of graph G is assigned by vertex weight. The vertex weight of graph G is obtained by summing all edge labels that incident with that vertex. The rainbow vertex antimagic connection number of graph G, denoted by rvac(G) is the smallest number of different colors induced by rainbow vertex antimagic coloring. In this research, we determine the upper bound of the rainbow vertex antimagic connection number (rvac) on a cycle graph (Cn) and create a secured cryptosystem using a modified Affine Cipher based on rainbow vertex antimagic coloring.

Locality preserving triplet discriminative projections for dimensionality reduction

The graph embedding framework is widely used for developing dimensionality-reduction algorithms. Many such supervised algorithms construct an intrinsic graph to compact intra-class samples or describe their local structures and build a penalty graph to increase the separability of inter-class samples. However, in the available intrinsic graph construction, manually selecting a set of appropriate neighbors associated with each sample is challenging. In addition, the construction of a penalty graph may seriously impair the intrinsic structures of the samples. Thus, in an attempt to address these issues, this study proposes an algorithm referred to as locality-preserving triplet discriminative projections. The proposed algorithm comprises locality-preserving and discriminative graphs. First, a weighted least-square function is used to calculate the edge weights of the locality-preserving graph. An improvement of the locality-preserving graph constructed in this study is that suitable neighbors are soft-selected. Meanwhile, the triplets of the samples are exploited for discriminative graph construction. Through the separation of the marginal samples and using less focus on samples with good discriminability, this graph enhances the discriminability with less damage to the intrinsic structure. In addition, to further improve the performance of the discriminative graph, a class-relevant margin is added to separate similar classes. The experimental results on four public datasets show that the proposed algorithm outperforms several other dimensionality reduction methods.

PU-WGCN: Point Cloud Upsampling Using Weighted Graph Convolutional Networks

Point clouds are sparse and unevenly distributed, which makes upsampling a challenging task. The current upsampling algorithm encounters the problem that neighboring nodes are similar in terms of specific features, which tends to produce hole overfilling and boundary blurring. The local feature variability of the point cloud is small, and the aggregated neighborhood feature operation treats all neighboring nodes equally. These two reasons make the local node features too similar. We designed the graph feature enhancement module to reduce the similarity between different nodes as a solution to the problem. In addition, we calculate the feature similarity between neighboring nodes based on both spatial information and features of the point cloud, which is used as the boundary weight of the point cloud graph to solve the problem of boundary blurring. We fuse the graph feature enhancement module with the boundary information weighting module to form the weighted graph convolutional networks (WGCN). Finally, we combine the WGCN module with the upsampling module to form a point cloud upsampling network named PU-WGCN. Compared with other upsampling networks, the experimental results show that PU-WGCN can solve the problems of hole overfilling and boundary blurring and improve the upsampling accuracy.

A novel CapsNet neural network based on MobileNetV2 structure for robot image classification.

Image classification indicates that it classifies the images into a certain category according to the information in the image. Therefore, extracting image feature information is an important research content in image classification. Traditional image classification mainly uses machine learning methods to extract features. With the continuous development of deep learning, various deep learning algorithms are gradually applied to image classification. However, traditional deep learning-based image classification methods have low classification efficiency and long convergence time. The training networks are prone to over-fitting. In this paper, we present a novel CapsNet neural network based on the MobileNetV2 structure for robot image classification. Aiming at the problem that the lightweight network will sacrifice classification accuracy, the MobileNetV2 is taken as the base network architecture. CapsNet is improved by optimizing the dynamic routing algorithm to generate the feature graph. The attention module is introduced to increase the weight of the saliency feature graph learned by the convolutional layer to improve its classification accuracy. The parallel input of spatial information and channel information reduces the computation and complexity of network. Finally, the experiments are carried out in CIFAR-100 dataset. The results show that the proposed model is superior to other robot image classification models in terms of classification accuracy and robustness.

Activity recognition via correlation coefficients based graph with nodes updated by multi-aggregator approach

This paper proposes a graph theory approach to perform the human activity recognition. However, as the most common signal employed for performing the activity recognitions is the motion signal while the motion signal is well structured, ordered and independent one another, the graph theory cannot be applied directly. To address this issue, this paper proposes the correlation coefficient based method for generating the graph using the signals in the UCI-HAR dataset. Here, the predefined thresholds are used for determining whether the nodes are connected or not. The features are updated according to the activities via the multi-aggregation fusion approach. Finally, the random forest is used to classify these activities. To demonstrate the effectiveness of our proposed method, the percentage accuracy and the macro averaged F1 score yielded by our proposed method with the graph weights are compared to those without the graph weights as well as with the multi-aggregator are compared with the mean aggregator. Also, our proposed method is compared to some common methods such as those based on the CNN and SVM. It is found that our proposed method can achieve the percentage accuracy up to 98.74%, which significantly outperforms the existing methods.

Uniform convergence rates for Lipschitz learning on graphs

Abstract Lipschitz learning is a graph-based semisupervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence rates for solutions of the graph infinity Laplace equation as the number of vertices grows to infinity. Their continuum limits are absolutely minimizing Lipschitz extensions (AMLEs) with respect to the geodesic metric of the domain where the graph vertices are sampled from. We work under very general assumptions on the graph weights, the set of labeled vertices and the continuum domain. Our main contribution is that we obtain quantitative convergence rates even for very sparsely connected graphs, as they typically appear in applications like semisupervised learning. In particular, our framework allows for graph bandwidths down to the connectivity radius. For proving this we first show a quantitative convergence statement for graph distance functions to geodesic distance functions in the continuum. Using the ‘comparison with distance functions’ principle, we can pass these convergence statements to infinity harmonic functions and AMLEs.

Object-Based Dynamics: Applying Forman–Ricci Flow on a Multigraph to Assess the Impact of an Object on The Network Structure

Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman–Ricci flow, we assess the object’s impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman–Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist.