Plain Graphs Research Articles

New Solitary Waves for Thin-Film Ferroelectric Material Equation Arising in Dielectric Materials

Abstract In this paper, the thin-film ferroelectric material equation (TFFME), which enables the propagation of solitary polarisation in thin-film ferroelectric materials is investigated, will be expressed through the non-linear evolution models. Ferroelectrics are dielectric materials that explain wave propagation non-linear demeanors. The non-linear wave propagation form is administrated by TFFME. To investigate the characterisations of new waves and solitonic properties of the TFFME, the modified exponential Jacobi technique and rational exp(−ϕ(η))-expansion technique are used. Plenty of alternative responses may be achieved by employing individual formulas; each of these solutions is offered by some plain graphs. The validity of such schemes and solutions may be exhibited by assessing how well the relevant schemes and solutions match up. The effect of the free variables on the manner of acting of reached plots to a few solutions in the exact forms was also explored depending upon the nature of non-linearities. The descriptive characteristics of the reached results are presented and analysed by some density, two- and three-dimensional figures. We believe that our results would pave the way for future research generating optical memories based on non-linear solitons.

DeGAN - Decomposition-based unified anomaly detection in static networks

Graph anomaly detection aims to identify anomalous occurrences in networks. However, this is more challenging than the traditional anomaly detection problem because anomalies in graphs can manifest in three different forms: anomalous nodes, anomalous edges, and anomalous sub-graphs. It is crucial to detect all these anomaly types within a single framework to provide a unified solution to the graph anomaly detection task. The main objective of this study is to propose a model that is capable of detecting all static graph anomalies in a single architecture across various domains. In this paper, we introduce DeGAN (Decomposition-based unified Graph ANomaly detection), a novel framework for unified graph anomaly detection in static networks. DeGAN combines two deep learning concepts with graph decomposition to identify anomalous graph objects: a graph neural network and an adversarial autoencoder. DeGAN is featured with its capability to detect anomalies in a single process, and adopting graph decomposition has improved performance compared to the traditional adversarial learning approach. DeGAN is evaluated with six real-world datasets to demonstrate that our framework can work in multiple domains. Experimental results demonstrate that DeGAN is capable of detecting anomalous nodes, edges, and sub-graphs within a single model. Additionally, the effectiveness of the sub-components of DeGAN has been demonstrated through experimentation. Even though DeGAN is proposed for plain graphs, it can be extended to attributed and dynamic graphs.

Scalable High-Quality Hypergraph Partitioning

Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across k different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising efficient and scalable shared-memory algorithms for all components employed in the best sequential solvers without compromises with regards to solution quality. This work presents the scalable and high-quality hypergraph partitioning framework Mt-KaHyPar . Its most important components are parallel improvement algorithms based on the FM algorithm and maximum flows, as well as a parallel clustering algorithm for coarsening – which are used in a multilevel scheme with log (n) levels. As additional components, we parallelize the n -level partitioning scheme, devise a deterministic version of our algorithm, and present optimizations for plain graphs. We evaluate our solver on more than 800 graphs and hypergraphs, and compare it with 25 different algorithms from the literature. Our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration achieves the same solution quality as the best sequential partitioner KaHyPar , while being an order of magnitude faster with ten threads. Thus, two of our configurations occupy all fronts of the Pareto curve for hypergraph partitioning. Furthermore, our solvers exhibit good speedups, e.g., 29.6x in the geometric mean on 64 cores (deterministic), 22.3x (log (n) -level), and 25.9x ( n -level).

Autonomous hierarchy creation for computationally feasible near-optimal path planning in large environments

Mobile robots have increasingly been used in warehouses, factories, open spaces, on roads, and urban areas to transport goods and people. Path planning in complex and large environments using classical graph-based search is computationally too intensive. One of the main challenges of mobile robotics is describing the large robot’s workspaces with a reduction of graph complexity and improvement of path planning efficiency. A representation by a hierarchical graph (H-graph) facilitates graph creation and reduces the complexity of path planning. In this paper, we present an algorithm for autonomously generating a hierarchical graph of the environment from floor plans. The hierarchical abstraction depicts the environment in levels, from the most detailed to the most abstract representation of the environment, where pre-computed partial paths at the most detailed level are graph edges at a higher level. We use the E* algorithm to find partial paths in the most detailed abstraction level, and we propose the extraction of higher levels automatically from lower levels. We verified the proposed H-graph creation on three cases: our University premises as an example of a multi-building environment, a large warehouse with a lot of shelves, and an outdoor urban environment which is represented by a city map. All cases result in five abstract levels. The result shows that the path planning algorithm searches about 50 to 800 times fewer nodes when using the H-graph as the environment representation than when using a plain graph representing the entire environment as an occupancy grid map.

Pre-Train and Learn: Preserving Global Information for Graph Neural Networks

Graph neural networks (GNNs) have shown great power in learning on attributed graphs. However, it is still a challenge for GNNs to utilize information faraway from the source node. Moreover, general GNNs require graph attributes as input, so they cannot be appled to plain graphs. In the paper, we propose new models named G-GNNs (Global information for GNNs) to address the above limitations. First, the global structure and attribute features for each node are obtained via unsupervised pre-training, which preserve the global information associated to the node. Then, using the global features and the raw network attributes, we propose a parallel framework of GNNs to learn different aspects from these features. The proposed learning methods can be applied to both plain graphs and attributed graphs. Extensive experiments have shown that G-GNNs can outperform other state-of-the-art models on three standard evaluation graphs. Specially, our methods establish new benchmark records on Cora (84.31\%) and Pubmed (80.95\%) when learning on attributed graphs.

Land Deformation Prediction via Slope-Aware Graph Neural Networks

We introduce a slope-aware graph neural network (SA-GNN) to leverage continuously monitored data and predict the land displacement. Unlike general GNNs tackling tasks in the plain graphs, our method is capable of generalizing 3D spatial knowledge from InSAR point clouds. Specifically, we structure of the land surface, while preserving the spatial correlations among adjacent points. The point cloud can then be efficiently converted to a near-neighbor graph where general GNN methods can be applied to predict the displacement of the slope surface. We conducted experiments on real-world datasets and the results demonstrate that SA-GNN outperforms existing 3D CNN and point GNN methods.

Ontology-Mediated SPARQL Query Answering over Knowledge Graphs

Abstract Ontology-Mediated Query Answering (OMQA) is a well-established framework to answer queries over Knowledge Graphs (KGs), enriched with rdfs or owl ontologies. OMQA was originally designed for Unions of Conjunctive Queries (UCQs), and based on certain answers. More recently, OMQA has been extended to sparql queries, but to our knowledge, none of the efforts made in this direction (either in the literature, or the so-called W3C sparql entailment regimes) is able to capture both certain answers for UCQs and the standard interpretation of sparql over a plain graph. We formalize these as requirements to be met by any semantics that aims at conciliating certain answers and sparql answers, and extend these with three additional requirements. Then we define two semantics that satisfies all requirements for sparql queries with select , union , join , and optional . Finally, we investigate the combined complexity of query answering under these semantics over a KG enriched with a DL-Lite R ontology, showing that for several fragments of sparql , known upper-bounds for query answering over a plain KG are matched.

BiNeTClus

We investigate the problem of community detection in bipartite networks that are characterized by the presence of two types of nodes such that connections exist only between nodes of different types. While some approaches have been proposed to identify community structures in bipartite networks, there are a number of problems still to solve. In fact, the majority of the proposed approaches suffer from one or even more of the following limitations: (1) difficulty in detecting communities in the presence of many non-discriminating nodes with atypical connections that hide the community structures, (2) loss of relevant topological information due to the transformation of the bipartite network to standard plain graphs, and (3) manually specifying several input parameters, including the number of communities to be identified. To alleviate these problems, we propose BiNeTClus, a parameter-free community detection algorithm in bipartite networks that operates in two phases. The first phase focuses on identifying an initial grouping of nodes through a transactional data model capable of dealing with the situation that involves networks with many atypical connections, that is, sparsely connected nodes and nodes of one type that massively connect to all other nodes of the second type. The second phase aims to refine the clustering results of the first phase via an optimization strategy of the bipartite modularity to identify the final community structures. Our experiments on both synthetic and real networks illustrate the suitability of the proposed approach.

(Hyper)graph Kernels over Simplicial Complexes.

Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered. In this paper, four (hyper)graph kernels are proposed and their efficiency and effectiveness are compared in a twofold fashion. First, by inferring the simplicial complexes on the top of underlying graphs and by performing a comparison among 18 benchmark datasets against state-of-the-art approaches; second, by facing a real-world case study (i.e., metabolic pathways classification) where input data are natively represented by hypergraphs. With this work, we aim at fostering the extension of graph kernels towards hypergraphs and, more in general, bridging the gap between structural pattern recognition and the domain of hypergraphs.

Incorporating User's Preference into Attributed Graph Clustering

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GU</small> ) and Attribute Unimodality ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AU</small> ). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination as <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Compactness</small> . Further, we propose LOCLU to optimize the <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Compactness</small> score. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

Coupled Node Similarity Learning for Community Detection in Attributed Networks.

Attributed networks consist of not only a network structure but also node attributes. Most existing community detection algorithms only focus on network structures and ignore node attributes, which are also important. Although some algorithms using both node attributes and network structure information have been proposed in recent years, the complex hierarchical coupling relationships within and between attributes, nodes and network structure have not been considered. Such hierarchical couplings are driving factors in community formation. This paper introduces a novel coupled node similarity (CNS) to involve and learn attribute and structure couplings and compute the similarity within and between nodes with categorical attributes in a network. CNS learns and integrates the frequency-based intra-attribute coupled similarity within an attribute, the co-occurrence-based inter-attribute coupled similarity between attributes, and coupled attribute-to-structure similarity based on the homophily property. CNS is then used to generate the weights of edges and transfer a plain graph to a weighted graph. Clustering algorithms detect community structures that are topologically well-connected and semantically coherent on the weighted graphs. Extensive experiments verify the effectiveness of CNS-based community detection algorithms on several data sets by comparing with the state-of-the-art node similarity measures, whether they involve node attribute information and hierarchical interactions, and on various levels of network structure complexity.

Detecting semantic‐based communities in node‐attributed graphs

AbstractIn social network analysis, community detection on plain graphs has been widely studied. With the proliferation of available data, each user in the network is usually associated with additional attributes for elaborate description. However, many existing methods only concentrate on the topological structure and fail to deal with node‐attributed networks. These approaches are incapable of extracting clear semantic meanings for communities detected. In this paper, we combine the topological structure and attribute information into a unified process and propose a novel algorithm to detect overlapping semantic communities. Moreover, a new metric is designed to measure the density of semantic communities. The proposed algorithm is divided into 3 phases. First, we detect local semantic subcommunities from each node's perspective using a greedy strategy on the metric. Then, a supergraph, which consists of all these subcommunities is created. Finally, we find global semantic communities on the supergraph. The experimental results on real‐world data sets show the efficiency and effectiveness of our approach against other state‐of‐the‐art methods.

Automatic Segmentation of Dynamic Network Sequences with Node Labels

Given a sequence of snapshots of flu propagating over a population network, can we find a segmentation when the patterns of the disease spread change, possibly due to interventions? In this paper, we study the problem of segmenting graph sequences with labeled nodes. Memes on the Twitter network, diseases over a contact network, movie-cascades over a social network, etc. are all graph sequences with labeled nodes. Most related work on this subject is on plain graphs and hence ignores the label dynamics. Others require fix parameters or feature engineering. We propose SnapNETS , to automatically find segmentations of such graph sequences, with different characteristics of nodes of each label in adjacent segments. It satisfies all the desired properties (being parameter free, comprehensive and scalable) by leveraging a principled, multi-level, flexible framework which maps the problem to a path optimization problem over a weighted DAG. Also, we develop the parallel framework of SnapNETS which speeds up its running time. Finally, we propose an extension of SnapNETS to handle the dynamic graph structures and use it to detect anomalies (and events) in network sequences. Extensive experiments on several diverse real datasets show that it finds cut points matching ground-truth or meaningful external signals and detects anomalies outperforming non-trivial baselines. We also show that the segmentations are easily interpretable, and that SnapNETS scales near-linearly with the size of the input. Finally, we show how to use SnapNETS to detect anomaly in a sequence of dynamic networks.

Dynamic Cluster Formation Game for Attributed Graph Clustering.

Besides the topological structure, there are additional information, i.e., node attributes, on top of the plain graphs. Usually, these systems can be well modeled by attributed graphs, where nodes represent component actors, a set of attributes describe users' portraits and edges indicate their connections. An elusive question associated with attributed graphs is to study how clusters with common internal properties form and evolve in real-world networked systems with great individual diversity, which leads to the so-called problem of attributed graph clustering (AGC). In this paper, we comprehended AGC naturally as a dynamic cluster formation game (DCFG), where each node's feasible action set can be constrained by every cluster in a discrete-time dynamical system. Specifically, we carried out a deep research on a special case of finite dynamic games, named dynamic social game (DSG), the convergence of the finite Nash equilibrium sequence in a DSG was also proved strictly. By carefully defining the feasible action set and the utility function associated with each node, the proposed DCFG can be well related to a DSG; and we showed that a balanced solution of AGC could be found by solving a finite set of coupled static Nash equilibrium problems in the related DCFG. We, finally, proposed a self-learning algorithm, which can start from any arbitrary initial cluster configuration, and, finally, find the corresponding balanced solution of AGC, where all nodes and clusters are satisfied with the final cluster configuration. Extensive experiments were applied on real-world social networks to demonstrate both effectiveness and scalability of the proposed approach by comparing with the state-of-the-art graph clustering methods in the literature.

SnapNETS: Automatic Segmentation of Network Sequences with Node Labels

Given a sequence of snapshots of flu propagating over a population network, can we find a segmentation when the patterns of the disease spread change, possibly due to interventions? In this paper, we study the problem of segmenting graph sequences with labeled nodes. Memes on the Twitter network, diseases over a contact network, movie-cascades over a social network, etc. are all graph sequences with labeled nodes. Most related work is on plain graphs (and hence ignore the label dynamics) or fix parameters or require much feature engineering. Instead, we propose SnapNETS, to automatically find segmentations of such graph sequences, with different characteristics of nodes of each label in adjacent segments. It satisfies all the desired properties (being parameter-free, comprehensive and scalable) by leveraging a principled, multi-level, flexible framework which maps the problem to a path optimization problem over a weighted DAG. Extensive experiments on several diverse real datasets show that it finds cut points matching ground-truth or meaningful external signals outperforming non-trivial baselines. We also show that SnapNETS scales near-linearly with the size of the input.

Automatic analysis of D-partition

The paper is dedicated to automatization of D-partition analysis. D-partition is one of the most common methods for determination of solution stability in systems with time-delayed feedback control and its dependency on values of control parameters. A transition from analytical form of D-partition to plain graph has been investigated. An algorithm of graph faces determination and calculation of count of characteristic equation roots with positive real part for appropriate area of D-partition has been developed. The algorithm keeps an information about analytical formulas for edges of faces. It allows to make further analytical research based on the results of computer analysis.

Cement embolism confused with involvement of tuberculosis on plain graph

Cement embolism confused with involvement of tuberculosis on plain graph

Graph based anomaly detection and description: a survey

Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured graph data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we give a general framework for the algorithms categorized under various settings: unsupervised versus (semi-)supervised approaches, for static versus dynamic graphs, for attributed versus plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly attribution and highlight the major techniques that facilitate digging out the root cause, or the ‘why’, of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

Immobility Edge-Method of Plain Graph

This article introduced the immobilityedge-method for the calculation and analysis of color function.Meanwhile it give out an example to calculate the color function ofa graph with 4-cycle and explained the reducibility for theconfiguration of it, which is a different method compare withothers.

Borel sets and countable models

We show that certain families of sets and functions related to a countable structure A are analytic subsets of a Polish space. Examples include sets of automorphisms, endomorphisms and congruences of A and sets of the combinatorial nature such as coloring of countable plain graphs and domino tiling of the plane. This implies, without any additional set-theoretical assumptions, i.e., in ZFC alone, that cardinality of every such uncountable set is 2?0.