Graph Space Research Articles

Anchors-Based Incremental Embedding for Growing Knowledge Graphs

Knowledge graph embedding aims to transform the entities and relations of triplets into the low-dimensional vectors. Previous methods are oriented towards the static knowledge graphs, in which all entities and relations are assumed to be known and only some unknown triplets need to be predicted. However, the real-world knowledge graphs can grow dynamically, and some new knowledge are often added. To embed the new knowledge into the space of original knowledge graph, the classic models have to perform the entire re-embedding with including the new and original knowledge. This causes heavy computational burden for embedding. To address this problem, this study proposes a new model of anchors-based incremental embedding (ABIE) to implement the dynamical embedding for the growing knowledge graph. According to ABIE, every knowledge graph has some key entities, called anchors, which can fix the embedding space of knowledge graph. When some new knowledge is added into the graph, only a few updated entities and relations are embedded into the embedding space with the help of anchors, and the entire re-embedding on the whole graph is not necessary. By this way, the computational burden of embedding caused by the growth of knowledge graph is reduced significantly.

HGATE: Heterogeneous Graph Attention Auto-Encoders

Graph auto-encoder is considered a framework for unsupervised learning on graph-structured data by representing graphs in a low dimensional space. It has been proved very powerful for graph analytics. In the real world, complex relationships in various entities can be represented by heterogeneous graphs that contain more abundant semantic information than homogeneous graphs. In general, graph auto-encoders based on homogeneous graphs are not applicable to heterogeneous graphs. In addition, little work has been done to evaluate the effect of different semantics on node embedding in heterogeneous graphs for unsupervised graph representation learning. In this work, we propose a novel Heterogeneous Graph Attention Auto-Encoders (HGATE) for unsupervised representation learning on heterogeneous graph-structured data. Based on the consideration of semantic information, our architecture of HGATE reconstructs not only the edges of the heterogeneous graph but also node attributes, through stacked encoder/decoder layers. Hierarchical attention is used to learn the relevance between a node and its meta-path based neighbors, and the relevance among different meta-paths. HGATE is applicable to transductive learning as well as inductive learning. Node classification and link prediction experiments on real-world heterogeneous graph datasets demonstrate the effectiveness of HGATE for both transductive and inductive tasks.

Unsupervised Graph Embedding via Adaptive Graph Learning.

Graph autoencoders (GAEs) are powerful tools in representation learning for graph embedding. However, the performance of GAEs is very dependent on the quality of the graph structure, i.e., of the adjacency matrix. In other words, GAEs would perform poorly when the adjacency matrix is incomplete or be disturbed. In this paper, two novel unsupervised graph embedding methods, unsupervised graph embedding via adaptive graph learning (BAGE) and unsupervised graph embedding via variational adaptive graph learning (VBAGE) are proposed. The proposed methods expand the application range of GAEs on graph embedding, i.e, on the general datasets without graph structure. Meanwhile, the adaptive learning mechanism can initialize the adjacency matrix without being affected by the parameter. Besides that, the latent representations are embedded with the Laplacian graph structure to preserve the topology structure of the graph in the vector space. Moreover, the adjacency matrix can be self-learned for better embedding performance when the original graph structure is incomplete. With adaptive learning, the proposed method is much more robust to the graph structure. Experimental studies on several datasets validate our design and demonstrate that our methods outperform baselines by a wide margin in node clustering, node classification, link prediction, and graph visualization tasks.

Research on the cooperative control strategy of output current in a distributed generation system

In the ship degaussing system, a distributed power system is adopted, in which a single power module drives an independent coil load respectively. To ensure the degaussing effect, it is necessary to ensure the dynamic and static integrity of the load current. If an appropriate cooperative control strategy is not designed, the dynamic consistency of output current will be greatly affected by the difference in load. Therefore, this paper designs the cooperative control strategy based on the multi-agent consistency theory and proves the stability and consistency of the control strategy through the theory of discrete state space equation and graph theory. Through the simulation and experiment of multi distributed power system, it is verified that the control strategy has a good effect on improving the output current consistency of the power system.

Subspace graph topological space of graphs

A graph topology defined on a graph G is a collection 𝒯 of subgraphs of G which satisfies the properties such as K0, G ∈ 𝒯 and 𝒯 is closed under arbitrary union and finite intersection. Let (X, T) be a topological space and Y ⊆ X then, TY = {U ∩ Y : U ∈ T} is a topological space called a subspace topology or relative topology defined by T on Y. In this P1 we discusses the subspace or the relative graph topology defined by the graph topology 𝒯 on a subgraph H of G. We also study the properties of subspace graph topologies, open graphs, d-closed graphs and nbd-closed graphs of subspace graph topologies.

Risk Assessment of Water Transport Enterprises by Modeling Direct and Indirect Threats

Introduction. The methods of traffic modeling by water transport and assessing the risks associated with it is needed to identify the issues of the past period, proposing methods for assessing not only direct but also indirect risks to form the preconditions for preventing them in the postwar reconstruction. The coordination of different transport type’s actions of transport requires an assessment of risks impact of the previous stages of mixed transportation on the formation of the following risks’ stages. Existing methods of assessing such impact need to be improved.
 Aim and tasks. The aim of this study is creation of methodological approach to risk management in water transport based on a mathematical model for assessing the impact of both direct and indirect risks. The tasks are: to prove that the additive approach of taking risks into account leads to the systematic deviation appearance from the result; take into account the impact on the risk of cargo transportation.
 Results. It has proved that the calculation of risk as an additive function leads to a systematic deviation from the relevant result. It stated that the risk of each of the next stages of transportation depends on the risks of the previous stages. To increase risk analysis relevance in water transport, the use of an oriented graph in a multidimensional parameter space proposed. It stated that in order to calculate the integrated risk, it is essential building not only the risk matrix but also the risk incidence matrix to take into account their relation to business entities. It established the impact of even minor risks could take the form of a catastrophe, which leads to cargo flows reorientation. It established that: for calculation of integral risk, it is crucial consider direct and indirect influences of risks; risk calculation for water transport also requires risk analysis in related modes of transport.
 Conclusions. It was established that, when calculating integral risk, it is necessary to consider direct and indirect influences on risks and that the risk calculation for water transport also requires risk analysis in related modes of transport. The proposed approach significantly increases the relevance of water transport risk analysis and allows for managing changes in transportation routes in real time.

Multiobjective Design of Gravity-Assist Trajectories via Graph Transcription and Dynamic Programming

Multiple gravity-assist (MGA) trajectory design requires the solution of a mixed-integer programming problem to find the best sequence among all possible combinations of candidate planets and dates for spacecraft maneuvers. Current approaches require computing times rising steeply with the number of control parameters, and they strongly rely on narrow search spaces. Moreover, the challenging multiobjective optimization needs to be tackled to appropriately inform the mission design with full extent of launch opportunities. This paper describes a methodology based upon a trajectory model to transcribe the mixed-integer space into a discrete graph made by grids of interconnected nodes. The model is based on Lambert arc grids obtained for a range of departure dates and flight times between two planets. A Tisserand-based criterion selects planets to pass by. Dynamic programming is extended to multiobjective optimization of MGA trajectories and used to explore the graph, guaranteeing Pareto optimality with only moderate computational effort. Robustness is ensured by evaluating the relationship between graph and mixed-integer spaces. Missions to Jupiter and Saturn alongside challenging comet sample return transfers involving long MGA sequences are discussed. These examples illustrate the robustness and efficiency of the proposed approach in capturing globally optimal solutions and wide Pareto fronts on complex search spaces.

Fuzzy RDF Knowledge Graph Embeddings Through Vector Space Model

Resource description framework (RDF) is a World Wide Web consortium recommendation and has been widely accepted for semantic data models (e.g., knowledge graphs). As such, a large amount of RDF data is readily available. Information in the real world is often uncertain, and uncertain RDF data models have been proposed and received increasing attention. Knowledge graph embedding is an effective way to perform vector projection of structured knowledge, after which we can infer a large-scale knowledge graph. Nowadays, knowledge graph embedding models are widely proposed, but most of them can only handle crisp information. In this article, we concentrate on modeling fuzzy RDF graphs in the vector space. We propose a fuzzy RDF knowledge graph embedding model (FRKGE), which can project the fuzzy entities and fuzzy relations with membership degree to the vector space. Our proposed model preserves the structure of the fuzzy RDF knowledge graph and the explicit expression of membership degree in the vector space, which provides a natural expression of fuzzy RDF tuples. Our experimental results demonstrate that the FRKGE model is competent for the task of representation learning for fuzzy RDF knowledge graphs.

Crowdsourcing Truth Inference via Reliability-Driven Multi-View Graph Embedding

Crowdsourcing truth inference aims to assign a correct answer to each task from candidate answers that are provided by crowdsourced workers. A common approach is to generate workers’ reliabilities to represent the quality of answers. Although crowdsourced triples can be converted into various crowdsourced relationships, the available related methods are not effective in capturing these relationships to alleviate the harm to inference that is caused by conflicting answers. In this research, we propose aReliability-drivenMulti-viewGraphEmbedding framework forTruthinference (TiReMGE), which explores multiple crowdsourced relationships by organically integrating worker reliabilities into a graph space that is constructed from crowdsourced triples. Specifically, to create an interactive environment, we propose a reliability-driven initialization criterion for initializing vectors of tasks and workers as interactive carriers of reliabilities. From the perspective of multiple crowdsourced relationships, a multi-view graph embedding framework is proposed for reliability information interaction on a task-worker graph, which encodes latent crowdsourced relationships into vectors of workers and tasks for reliability update and truth inference. A heritable reliability updating method based on the Lagrange multiplier method is proposed to obtain reliabilities that match the quality of workers for interaction by a novel constraint law. Our ultimate goal is to minimize the Euclidean distance between the encoded task vector and the answer that is provided by a worker with high reliability. Extensive experimental results on nine real-world datasets demonstrate that TiReMGE significantly outperforms the nine state-of-the-art baselines.

A New Construction of Strongly Regular Graphs with Parameters of the Complement Symplectic Graph

The symplectic graph $Sp(2d, q)$ is the collinearity graph of the symplectic space of dimension $2d$ over the finite field of order $q$. A $k$-regular graph on $v$ vertices is a divisible design graph with parameters $(v,k,\lambda_1,\lambda_2,m,n)$ if its vertex set can be partitioned into $m$ classes of size $n$, such that any two different vertices from the same class have $\lambda_1$ common neighbours, and any two vertices from different classes have $\lambda_2$ common neighbours whenever it is not complete or edgeless. In this paper we propose a new construction of strongly regular graphs with the parameters of the complement of the symplectic graph using divisible design graphs.

A graph convolution network with subgraph embedding for mutagenic prediction in aromatic hydrocarbons

An aromatic hydrocarbon refers to an organic material having a carbon ring such as benzene and a functional group in the carbon ring. As the industry develops, natural pollution becomes harsh, new compounds emerge, and the exposure to aromatic hydrocarbons is continuously increasing. Predicting mutagenicity is one of the crucial issues in reducing the risk because these organisms may have properties that penetrate the DNA of living things to cause mutations. Recently, the accuracy of mutation prediction has improved due to the power of deep learning. However, most conventional methods do not consider the characteristics of molecular aromatic hydrocarbons, which dilutes local information and results in a severe deterioration of the prediction performance. In this paper, we propose a method of exploiting subgraph convolution neural networks that enables the extraction of local information of a graph by partitioning it to maintain the detailed information. For extracting the features of molecules, we use the Girvan Newman algorithm to partition the graph according to the carbon ring and functional group and obtain the embedding vectors of the subgraphs as well as the original graph with graph convolution network (GCN). The embedding vectors are combined to represent the whole graph information and predict mutagenicity. Experiments with MUTAG, NCI1 and NCI109, datasets for predicting mutagenicity of molecules in graph structure, confirm that we successfully segment carbon rings and functional groups from molecular graphs and predict mutations using the partitioned graphs, leading to a 2 %p performance improvement. In addition, the proposed method has prevented about 15 %p of information dilution in GCN, and an analysis of the latent space of graphs reveals that the subgraphs extracted maintain the local information appropriately.

Generative Consistency for Semi-Supervised Cerebrovascular Segmentation From TOF-MRA.

Cerebrovascular segmentation from Time-of-flight magnetic resonance angiography (TOF-MRA) is a critical step in computer-aided diagnosis. In recent years, deep learning models have proved its powerful feature extraction for cerebrovascular segmentation. However, they require many labeled datasets to implement effective driving, which are expensive and professional. In this paper, we propose a generative consistency for semi-supervised (GCS) model. Considering the rich information contained in the feature map, the GCS model utilizes the generation results to constrain the segmentation model. The generated data comes from labeled data, unlabeled data, and unlabeled data after perturbation, respectively. The GCS model also calculates the consistency of the perturbed data to improve the feature mining ability. Subsequently, we propose a new model as the backbone of the GSC model. It transfers TOF-MRA into graph space and establishes correlation using Transformer. We demonstrated the effectiveness of the proposed model on TOF-MRA representations, and tested the GCS model with state-of-the-art semi-supervised methods using the proposed model as backbone. The experiments prove the important role of the GCS model in cerebrovascular segmentation. Code is available at https://github.com/MontaEllis/SSL-For-Medical-Segmentation.

To the path counting on graphs in phase space

It was argued before that the Hilbert space of quantum harmonic oscillators can be realized in terms of particular trees. We generalize this approach for the Wigner functions defined on the phase space. Along this way, we derive a new representation for the Laguerre function in terms of canonical partition function of the statistical model defined on particular trees with loops.

Curvature estimates for graphs in warped product spaces

We prove local and global upper estimates for the infimum of the mean curvature, the scalar curvature and the norm of the shape operator of graphs in a warped product space. Using these estimates, we obtain some results on pseudo-hyperbolic spaces and space forms.

Cayley subspace sum graph of vector spaces

Let $\mathbb{V}$ be a finite dimensional vector space over the field $\mathbb{F}$. Let $S(\mathbb{V})$ be the set of all subspaces of $\mathbb{V}$ and $\mathbb{A}\subseteq S^*(\mathbb{V})=S(\mathbb{V})\backslash\{0\}.$ In this paper, we define the Cayley subspace sum graph of $\mathbb{V},$ denoted by Cay$(S^*(\mathbb{V}),\mathbb{A}), $ as the simple undirected graph with vertex set $S^*(\mathbb{V})$ and two distinct vertices $X$ and $Y$ are adjacent if $X+Z=Y$ or $Y+Z=X$ for some $Z\in \mathbb{A}$. Having defined the Cayley subspace sum graph, we study about the connectedness, diameter and girth of several classes of Cayley subspace sum graphs Cay$(S^*(\mathbb{V}), \mathbb{A})$ for a finite dimensional vector space $\mathbb{V}$ and $\mathbb{A}\subseteq S^*(\mathbb{V})=S(\mathbb{V})\backslash\{0\}.$

Some results on the open subset intersection graph of a product topological space

In the recent paper, R. A. Muneshwar et al., introduced a graph structure called open subset intersection graph g(t) on a topological space (X, t). In this paper, we study some important results of a graph g(t) of a product topological space (X × Y, t). We also determine relationship between diameter, girth, clique number, chromatic number, domination number etc. of an open subset intersection graph of a topological space (X × Y, t), (X, tX) and (Y, tY). Moreover, we proved that, if (X, tX) and (Y, tY) are discrete topological space then w(g(tX × tY)) = w(g(tX)) * w(g(tY)) – 2 and c(g(tX × tY)) = c(g(tX)) * c(g(tY)) – 2 and domination number of g(tX × tY) is 2. We also determine diameter and girth of intersection Graph of Product Topology on X × Y for different values of m and n.

TNN: Tree Neural Network for Airway Anatomical Labeling.

Detailed anatomical labeling of bronchial trees extracted from CT images can be used as fine-grained maps for intra-operative navigation. To cater to the sparse distribution of airway voxels and large class imbalance in 3D image space, a graph-neural-network-based method is proposed to map branches to nodes in a graph space and assign anatomical labels down to subsegmental level. To address the inherent problem of overlapping distribution of positional and morphological features, especially for subsegmental categories, the proposed method focuses on the relative position between sibling subsegments which is fixed in most cases. The hierarchical nomenclature is represented by multi-level labeling and each category is associated with one or two subtrees in the graph. Hyperedges are used to extract the representation of subtrees while a hypergraph neural network is developed to encode their intrinsic relationship through hyperedge interaction. A filter module is further designed to guide feature aggregation between nodes and hyperedges. With the proposed method, the final accuracies for segmental and subsegmental node classification can achieve 93.6% and 82.0% respectively. The corresponding code is publicly available at https://github.com/haozheng-sjtu/airway-labeling.

Learning Hidden Graphs from Samples.

Several real-world problems, like molecular biology and chemical reactions, have hidden graphs, and we need to learn the hidden graph using edge-detecting samples. In this problem, the learner receives examples explaining whether a set of vertices induces an edge of the hidden graph. This paper examines the learnability of this problem using the PAC and Agnostic PAC learning models. By computing the VC-dimension of hypothesis spaces of hidden graphs, hidden trees, hidden connected graphs, and hidden planar graphs through edge-detecting samples, we also find the sample complexity of learning these spaces. We study the learnability of this space of hidden graphs in two cases, namely for known and unknown vertex sets. We show that the class of hidden graphs is uniformly learnable when the vertex set is known. Furthermore, we prove that the family of hidden graphs is not uniformly learnable but is nonuniformly learnable when the vertex set is unknown.

Про формалізацію планів дій з протидії надзвичайним ситуаціям

The problem of formalization of action plans to counter emergency situations is being studied. It is noted that traditional action plans are text documents that are not suitable for solving the tasks of automating the management of emergency situations. A formal description of the state space is given and the expediency of using the state space graph to represent electronic action plans is substantiated. Based on the analysis of the internal structure of the process of countering an abstract emergency, a set of functional groups and their constituent operations are identified, using which an arbitrary action plan can be built. The identification of a set of types of parameters is carried out, through which the formalization of operations is provided. The advantages of using the proposed formalization of action plans for automating the processes of emergency response management are given.

Towards Accurate Microstructure Estimation via 3D Hybrid Graph Transformer.

Deep learning has drawn increasing attention in microstructure estimation with undersampled diffusion MRI (dMRI) data. A representative method is the hybrid graph transformer (HGT), which achieves promising performance by integrating -space graph learning and -space transformer learning into a unified framework. However, this method overlooks the 3D spatial information as it relies on training with 2D slices. To address this limitation, we propose 3D hybrid graph transformer (3D-HGT), an advanced microstructure estimation model capable of making full use of 3D spatial information and angular information. To tackle the large computation burden associated with 3D -space learning, we propose an efficient -space learning model based on simplified graph neural networks. Furthermore, we propose a 3D -space learning module based on the transformer. Extensive experiments on data from the human connectome project show that our 3D-HGT outperforms state-of-the-art methods, including HGT, in both quantitative and qualitative evaluations.