Dynamic Subgraph Research Articles

Dynamic frequent subgraph mining algorithms over evolving graphs: a survey

Frequent subgraph mining (FSM) is an essential and challenging graph mining task used in several applications of the modern data science. Some of the FSM algorithms have the objective of finding all frequent subgraphs whereas some of the algorithms focus on discovering frequent subgraphs approximately. On the other hand, modern applications employ evolving graphs where the increments are small graphs or stream of nodes and edges. In such cases, FSM task becomes more challenging due to growing data size and complexity of the base algorithms. Recently we see frequent subgraph mining algorithms designed for dynamic graph data. However, there is no comparative review of the dynamic subgraph mining algorithms focusing on the discovery of frequent subgraphs over evolving graph data. This article focuses on the characteristics of dynamic frequent subgraph mining algorithms over evolving graphs. We first introduce and compare dynamic frequent subgraph mining algorithms; trying to highlight their attributes as increment type, graph type, graph representation, internal data structure, algorithmic approach, programming approach, base algorithm and output type. Secondly, we introduce and compare the approximate frequent subgraph mining algorithms for dynamic graphs with additional attributes as their sampling strategy, data in the sample, statistical guarantees on the sample and their main objective. Finally, we highlight research opportunities in this specific domain from our perspective. Overall, we aim to introduce the research area of frequent subgraph mining over evolving graphs with the hope that this can serve as a reference and inspiration for the researchers of the field.

Digital modelling method of coal-mine roadway based on millimeter-wave radar array

The roadway space of coal mine is narrow, and the illumination is low and uneven. Dynamic mining is accompanied by dust and water mist. The accuracy and reliability of roadway data collected by vision and laser sensors are poor. Based on this, a digital modeling method of coal mine roadway based on millimeter-wave radar array is proposed. Firstly, aiming at the problem of complex environmental interference, combined with the characteristics of small amount of single frame data of millimeter-wave point cloud, a multi-layer filtering noise reduction processing and dynamic subgraph registration method of millimeter-wave point cloud is proposed to filter out interference points and realize single radar point cloud registration. Secondly, aiming at the problem that a single millimeter-wave radar cannot scan the complete roadway information at one time, combined with the characteristics of small elevation field of view of millimeter-wave radar, a millimeter-wave radar array acquisition system is built, and an improved iterative closest point (ICP) registration algorithm based on point cloud features is established to construct the roadway point cloud fusion model. Finally, aiming at the problem of uneven and sparse point cloud after array fusion, a Poisson surface reconstruction method based on point cloud density weighted interpolation is proposed to refine the roadway structure and realize the accurate reconstruction of digital roadway model. The experimental results show that the digital modeling method of millimeter-wave radar array can accurately obtain the information of roadway surrounding rock, the density of roadway point cloud is increased by 22.4%, and the average absolute error percentage of the width and height of the reconstructed roadway model is only 0.82% and 0.72%, which provides a new research method for the reconstruction of underground roadway and an important basis for the digital modeling method of coal mine roadway.

TIGER: Training Inductive Graph Neural Network for Large-Scale Knowledge Graph Reasoning

Knowledge Graph (KG) Reasoning plays a vital role in various applications by predicting missing facts from existing knowledge. Inductive KG reasoning approaches based on Graph Neural Networks (GNNs) have shown impressive performance, particularly when reasoning with unseen entities and dynamic KGs. However, such state-of-the-art KG reasoning approaches encounter efficiency and scalability challenges on large-scale KGs due to the high computational costs associated with subgraph extraction - a key component in inductive KG reasoning. To address the computational challenge, we introduce TIGER, an inductive GNN training framework tailored for large-scale KG reasoning. TIGER employs a novel, efficient streaming procedure that facilitates rapid subgraph slicing and dynamic subgraph caching to minimize the cost of subgraph extraction. The fundamental challenge in TIGER lies in the optimal subgraph slicing problem, which we prove to be NP-hard. We propose a novel two-stage algorithm SiGMa to solve the problem practically. By decoupling the complicated problem into two classical ones, SiGMa achieves low computational complexity and high slice reuse. We also propose four new benchmarks for robust evaluation of large-scale inductive KG reasoning, the biggest of which performs on the Freebase KG (encompassing 86M entities, 285M edges). Through comprehensive experiments on state-of-the-art GNN-based KG reasoning models, we demonstrate that TIGER significantly reduces the running time of subgraph extraction, achieving an average 3.7× speedup relative to the basic training procedure.

Knowledge Graph Reasoning via Dynamic Subgraph Attention with Low Resource Computation

Knowledge graphs (KGs) suffer from inherent incompleteness, which has spurred research into knowledge graph reasoning (KGR), i.e., ways to infer missing facts based on existing triples. The most prevalent approaches employ a static mechanism for entity representation across the entire graph, sharing entity embeddings for different query relations. Nevertheless, these static entity embeddings fail to capture specific semantics for various query scenarios, resulting in inaccurate entity representations and susceptibility to reasoning errors. Furthermore, the whole graph learning style requires substantial computational resources, especially since KGs are often of large-scale. Consequently, these methods are impractical in low-resource environments. To address these issues, we devise a framework called dynamic subgraph attention (DSA), which learns dynamic entity embeddings for different query relations across subgraphs. In our approach, by utilizing multi-hop path history information obtained through path-based learning, we guide a dynamic attention mechanism to generate dynamic entity embeddings for different query relations. To ensure the semantic information of entities, the embedding-based and path-based learning are jointly trained for KGR. Additionally, the proposed dynamic aggregation mechanism operates on subgraphs, resulting in a remarkable 6–7 times resource conservation compared to GPU computations. Empirical experiments further demonstrate that DSA outperforms the current methods significantly on three benchmark datasets.

Dynamic Sub-graph Distillation for Robust Semi-supervised Continual Learning

Continual learning (CL) has shown promising results and comparable performance to learning at once in a fully supervised manner. However, CL strategies typically require a large number of labeled samples, making their real-life deployment challenging. In this work, we focus on semi-supervised continual learning (SSCL), where the model progressively learns from partially labeled data with unknown categories. We provide a comprehensive analysis of SSCL and demonstrate that unreliable distributions of unlabeled data lead to unstable training and refinement of the progressing stages. This problem severely impacts the performance of SSCL. To address the limitations, we propose a novel approach called Dynamic Sub-Graph Distillation (DSGD) for semi-supervised continual learning, which leverages both semantic and structural information to achieve more stable knowledge distillation on unlabeled data and exhibit robustness against distribution bias. Firstly, we formalize a general model of structural distillation and design a dynamic graph construction for the continual learning progress. Next, we define a structure distillation vector and design a dynamic sub-graph distillation algorithm, which enables end-to-end training and adaptability to scale up tasks. The entire proposed method is adaptable to various CL methods and supervision settings. Finally, experiments conducted on three datasets CIFAR10, CIFAR100, and ImageNet-100, with varying supervision ratios, demonstrate the effectiveness of our proposed approach in mitigating the catastrophic forgetting problem in semi-supervised continual learning scenarios. Our code is available: https://github.com/fanyan0411/DSGD.

BioDynGrap: Biomedical event prediction via interpretable learning framework for heterogeneous dynamic graphs

Model dynamic graphs with entity-specific heterogeneity has achieved remarkable success across various domains. By utilizing a novel dynamic graph encoding mechanism that employs rich temporal reasoning, we introduce BioDynGraph — a versatile and innovative framework for biomedical event prediction that bridges the gap between historical search and future reasoning. Existing studies tend to overlook clinical relationships between diseases during a patient’s visit by treating diagnoses as independent illnesses. Many machine learning techniques assume that disease progression within each time period is static and stationary, attenuating the information of all previous time steps using a homogeneous approach. However, in practice, disease progression is non-stationary, necessitating better use of combinational disease information to learn more about the dynamics of diseases. To address this problem, we use event clue searching and event temporal reasoning to infuse entity and relation information into dynamic subgraphs efficiently. BioDynGraph learns a global disease co-occurrence graph through event clue searching and acquires dynamic subgraphs for each patient’s visit using event temporal reasoning. Experimental results demonstrate that BioDynGraph exhibits superior performance compared to state-of-the-art (SOTA) baseline methods on biomedical event prediction using three electronic medical records datasets. Additionally, the clues found by BioDynGraph provide interpretability of the event prediction, showcasing its potential as an effective general-purpose interpretability algorithm for biomedical graph data.

A dynamic graph expansion network for multi-hop knowledge base question answering

Knowledge base question answering aims to answer a question over a knowledge base. Multi-hop knowledge base question answering is a challenging task because it requires multi-step reasoning according to the question to get the answer. Existing models infer the answer over a static subgraph or attend to different parts of the question through an intermediate signal. The former obtains limited semantic information, and the latter provides limited reasoning due to the weak supervision signal. In this paper, we eliminate the limitation of static subgraph reasoning by dynamically expanding subgraphs, which connect the question and subgraph to form a joint subgraph. We then adjust the dynamic subgraph to enable reasoning at each step. Specifically, at each step, the question connects different subgraphs, respects the context while paying attention to a specific part of the question, generates a strong intermediate signal, acts on the subsequent reasoning, and finally obtains a correct answer. A large number of experiments on three datasets show that our method performs better than previous state-of-the-art models.

(2.5+1)D Spatio-Temporal Scene Graphs for Video Question Answering

Spatio-temporal scene-graph approaches to video-based reasoning tasks, such as video question-answering (QA), typically construct such graphs for every video frame. These approaches often ignore the fact that videos are essentially sequences of 2D ``views'' of events happening in a 3D space, and that the semantics of the 3D scene can thus be carried over from frame to frame. Leveraging this insight, we propose a (2.5+1)D scene graph representation to better capture the spatio-temporal information flows inside the videos. Specifically, we first create a 2.5D (pseudo-3D) scene graph by transforming every 2D frame to have an inferred 3D structure using an off-the-shelf 2D-to-3D transformation module, following which we register the video frames into a shared (2.5+1)D spatio-temporal space and ground each 2D scene graph within it. Such a (2.5+1)D graph is then segregated into a static sub-graph and a dynamic sub-graph, corresponding to whether the objects within them usually move in the world. The nodes in the dynamic graph are enriched with motion features capturing their interactions with other graph nodes. Next, for the video QA task, we present a novel transformer-based reasoning pipeline that embeds the (2.5+1)D graph into a spatio-temporal hierarchical latent space, where the sub-graphs and their interactions are captured at varied granularity. To demonstrate the effectiveness of our approach, we present experiments on the NExT-QA and AVSD-QA datasets. Our results show that our proposed (2.5+1)D representation leads to faster training and inference, while our hierarchical model showcases superior performance on the video QA task versus the state of the art.

Context-Aware Health Event Prediction via Transition Functions on Dynamic Disease Graphs

With the wide application of electronic health records (EHR) in healthcare facilities, health event prediction with deep learning has gained more and more attention. A common feature of EHR data used for deep-learning-based predictions is historical diagnoses. Existing work mainly regards a diagnosis as an independent disease and does not consider clinical relations among diseases in a visit. Many machine learning approaches assume disease representations are static in different visits of a patient. However, in real practice, multiple diseases that are frequently diagnosed at the same time reflect hidden patterns that are conducive to prognosis. Moreover, the development of a disease is not static since some diseases can emerge or disappear and show various symptoms in different visits of a patient. To effectively utilize this combinational disease information and explore the dynamics of diseases, we propose a novel context-aware learning framework using transition functions on dynamic disease graphs. Specifically, we construct a global disease co-occurrence graph with multiple node properties for disease combinations. We design dynamic subgraphs for each patient's visit to leverage global and local contexts. We further define three diagnosis roles in each visit based on the variation of node properties to model disease transition processes. Experimental results on two real-world EHR datasets show that the proposed model outperforms state of the art in predicting health events.

Pre-training on dynamic graph neural networks

The pre-training of the graph neural network model is to learn the general characteristics of large-scale graphs or the similar type of graphs usually through a self-supervised method, which allows the model to work even when node labels are missing. However, the existing pre-training methods do not take the temporal information of edge generation and the evolution process of graph into consideration. To address this issue, this paper proposes a pre-training method based on dynamic graph neural networks (PT-DGNN), which uses the dynamic graph generation task to simultaneously learn the structure, semantics, and evolution features of the graph. The method mainly includes two steps: 1) dynamic subgraph sampling, and 2) pre-training using two graph generation tasks. The former preserves the local time-aware structure of the original graph by sampling the latest and frequently interacting nodes. The latter uses observed edges to predict unobserved edges to capture the evolutionary characteristics of the network. Comparative experiments on three realistic dynamic network datasets show that the proposed pre-training method achieves the best results on the link prediction fine-tuning task and the ablation study and further verifies the effectiveness of the above two steps.

Dynamic and Static Features-Aware Recommendation with Graph Neural Networks.

Recommender systems are designed to deal with structured and unstructured information and help the user effectively retrieve needed information from the vast number of web pages. Dynamic information of users has been proven useful for learning representations in the recommender system. In this paper, we construct a series of dynamic subgraphs that include the user and item interaction pairs and the temporal information. Then, the dynamic features and the long- and short-term information of users are integrated into the static recommendation model. The proposed model is called dynamic and static features-aware graph recommendation, which can model unstructured graph information and structured tabular data. Particularly, two elaborately designed modules are available: dynamic preference learning and dynamic sequence learning modules. The former uses all user-item interactions and the last dynamic subgraph to model the dynamic interaction preference of the user. The latter captures the dynamic features of users and items by tracking the preference changes of users over time. Extensive experiments on two publicly available datasets show that the proposed model outperforms several compelling state-of-the-art baselines.

Temporal Graph Traversals Using Reinforcement Learning With Proximal Policy Optimization

Graphs in real-world applications are dynamic both in terms of structures and inputs. Information discovery in such networks, which present dense and deeply connected patterns locally and sparsity globally can be time consuming and computationally costly. In this paper we address the shortest path query in spatio-temporal graphs which is a fundamental graph problem with numerous applications. In spatio-temporal graphs, shortest path query classical algorithms are insufficient or even flawed because information consistency can not be guaranteed between two timestamps and path recalculation is computationally costly. In this work, we address the complexity and dynamicity of the shortest path query in spatio-temporal graphs with a simple, yet effective model based on Reinforcement Learning with Proximal Policy Optimization. Our solution simplifies the problem by decomposing the spatio-temporal graph in two components: a static and a dynamic sub-graph. The static graph, known and immutable, is efficiently solved with $A^{*}$ algorithm. The sub-graphs interconnecting the static graph have unknown dynamics and we address such issue by estimating the unknown dynamic portion of the graph as a Markov Chain which correlates the observations of the agents in the environment and the path to be followed. We then derive an action policy through Proximal Policy Optimization to select the local optimal actions in the Markov Process that will lead to the shortest path, given the estimated system dynamics. We evaluate the system in a simulation environment constructed in Unity3D. In partially structured and unknown environments, with variable environment parameters we’ve obtained an efficiency 75% greater than the comparable deterministic solution.

Finding events in temporal networks: segmentation meets densest subgraph discovery

In this paper, we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naïve solution to our optimization problem has polynomial but prohibitively high running time. We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard; however, we show that on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extend this greedy approach for temporal networks, but we lose the approximation guarantee in the process. Finally, we demonstrate empirically that our algorithms recover solutions with good quality.

Mining Heavy Temporal Subgraphs: Fast Algorithms and Applications

Anomaly detection is a fundamental problem in dynamic networks. In this paper, we study an approach for identifying anomalous subgraphs based on the Heaviest Dynamic Subgraph (HDS) problem. The HDS in a time-evolving edge-weighted graph consists of a pair containing a subgraph and subinterval whose sum of edge weights is maximized. The HDS problem in a static graph is equivalent to the Prize Collecting Steiner Tree (PCST) problem with the Net-Worth objective---this is a very challenging problem, in general, and numerous heuristics have been proposed. Prior methods for the HDS problem use the PCST solution as a heuristic, and run in time quadratic in the size of the graph. As a result, they do not scale well to large instances. In this paper, we develop a new approach for the HDS problem, which combines rigorous algorithmic and practical techniques and has much better scalability. Our algorithm is able to extend to other variations of the HDS problem, such as the problem of finding multiple anomalous regions. We evaluate our algorithms in a diverse set of real and synthetic networks, and we find solutions with higher score and better detection power for anomalous events compared to earlier heuristics.

Beyond modularity: Fine-scale mechanisms and rules for brain network reconfiguration

The human brain is in constant flux, as distinct areas engage in transient communication to support basic behaviors as well as complex cognition. The collection of interactions between cortical and subcortical areas forms a functional brain network whose topology evolves with time. Despite the nontrivial dynamics that are germane to this networked system, experimental evidence demonstrates that functional interactions organize into putative brain systems that facilitate different facets of cognitive computation. We hypothesize that such dynamic functional networks are organized around a set of rules that constrain their spatial architecture – which brain regions may functionally interact – and their temporal architecture – how these interactions fluctuate over time. To objectively uncover these organizing principles, we apply an unsupervised machine learning approach called non-negative matrix factorization to time-evolving, resting state functional networks in 20 healthy subjects. This machine learning approach automatically groups temporally co-varying functional interactions into subgraphs that represent putative topological modes of dynamic functional architecture. We find that subgraphs are stratified based on both the underlying modular organization and the topographical distance of their strongest interactions: while many subgraphs are largely contained within modules, others span between modules and are expressed differently over time. The relationship between dynamic subgraphs and modular architecture is further highlighted by the ability of time-varying subgraph expression to explain inter-individual differences in module reorganization. Collectively, these results point to the critical role that subgraphs play in constraining the topography and topology of functional brain networks. More broadly, this machine learning approach opens a new door for understanding the architecture of dynamic functional networks during both task and rest states, and for probing alterations of that architecture in disease.

Online Subgraph Skyline Analysis over Knowledge Graphs

Subgraph search is very useful in many real-world applications. However, users may be overwhelmed by the masses of matches. In this paper, we propose a subgraph skyline analysis problem, denoted as $S^2A$ , to support more complicated analysis over graph data. Specifically, given a large graph $G$ and a query graph $q$ , we want to find all the subgraphs $g$ in $G$ , such that $g$ is graph isomorphic to $q$ and not dominated by any other subgraphs. In order to improve the efficiency, we devise a hybrid feature encoding incorporating both structural and numeric features based on a partitioning strategy, and discuss how to optimize the space partitioning. We also present a skylayer index to facilitate the dynamic subgraph skyline computation. Moreover, an attribute cluster-based method is proposed to deal with the curse of dimensionality. Extensive experiments over real datasets confirm the effectiveness and efficiency of our algorithm.

The h-Index of a Graph and its Application to Dynamic Subgraph Statistics

We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of each possible three-vertex subgraph in time O(h) per update, where h is the h-index of the graph, the maximum number such that the graph contains $h$ vertices of degree at least h. We also show how to maintain the h-index itself, and a collection of h high-degree vertices in the graph, in constant time per update. Our data structure has applications in social network analysis using the exponential random graph model (ERGM); its bound of O(h) time per edge is never worse than the Theta(sqrt m) time per edge necessary to list all triangles in a static graph, and is strictly better for graphs obeying a power law degree distribution. In order to better understand the behavior of the h-index statistic and its implications for the performance of our algorithms, we also study the behavior of the h-index on a set of 136 real-world networks.

Dynamic Subgraph Connectivity with Geometric Applications

Inspired by dynamic connectivity applications in computational geometry, we consider a problem we call dynamic subgraph connectivity: design a data structure for an undirected graph $G=(V,E)$ and a subset of vertices $S \subseteq V$ to support insertions/deletions in S and connectivity queries (are two vertices connected?) in the subgraph induced by S. We develop the first sublinear, fully dynamic method for this problem for general sparse graphs, using a combination of several simple ideas. Our method requires $\widetilde O(|E|^{4\omega/(3\omega+3)})=O(|E|^{0.94})$ amortized update time, and $\widetilde O(|E|^{1/3})$ query time, after $\widetilde O(|E|^{(5\omega+1)/(3\omega+3)})$ preprocessing time, where ω is the matrix multiplication exponent and $\widetilde O$ hides polylogarithmic factors.

Prevention of endotoxaemia by non-absorbable antibiotics in heat stress.

Four anaesthetised monkeys were given oral kanamycin (15 mg 1 kg 12 hourly) over five consecutive days before being heat stressed. Four other anaesthetised monkeys served as controls. The plasma lipopolysaccharide concentration in control primates increased initially from 0.044 (SEM 0.004) ng/ml to 0.062 (0.006) ng/ml as the rectal temperature increased from 37.5 to 39.5 degrees C. A second increase in lipopolysaccharides started at 42 degrees C and reached 0.308 (0.038) ng/ml (p less than 0.01) at 44.5 degrees C. Before heat stress the plasma lipopolysaccharide concentration in the primates who had been pretreated with kanamycin was 0.007 (0.006) ng/ml, and despite heating these animals to 44.5 degrees C no increase in plasma lipopolysaccharide concentrations were seen in this group. The cardiovascular variable during heat stress were more unstable in the control group and began to deteriorate at a lower temperature than in the group receiving antibiotic. These data suggest that the increased plasma lipopolysaccharide concentration during heat stress originates mainly from the gut.