Spatial Graph Research Articles

Deep spatio-temporal feature fusion learning for multi-step building cooling load forecasting

Accurate forecasting of building cooling load is essential for optimizing control strategies and energy efficiency in heating, ventilation, and air conditioning (HVAC) systems. However, existing machine learning and deep learning algorithms encounter challenges in addressing the dynamics and uncertain nature of cooling load demand, as they solely focus on temporal analysis. To tackle this issue, the paper proposes CRG-Informer, a deep learning approach that integrates spatio-temporal features to enhance multi-step predictive performance. Firstly, a time series spatial control relationship graph set is constructed based on the interconnected structure, static attributes, and control characteristics of the cooling system. Then, a graph neural network (GNN) is designed for graph embedding to extract spatial correlation information at each instance. Additionally, the Informer model with the ProbSparse self-attention mechanism is utilized to capture long-term temporal dependencies among input sequences. This integration of components enables feature fusion, and the proposed approach is evaluated using data from an office building in Hangzhou, China, over an entire cooling season. Extensive experiments were conducted to compare our method with five superior baseline models for 6, 12, 24, 72, and 144-step cooling load forecasting across four types of data acquisition intervals. The results demonstrate that the CRG-Informer, through spatio-temporal feature fusion, outperforms existing methods and provides a novel solution for improving cooling load forecasting performance.

A novel structural deformation prediction method based on graph convolutional network during shield tunnel construction

During shield tunneling through existing steel reinforced concrete structures, superstructure deformation is an important parameter that reflects the disturbance degree of engineering construction to existing structure. Precisely predicting structural deformation can help engineers adjust shield machine operational parameters and ensure the success of the project. There has been no attempt to study the feasibility and applicability of machine learning for predicting structural deformation when shield machine cut through existing structure. To address this problem, this paper proposes a novel hybrid model (DSGCN-TCN), combining dynamic spatial graph convolutional network (DSGCN) and temporal convolutional network (TCN), to predict structural deformation. First, dynamic adjacency matrix is constructed based on correlation coefficient and attention mechanism to describe the dynamic change of irregular graph structure. Then dynamic adjacency matrices and feature matrices as the input of the GCN model to extract the dynamic spatial feature of structural deformation data. Followed by TCN and attention layer to capture the temporal correlation of structural deformation data. Finally, the prediction performance of the proposed method is verified using measured data from practical engineering. The experiment results show that compared with the selected baseline models and sub-models, the proposed model can predict the structural deformation more accurately.

Graph Fourier transform for spatial omics representation and analyses of complex organs

Spatial omics technologies decipher functional components of complex organs at cellular and subcellular resolutions. We introduce Spatial Graph Fourier Transform (SpaGFT) and apply graph signal processing to a wide range of spatial omics profiling platforms to generate their interpretable representations. This representation supports spatially variable gene identification and improves gene expression imputation, outperforming existing tools in analyzing human and mouse spatial transcriptomics data. SpaGFT can identify immunological regions for B cell maturation in human lymph nodes Visium data and characterize variations in secondary follicles using in-house human tonsil CODEX data. Furthermore, it can be integrated seamlessly into other machine learning frameworks, enhancing accuracy in spatial domain identification, cell type annotation, and subcellular feature inference by up to 40%. Notably, SpaGFT detects rare subcellular organelles, such as Cajal bodies and Set1/COMPASS complexes, in high-resolution spatial proteomics data. This approach provides an explainable graph representation method for exploring tissue biology and function.

Multiple habitat graphs: how connectivity brings forth landscape ecological processes

PurposeHabitat connectivity is integral to current biodiversity science and conservation strategies. Originally, the connectivity concept stressed the role of individual movements for landscape-scale processes. Connectivity determines whether populations can survive in sub-optimal patches (i.e., source-sink effects), complete life cycles relying on different habitat types (i.e., landscape complementation), and benefit from supplementary resources distributed over the landscape (i.e., landscape supplementation). Although the past decades have witnessed major improvements in habitat connectivity modeling, most approaches have yet to consider the multiplicity of habitat types that a species can benefit from. Without doing so, connectivity analyses potentially fail to meet one of their fundamental purposes: revealing how complex individual movements lead to landscape-scale ecological processes.MethodsTo bridge this conceptual and methodological gap, we propose to include multiple habitat types in spatial graph models of habitat connectivity, where nodes traditionally represent a single habitat type. Multiple habitat graphs will improve how we model connectivity and related landscape ecological processes, and how they are impacted by land cover changes.ResultsIn three case studies, we use these graphs to model (i) source-sink effects, (ii) landscape supplementation, and (iii) complementation processes, in urban ecosystems, agricultural landscapes, and amphibian habitat networks, respectively. A new version of the Graphab open-source software implements the proposed approach.ConclusionMultiple habitat graphs help address crucial conservation challenges (e.g., urban sprawl, biological control, climate change) by representing more accurately the dynamics of populations, communities, and their interactions. Our approach thereby extends the ecologist’s toolbox and aims at fostering the alignment between landscape ecology theory and practice.

HyGate-GCN: Hybrid-Gate-Based Graph Convolutional Networks with dynamical ratings estimation for personalized POI recommendation

The presence of user-generated ratings has dramatically facilitated the development of recommendation systems to aid users in discovering relevant and personalized points of interest (POI). It is worth mentioning that users’ choices and preferences are not static but rather dynamic, reflecting the ever-changing nature of human experiences and influences. Furthermore, the utilization of social influence and geographical proximity of users is still insufficient to capture the homophily effect within networks. In this paper, an interesting Hybrid Gate-based Graph Convolutional Network (HyGate-GCN) combining with feature vectors embedding and interaction, where a modified gated-GCN is proposed for personalized recommendations by adequately employing the behavior of users’ check-ins, temporal properties of users’ decisions, social properties of users, as well as the user/POI profile information data. Specifically, a novel POI graph reflecting the geographical proximity is first established to describe the behavior of users’ check-ins and, at the same time, an improved overlap ratio about POIs is employed to effectively describe temporal properties of users’ decisions. Then, an attention mechanism is developed to encode feature vectors of both the users and POIs, with the objective of assigning higher importance to features that are deemed relevant. Furthermore, a temporal Kalman filter dynamically estimating ratings is developed to exploit the information about the evolving preferences of users over time. Finally, a modified gated-GCN model with merging and refining gates is constructed to effectively acquire the homophily phenomenon in both trust network graphs and spatial adjacency matrix graphs of users and POIs respectively. Experimental results provide evidence of the effectiveness of our approach in improving accuracy and personalization.

Exploring the conflict risk characteristics of air weaving sections in Metroplex terminal areas with flight trajectory data and adaptive graph spatial-temporal transformer

Metroplex terminal areas is involved with numerous air weaving sections, where various types of arrival and departure traffic flows intersect or converge, leading to high-risk aircraft conflicts and inefficient Metroplex operation. The primary objective of this study is to explore the conflict risk characteristics of operational interactions between airports in Metroplex terminal areas with large-scale trajectory data, including risk evaluation, risk propagation and risk prediction. One complete month of ADS-B trajectory data is collected from a representative multi-airport system in Central and South China to illustrate the procedure. Specifically, flight trajectories are firstly clustered within Metroplex terminal areas, and a trajectory-tube model is then built to characterize the airport flows within the same cluster. Then, a clustering-based collision probability calculation method is proposed to evaluate the risk of air weaving sections. The spatial patterns of risks in air weaving sections reveal that operational interactions among Metroplex airports are quite different under various runway configurations. Furthermore, an adaptive graph spatial-temporal transformer (ASTT) network is developed to predict the future risk of each air weaving section in Metroplex terminal areas. The results indicate that the developed ASTT network can collaboratively encode the spatiotemporal characteristics in the air weaving section risk data, which achieves more accurate and robust prediction performance than other compared models during multiple look-ahead time steps. Moreover, the adaptive spatial graph technique designed in the ASTT can also reveal the hidden risk propagation effects among air weaving sections. The results of this study could provide insightful suggestions to air traffic authorities for developing effective coordination and conflict mitigation strategies, such as redesigning flight procedures, reallocating routes, and optimizing aircraft sequences to enhance the efficiency and safety of Metroplex operations.

Multi-granularity spatial temporal graph convolution network with consecutive attention for human motion prediction

Human motion prediction is attracting increasing attention for its numerous potential applications in fields including autonomous driving, video surveillance and virtual reality. However, accurate motion prediction is challenging due to the complex spatial dependencies, dynamic temporal correlations and high dimension of human pose sequences. Existing graph-based methods rarely consider positional and channel information of the feature map, resulting in lower prediction accuracy. Therefore, we propose a novel multi-granularity spatial temporal graph convolution network with consecutive attention (MSTCA) for human motion prediction. Firstly, a multi-granularity spatial convolution network is introduced to capture spatial joint features through multiple kernel sizes. Then, consecutive attention module is proposed to capture both positional and channel information of the feature map. Next, MSTCA uses multi-granularity temporal convolutional network to extract temporal correlations with multiple receptive fields and predict future poses. Finally, a decoder composed of a 2D convolution layer and several PRelu layers integrates the output of the whole model. Experimental results on the GTA-IM and PROX datasets demonstrate that our method significantly improves the accuracy of human motion prediction in comparison to the existing approaches.

Splittings of tangles and spatial graphs

Menasco proved that if G is a reduced, alternating, connected diagram of a link L and G is prime then L is prime. This surprising and important result has been generalized to other classes of links, as well as to tangles and spatial graphs. After exploring some issues with previous results, we obtain new splitting results for tangles and spatial graphs.

Spatial and temporal attention embedded spatial temporal graph convolutional networks for skeleton based gait recognition with multiple IMUs

Gait recognition is one of the key technologies for exoskeleton robot control, while the current IMU-based gait recognition methods only use inertial data and do not fully consider the interconnections of human spatial structure and human joints. In this regard, a skeleton-based gait recognition approach with inertial measurement units using spatial temporal graph convolutional networks with spatial and temporal attention is proposed. A human forward kinematics solver module was used for constructing different human skeleton models and a temporal attention module was added for capturing the more important time frames in the gait cycle. Moreover, the two-stream structure was used to construct spatial temporal graph convolutional networks with spatial and temporal attention for gait recognition, and an average accuracy of about 99% was obtained in user experiments, which is the best performance compared to other algorithms, provides certain reference for gait recognition and real-time control of exoskeleton robots.

ANALYSIS OF RESOLVING EFFICIENT DOMINATING SET AND ITS APPLICATION SCHEME IN SOLVING ETLE PROBLEMS

This research focuses on the analysis of Resolving Efficient Dominating Set (REDS) and its application in solving Electronic Traffic Law Enforcement (ETLE) problems using the Spatial Temporal Graph Neural Network (STGNN). Resolving Efficient Dominating Set (REDS) is a concept in graph theory that studies a set of points in a graph that efficiently monitors other points. It involves ensuring that each point v ∈ V (G) - D is dominated by exactly one point in D, with no adjacent points in D, and the representation of point v ∈ V (G) concerning D is not the same, which is termed as a resolving efficient dominating set. In the context of Electronic Traffic Law Enforcement (ETLE), the analysis of REDS has a significant impact. The theorem resulting from the analysis of REDS enables the determination of the number of traffic violation sensors required. Furthermore, by taking simulation data from road points, violation forecasting can be performed. The accurate predictions from this forecasting can assist authorities in anticipating and addressing traffic violation issues more effectively.

Graph-based multi-agent reinforcement learning for collaborative search and tracking of multiple UAVs

This paper investigates the challenges associated with Unmanned Aerial Vehicle (UAV) collaborative search and target tracking in dynamic and unknown environments characterized by limited field of view. The primary objective is to explore the unknown environments to locate and track targets effectively. To address this problem, we propose a novel Multi-Agent Reinforcement Learning (MARL) method based on Graph Neural Network (GNN). Firstly, a method is introduced for encoding continuous-space multi-UAV problem data into spatial graphs which establish essential relationships among agents, obstacles, and targets. Secondly, a Graph AttenTion network (GAT) model is presented, which focuses exclusively on adjacent nodes, learns attention weights adaptively and allows agents to better process information in dynamic environments. Reward functions are specifically designed to tackle exploration challenges in environments with sparse rewards. By introducing a framework that integrates centralized training and distributed execution, the advancement of models is facilitated. Simulation results show that the proposed method outperforms the existing MARL method in search rate and tracking performance with less collisions. The experiments show that the proposed method can be extended to applications with a larger number of agents, which provides a potential solution to the challenging problem of multi-UAV autonomous tracking in dynamic unknown environments.

Discovery and generalization of tissue structures from spatial omics data

Tissues are organized into anatomical and functional units at different scales. New technologies for high-dimensional molecular profiling in situ have enabled the characterization of structure-function relationships in increasing molecular detail. However, it remains a challenge to consistently identify key functional units across experiments, tissues, and disease contexts, a task that demands extensive manual annotation. Here, we present spatial cellular graph partitioning (SCGP), a flexible method for the unsupervised annotation of tissue structures. We further present a reference-query extension pipeline, SCGP-Extension, that generalizes reference tissue structure labels to previously unseen samples, performing data integration and tissue structure discovery. Our experiments demonstrate reliable, robust partitioning of spatial data in a wide variety of contexts and best-in-class accuracy in identifying expertly annotated structures. Downstream analysis on SCGP-identified tissue structures reveals disease-relevant insights regarding diabetic kidney disease, skin disorder, and neoplastic diseases, underscoring its potential to drive biological insight and discovery from spatial datasets.

Separable Spatial-Temporal Residual Graph for Cloth-Changing Group Re-Identification.

Group re-identification (GReID) aims to correctly associate group images belonging to the same group identity, which is a crucial task for video surveillance. Existing methods only model the member feature representations inside each image (regarded as spatial members), which leads to potential failures in long-term video surveillance due to cloth-changing behaviors. Therefore, we focus on a new task called cloth-changing group re-identification (CCGReID), which needs to consider group relationship modeling in GReID and robust group representation against cloth-changing members. In this paper, we propose the separable spatial-temporal residual graph (SSRG) for CCGReID. Unlike existing GReID methods, SSRG considers both spatial members inside each group image and temporal members among multiple group images with the same identity. Specifically, SSRG constructs full graphs for each group identity within the batched data, which will be completely and non-redundantly separated into the spatial member graph (SMG) and temporal member graph (TMG). SMG aims to extract group features from spatial members, and TMG improves the robustness of the cloth-changing members by feature propagation. The separability enables SSRG to be available in the inference rather than only assisting supervised training. The residual guarantees efficient SSRG learning for SMG and TMG. To expedite research in CCGReID, we develop two datasets, including GroupPRCC and GroupVC, based on the existing CCReID datasets. The experimental results show that SSRG achieves state-of-the-art performance, including the best accuracy and low degradation (only 2.15% on GroupVC). Moreover, SSRG can be well generalized to the GReID task. As a weakly supervised method, SSRG surpasses the performance of some supervised methods and even approaches the best performance on the CSG dataset.

Effective Emotion Recognition by Learning Discriminative Graph Topologies in EEG Brain Networks.

Multichannel electroencephalogram (EEG) is an array signal that represents brain neural networks and can be applied to characterize information propagation patterns for different emotional states. To reveal these inherent spatial graph features and increase the stability of emotion recognition, we propose an effective emotion recognition model that performs multicategory emotion recognition with multiple emotion-related spatial network topology patterns (MESNPs) by learning discriminative graph topologies in EEG brain networks. To evaluate the performance of our proposed MESNP model, we conducted single-subject and multisubject four-class classification experiments on two public datasets, MAHNOB-HCI and DEAP. Compared with existing feature extraction methods, the MESNP model significantly enhances the multiclass emotional classification performance in the single-subject and multisubject conditions. To evaluate the online version of the proposed MESNP model, we designed an online emotion monitoring system. We recruited 14 participants to conduct the online emotion decoding experiments. The average online experimental accuracy of the 14 participants was 84.56%, indicating that our model can be applied in affective brain-computer interface (aBCI) systems. The offline and online experimental results demonstrate that the proposed MESNP model effectively captures discriminative graph topology patterns and significantly improves emotion classification performance. Moreover, the proposed MESNP model provides a new scheme for extracting features from strongly coupled array signals.

Planar Stick Indices of Some Knotted Graphs

Two isomorphic graphs can have inequivalent spatial embeddings in 3-space. In this way, an isomorphism class of graphs contains many spatial graph types. A common way to measure the complexity of a spatial graph type is to count the minimum number of straight sticks needed for its construction in 3-space. In this paper, we give estimates of this quantity by enumerating stick diagrams in a plane. In particular, we compute the planar stick indices of knotted graphs with low crossing numbers. We also show that if a bouquet graph or a theta-curve has the property that its proper subgraphs are all trivial, then the planar stick index must be at least seven.

Структура машиностроительного изделия

The structure of the product design affects the efficiency of its operation and the labor-output ratio. The structure of the product design can be represented using flat and spatial graphs, which are characterized by the number of levels and the number of elements located at each level, where both a node and a part can act as an element. Flat graph shows the connec-tions between the elements of the product design, their dependence, indicating the bases of each element, but at the same time it does not reflect their spatial location. The spatial graph illustrates the layout of the product structure in space. Hence, the structure of the product design should be understood as the relative location of the product design elements, their types and the number of each element. There is a direct connection between the structure of the product design and the level of its complexity. The more complex the product design structure, the higher the level of design complexity. Such connection allows

XSiGra: explainable model for single-cell spatial data elucidation.

Recent advancements in spatial imaging technologies have revolutionized the acquisition of high-resolution multichannel images, gene expressions, and spatial locations at the single-cell level. Our study introduces xSiGra, an interpretable graph-based AI model, designed to elucidate interpretable features of identified spatial cell types, by harnessing multimodal features from spatial imaging technologies. By constructing a spatial cellular graph with immunohistology images and gene expression as node attributes, xSiGra employs hybrid graph transformer models to delineate spatial cell types. Additionally, xSiGra integrates a novel variant of gradient-weighted class activation mapping component to uncover interpretable features, including pivotal genes and cells for various cell types, thereby facilitating deeper biological insights from spatial data. Through rigorous benchmarking against existing methods, xSiGra demonstrates superior performance across diverse spatial imaging datasets. Application of xSiGra on a lung tumor slice unveils the importance score of cells, illustrating that cellular activity is not solely determined by itself but also impacted by neighboring cells. Moreover, leveraging the identified interpretable genes, xSiGra reveals endothelial cell subset interacting with tumor cells, indicating its heterogeneous underlying mechanisms within complex cellular interactions.

A spatial scene reconstruction framework in emergency response scenario

Rapid and accurate acquisition and analysis of information is crucial for emergency management, but traditional methods have limitations such as incomplete information acquisition and slow processing speed. The natural language oriented spatial scene reconstruction method provides a new solution for emergency management, but existing generative models have limited understanding of spatial relationships and lack high-quality training samples. To address these issues, this paper proposes a novel spatial scene reconstruction framework. Specifically, the BERT based spatial information knowledge graph extraction method is used to encode the input text, label and classify the encoded text, identify spatial objects and relationships in the text, and accurately extract spatial information. Additionally, a large number of manual experiments were conducted to explore quantitative biases in human spatial cognition, and based on the obtained biases, a greedy resolution method based on cost functions was used to fine tune the layout of conflicting spatial objects and solve the conflicting spatial information in the spatial information knowledge graph. Finally, use graph convolutional neural networks to obtain scene knowledge graph embeddings that consider spatial constraints. In addition, a high-quality training sample set of “text-scene-knowledge graph” was constructed.

Micro-expression recognition based on a novel GCN-transformer cooperation model for IoT-eHealth

If a person is truly healthy, his/her well-being encompasses both physical and psychological health. However, the existing IoT-eHealth system typically focus only on monitoring the user’s physical data through various sensors, neglecting their mental state. To enhance the intelligence level of IoT-eHealth system and enable it to have the psychological monitoring ability, a novel collaborative model based on Graph Convolutional Network (GCN) and Transformer is designed for Micro-Expression (ME) recognition in this paper. Firstly, facial information within each frame is transformed into a Spatial Topological Relationship Graph (STRG) by using facial landmarks detection and psychological relationship of local patches. Then, in order to automatically aggregate the key information on facial patches that contribute to ME recognition from the structured graph data, a Hierarchical Adaptive Graph Pooling (HAGP) module is designed for obtaining discriminative frame-level feature based on GCN utilizing graph structure and vertex global dependencies. Finally, in order to model the long-term dependencies among frames and capture the key frame-level features that are beneficial for ME recognition, a Temporal Sensitive Self-Attention (TSSA) mechanism is designed, and a novel Temporal Sensitive Transformer (TST) encoder is constructed based on TSSA to explore the evolution law of facial patterns and obtain discriminative video-level features that are helpful for ME recognition. In the comparative experiments of standard dataset verification and practical dataset testing, designed collaborative model is superior to other methods and can achieve the highest recognition accuracy, which almost can meet the application requirements of IoT-eHealth system.

Multi‐scale skeleton simplification graph convolutional network for skeleton‐based action recognition

AbstractHuman action recognition based on graph convolutional networks (GCNs) is one of the hotspots in computer vision. However, previous methods generally rely on handcrafted graph, which limits the effectiveness of the model in characterising the connections between indirectly connected joints. The limitation leads to weakened connections when joints are separated by long distances. To address the above issue, the authors propose a skeleton simplification method which aims to reduce the number of joints and the distance between joints by merging adjacent joints into simplified joints. Group convolutional block is devised to extract the internal features of the simplified joints. Additionally, the authors enhance the method by introducing multi‐scale modelling, which maps inputs into sequences across various levels of simplification. Combining with spatial temporal graph convolution, a multi‐scale skeleton simplification GCN for skeleton‐based action recognition (M3S‐GCN) is proposed for fusing multi‐scale skeleton sequences and modelling the connections between joints. Finally, M3S‐GCN is evaluated on five benchmarks of NTU RGB+D 60 (C‐Sub, C‐View), NTU RGB+D 120 (X‐Sub, X‐Set) and NW‐UCLA datasets. Experimental results show that the authors’ M3S‐GCN achieves state‐of‐the‐art performance with the accuracies of 93.0%, 97.0% and 91.2% on C‐Sub, C‐View and X‐Set benchmarks, which validates the effectiveness of the method.