Sparse Graphs Research Articles

Exploring & exploiting high-order graph structure for sparse knowledge graph completion

Exploring & exploiting high-order graph structure for sparse knowledge graph completion

RT-GNN: Accelerating Sparse Graph Neural Networks by Tensor-CUDA Kernel Fusion

Graph Neural Networks (GNNs) have achieved remarkable successes in various graph-based learning tasks, thanks to their ability to leverage advanced GPUs. However, GNNs currently face challenges arising from the concurrent use of advanced Tensor Cores (TCs) and CUDA Cores (CDs) in GPUs. These challenges are further exacerbated due to repeated, inefficient, and redundant aggregations in GNN that result from the high sparsity and irregular non-zero distribution of real-world graphs. We propose RT-GNN, a GNN framework based on the fusion of advanced TC and CD units, to eliminate the aforementioned redundancies by exploiting the properties of an adjacency matrix. First, a novel GNN representation technique, hierarchical embedding graph (HEG) is proposed to manage the intermediate aggregation results hierarchically, which can further avoid redundancy in intermediate aggregations elegantly. Next, to address the inherent sparsity of graphs, RT-GNN places the blocks (a.k.a tiles) in HEG onto TCs and CDs according to their sparsity by a new block-based row-wise multiplication approach, which assembles TCs and CDs to work concurrently. Experimental results demonstrate that HEG outperforms HAG by an average speedup of 19.3 × for redundancy elimination performance, especially up to 72 × speedup on the dataset of ARXIV. Moreover, for overall performance, RT-GNN outperforms state-of-the-art GNN frameworks (including DGL, HAG, GNNAdvisor, and TC-GNN) by an average factor of 3.1 × while maintaining or even improving the task accuracy.

Implementation of a continuous-time quantum walk on a sparse graph

Implementation of a continuous-time quantum walk on a sparse graph

Trading Community Analysis of Countries’ Roll-On/Roll-Off Shipping Networks Using Fine-Grained Vessel Trajectory Data

Roll-on/roll-off vessels (RO/RO vessels) are playing an increasingly critical role in international automobile transport, facilitating the efficient movement of vehicles and heavy machinery across continents. Despite this growing significance, there is still limited research specifically focused on the RO/RO shipping network and its impact on global trade. This paper studies the global RO/RO shipping network using AIS data on RO/RO vessels collected from 2020 to 2023. We construct a method based on the complex network theory and the graph feature extraction method to quantitatively assess the features of the RO/RO shipping network. This method assesses the complexity, sparsity, homogeneity, modularity, and hierarchy of the RO/RO shipping network across various ports and countries and employs the graph convolutional neural network (GCN) model to extract network features for community detection. This process enables the identification of port clusters that are frequently linked to RO/RO vessels, as well as regional transport modes. The paper’s findings support these conclusions: (1) From 2020 to 2023, the number of nodes in the RO/RO shipping network increased by 22%, primarily concentrated in African countries. The RO/RO shipping network underwent restructuring after the pandemic, with major complex network parameters showing an upward trend. (2) The RO/RO shipping network is complex, with a stable graph density of 0.106 from 2020 to 2023. The average degree increased by 7% to 4.224. Modularity decreased by 6.5% from 0.431 in 2022 to 0.403, while the hierarchy coefficient rose to 0.575, suggesting that post-pandemic, community routes have become more diverse, reflecting the reconstruction and maturation of the overall network. (3) The model yielded a silhouette coefficient of 0.548 and a Davies–Bouldin index of 0.559 using an improved automatic feature extraction method. In comparison between 2020 and 2023, the changes in the two indicators are small. This shows that GINs can effectively extract network features and give us results that we can understand for community detection. (4) In 2023, key communities divide the RO/RO shipping network, with one community handling 39% of global routes (primarily Europe–Asia), another community handling 23% (serving Asia–Pacific, Africa, and the Middle East), and a third community managing 38% (linking Asia, Europe, and South America).

ScGraphformer: unveiling cellular heterogeneity and interactions in scRNA-seq data using a scalable graph transformer network

The precise classification of cell types from single-cell RNA sequencing (scRNA-seq) data is pivotal for dissecting cellular heterogeneity in biological research. Traditional graph neural network (GNN) models are constrained by reliance on predefined graphs, limiting the exploration of complex cell-to-cell relationships. We introduce scGraphformer, a transformer-based GNN that transcends these limitations by learning an all-encompassing cell-cell relational network directly from scRNA-seq data. Through an iterative refinement process, scGraphformer constructs a dense graph structure that captures the full spectrum of cellular interactions. This comprehensive approach enables the identification of subtle and previously obscured cellular patterns and relationships. Evaluated on multiple datasets, scGraphformer demonstrates superior performance in cell type identification compared to existing methods and showcases its scalability with large-scale datasets. Our method not only provides enhanced cell type classification ability but also reveals the underlying cell interactions, offering deeper insights into functional cellular relationships. The scGraphformer thus holds the potential to significantly advance the field of single-cell analysis and contribute to a more nuanced understanding of cellular behavior.

Analysis and knowledge extraction of newborn resuscitation activities from annotation files.

Deprivation of oxygen in an infant during and after birth leads to birth asphyxia, which is considered one of the leading causes of death in the neonatal period. Adequate resuscitation activities are performed immediately after birth to save the majority of newborns. The primary resuscitation activities include ventilation, stimulation, drying, suction, and chest compression. While resuscitation guidelines exist, little research has been conducted on measured resuscitation episodes. Objective data collected for measuring and registration of the executed resuscitation activities can be used to generate temporal timelines. This paper is primarily aimed to introduce methods for analyzing newborn resuscitation activity timelines, through visualization, aggregation, redundancy and dimensionality reduction. We are using two datasets: 1) from Stavanger University Hospital with 108 resuscitation episodes, and 2) from Haydom Lutheran Hospital with 76 episodes. The resuscitation activity timelines were manually annotated, but in future work we will use the proposed method on automatically generated timelines from video and sensor data. We propose an encoding generator with unique codes for combination of activities. A visualization of aggregated episodes is proposed using sparse nearest neighbor graph, shown to be useful to compare datasets and give insights. Finally, we propose a method consisting of an autoencoder trained for reducing redundancy in encoded resuscitation timeline descriptions, followed by a neighborhood component analysis for dimensionality reduction. Visualization of the resulting features shows very good class separability and potential for clustering the resuscitation files according to the outcome of the newborns as dead, admitted to NICU or normal. This shows great potential for extracting important resuscitation patterns when tested on larger datasets.

Metrological parameter planning method based on a multi-head sparse graph attention network for airborne products

The airborne system plays a crucial role in upholding the operational capabilities of an aircraft, and the caliber of its products significantly influences the overall reliability and safety of the aircraft. The foundational task in guaranteeing product quality is metrology, wherein metrological parameters play a pivotal role in shaping the ultimate product quality and determining metrological efficiency. Because the metrology documents are scattered in various departments and the data are highly isolated, manual planning methods are highly subjective, resulting in error-prone and inefficient results. The existing parameter planning methods based on deep learning suffer from the problems of strong training data dependency and poor model interpretability. For this reason, this paper proposes a metrological parameter planning method based on a multi-head sparse graph attention network (MHSGAT) for airborne products. First, an attribute graph structure is designed to represent product metrology information, and a metrology parameter graph dataset is constructed based on historical documents. Then, the proposed MHSGAT assigns sparse attention coefficients to the neighbors of nodes for feature aggregation. Finally, the metrology parameter planning results are output in the dense layer. The experimental results show that the proposed method outperforms the other four baseline methods. The significance of the proposed method in enhancing the metrological accuracy of airborne products and ensuring their quality is demonstrated by application cases.

Network community detection via neural embeddings

Recent advances in machine learning research have produced powerful neural graph embedding methods, which learn useful, low-dimensional vector representations of network data. These neural methods for graph embedding excel in graph machine learning tasks and are now widely adopted. However, how and why these methods work—particularly how network structure gets encoded in the embedding—remain largely unexplained. Here, we show that node2vec—shallow, linear neural network—encodes communities into separable clusters better than random partitioning down to the information-theoretic detectability limit for the stochastic block models. We show that this is due to the equivalence between the embedding learned by node2vec and the spectral embedding via the eigenvectors of the symmetric normalized Laplacian matrix. Numerical simulations demonstrate that node2vec is capable of learning communities on sparse graphs generated by the stochastic blockmodel, as well as on sparse degree-heterogeneous networks. Our results highlight the features of graph neural networks that enable them to separate communities in the embedding space.

Identification of mild cognitive impairment using multimodal 3D imaging data and graph convolutional networks

Abstract Objective. Mild cognitive impairment (MCI) is a precursor stage of dementia characterized by mild cognitive decline in one or more cognitive domains, without meeting the criteria for dementia. MCI is considered a prodromal form of Alzheimer's disease (AD). Early identification of MCI is crucial for both intervention and prevention of AD. To accurately identify MCI, a novel multimodal 3D imaging data integration graph convolutional network model is designed in this paper. Approach. The proposed model utilizes 3D-VGGNet to extract three-dimensional features from multimodal imaging data (such as sMRI and FDG-PET), which are then fused into feature vectors as the node features of a population graph. Non-imaging features of participants are combined with the multimodal imaging data to construct a population sparse graph. Additionally, in order to optimize the connectivity of the graph, we employed the Pairwise Attribute Estimation (PAE) method to compute the edge weights based on non-imaging data, thereby enhancing the effectiveness of the graph structure. Subsequently, a population-based graph convolutional network (GCN) integrates the structural and functional features of different modal images into the features of each participant for MCI classification. Main results. Experiments on the ADNI demonstrated accuracies of 98.57%, 96.03%, and 96.83% for the NC-EMCI, NC-LMCI, and EMCI-LMCI classification tasks, respectively. The AUC, specificity, sensitivity, and F1-score are also superior to state-of-the-art models, demonstrating the effectiveness of the proposed model. Furthermore, the proposed model is applied to the ABIDE dataset for autism diagnosis, achieving an accuracy of 91.43% and outperforming the state-of-the-art models, indicating excellent generalization capabilities of the proposed model. Significance. This study demonstrate the proposed model’s ability to integrate multimodal imaging data and its excellent ability to recognize MCI. This will help achieve early warning for AD and intelligent diagnosis of other brain neurodegenerative diseases.

Sparse graph structure fusion convolutional network for machinery remaining useful life prediction

Effective prediction of machinery remaining useful life (RUL) is prominent to achieve intelligent preventive maintenance in manufacturing systems. In this paper, a sparse graph structure fusion convolutional network (SGSFCN) is proposed for more accurate end-to-end RUL prediction of machine. A novel node-level graph structure called time series shapelet distance graph (TSSDG) is designed to convert the time series to node feature. The SGSFCN model is proposed to learn degradation information from the graph structure. In SGSFCN, a sparse graph structure (SGS) layer and a fusion graph structure (FGS) layer preceding the graph convolutional network (GCN) are designed to learn the SGS from node representation and fuse the original graph structure, enabling the graph structure and node update iteratively in subsequent layers. Concurrently, a bidirectional long short-term memory network (BiLSTM) layer is integrated to capture the global temporal dependencies. The method is validated by two test rig data, and results demonstrate that the proposed method offers significantly higher prediction accuracy of RUL compared to several state-of-art methods.

High performance method for COPD features extraction using complex network.

Objectives. The paper proposes a novel methodology for the classification of Chronic Obstructive Pulmonary Disease (COPD) utilizing respiratory sound attributes.Methods. The approach involves segmenting respiratory sounds into individual breaths and conducting extensive studies on this dataset. Spectral Transforms, various Wavelet Transforms are applied to capture distinct signal features. Complex Network is also employed to extract characteristic elements, generating novel representations of spectrogram data based on graph factors, including entropy, density, and position. The normalized and enriched data is then used to develop COPD classifiers using six machine learning algorithms, fine-tuning with appropriate training details and hyperparameter tuning.Results. Our results demonstrate robust performance, with ROC curves consistently exhibiting an Area Under the Curve (AUC) > 96% across different time-frequency transformations. Notably, the Random Forest algorithm achieves an AUC of 99.67%, outperforming other algorithms. Moreover, the Wavelet Daubechies 2 (Db2) consistently approaches 98% accuracy, particularly noteworthy in conjunction with the Naive Bayes algorithm.Conclusion. This study diagnosis patients through spectrogram images extracted from lung sounds. The application of Inverse Transforms, Complex Network, and Optimized Classification Algorithms yielded results beyond expectations. This methodology provides a promising approach for accurate COPD diagnosis, leveraging Machine Learning techniques applied to respiratory sound analysis.

Analysis of Behaviour Pattern of Bicycle-sharing Users Based on Complex Network: a Case Study of Beijing Downtown Area

Abstract. The introduction of the Bicycle-sharing System (BSS) has provided great convenience for residents for short travel in city. However, the parking lot planning and bicycle logistics distribution remain suboptimal, adversely affecting traffic order. Studying the spatial and temporal usage patterns can be helpful for better management of BSS. In this paper, we propose an analytical framework for detecting the bicycle-sharing pattern based on the community detection algorithms from complex networks to study the spatial-temporal patterns of usage.Firstly we identify the potential demand for bicycle among urban residents with a dataset from the BSS in Beijing downtown area. Then we construct a linkage network for modelling the BSS by applying community detection algorithms to identify regions of both high and low connectivity. Following this, based on the division of sub-areas, three indicators (graph density, cross-area travel demand, and confidence ellipses) are established for characterizing these sub-areas. Our findings include: (1) The usage pattern of the BSS within the downtown area consistently exhibits relatively stable clustering phenomena over time. (2) The usage pattern is related to the urban spatial structure, with significant differences between weekdays and weekends. (3) Residents tend to complete their cycling within the current sub-areas. (4) Generally, smaller sub-areas tend to have denser bicycle travel behaviour. These insights are vital for improving BSS parking lot planning and logistics distribution.

Effective data reduction for strongly stable matching in very sparse graphs

We provide a linear-time computable problem kernel of linear size for Strongly Stable Roommates parameterized by the feedback edge number of the acceptability graph (which encodes which agents may be matched to each other).

Counting and hardness-of-finding fixed points in cellular automata on random graphs

Abstract We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on its state and the total number of its neighbors in each possible state. Examples of this setting include classical problems such as independent sets or assortative/dissasortative partitions. We analyse the existence and number of fixed points in the large system limit using the cavity method, under both the replica symmetric (RS) and one-step replica symmetry breaking (1RSB) assumption. This method allows us to characterize the structure of the space of solutions, in particular, if the solutions are clustered and whether the clusters contain frozen variables. This last property is conjectured to be linked to the typical algorithmic hardness of the problem. We bring experimental evidence for this claim by studying the performance of the belief-propagation reinforcement algorithm, a message-passing-based solver for these constraint satisfaction problems.

Diversity and interactions of rhizobacteria determine multinutrient traits in tomato host plants under nitrogen and water disturbances

Abstract Coevolution within the plant holobiont extends the capacity of host plants for nutrient acquisition and stress resistance. However, the role of the rhizospheric microbiota in maintaining multinutrient utilization (i.e., multinutrient traits) in the host remains to be elucidated. Multinutrient cycling index (MNC), analogous to the widely used multifunctionality index, provides a straightforward and interpretable measure of the multinutrient traits in host plants. Using tomato as a model plant, we characterized MNC (based on multiple aboveground nutrient contents) in host plants under different nitrogen and water supply regimes and explored the associations between rhizospheric bacterial community assemblages and host-plant multinutrient profiles. Rhizosphere bacterial community diversity, quantitative abundance, predicted function, and key topological features of the co-occurrence network were more sensitive to water supply than to nitrogen supply. A core bacteriome comprising 61 genera, such as Candidatus Koribacter and Streptomyces, persisted across different habitats and served as a key predictor of host-plant nutrient uptake. The MNC index increased with greater diversity and higher core taxon abundance in the rhizobacterial community, while decreasing with higher average degree and graph density of rhizobacterial co-occurrence network. Multinutrient absorption by host plants was primarily regulated by community diversity and rhizobacterial network complexity under the interaction of nitrogen and water. The high biodiversity and complex species interactions of the rhizospheric bacteriome play crucial roles in host-plant performance. This study supports the development of rhizosphere microbiome engineering, facilitating effective manipulation of the microbiome for enhanced plant benefits, which supports sustainable agricultural practices and plant health.

Triangle Centrality

Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none at all. Given a simple, undirected graph \(G=(V,E)\) with \(n=|V|\) vertices and \(m=|E|\) edges, let \(\triangle(v)\) and \(\triangle(G)\) denote the respective triangle counts of \(v\) and \(G\) . Let \(N(v)\) be the neighborhood set of \(v\) . Respectively, \(N_{\triangle}(v)\) and \(N_{\triangle}[v]=\{v\}\cup N_{\triangle}(v)\) denote the set of neighbors that are in triangles with \(v\) and the closed set including \(v\) . Then the triangle centrality for a vertex \(v\) is \(\begin{align*}TC(v)=\frac{\frac{1}{3}\sum_{u\in N_{\triangle}[v]}\triangle(u)+\sum_{w\in\{N(v)\setminus N_{\triangle}(v)\}}\triangle(w)}{\triangle(G)}.\end{align*}\) We show experimentally that triangle centrality is broadly applicable to many different types of networks. Our empirical results demonstrate that 30% of the time triangle centrality identified central vertices that differed with those found by five well-known centrality measures, which suggests novelty without being overly specialized. It is also asymptotically faster to compute on sparse graphs than all but the most trivial of these other measures. We introduce optimal algorithms that compute triangle centrality in \(O(m\overline{\delta})\) time and \(O(m+n)\) space, where \(\overline{\delta}\leq O(\sqrt{m})\) is the average degeneracy introduced by Burkhardt, Faber, and Harris (2020). In practical applications, \(\overline{\delta}\) is much smaller than \(\sqrt{m}\) so triangle centrality can be computed in nearly linear time. On a Concurrent Read Exclusive Write (CREW) Parallel Random Access Machine (PRAM), we give a near work-optimal parallel algorithm that takes \(O(\log n)\) time using \(O(m\sqrt{m})\) CREW PRAM processors. In MapReduce, we show it takes four rounds using \(O(m\sqrt{m})\) communication bits and is therefore optimal. We also derive a linear algebraic formulation of triangle centrality which can be computed in \(O(m\overline{\delta})\) time on sparse graphs.

Predictions on new Cu-based ABO3 (A=Cu and B=Lu, Y) oxide-perovskite for energy storage and optoelectronic applications: A DFT study

Cu-based novel oxide-perovskite ABO3(A = Cu and B=Lu, Y) compounds have been investigated for their physical properties using the Generalized Gradient Approximation and Revised-Perdew-Burke-Ernzerhof (GGA-RPBE) exchanging correlation-functional within the density functional theory (DFT). The calculations show that both compounds comprise a cubic structure with the space group of Pm3m. The calculations also indicate that the results we have discovered represent unique compounds. Formation enthalpy computations have been used to assess the overall structural stability of both compounds. The density of states and band structure graphs for both perovskite compounds provide strong evidence of their semiconducting behavior. In-depth research is also done on optical properties such as the refractive index, extinction coefficient, absorption, reflectivity, electrical conductivity, and the energy loss function. At high-energy photons, both compounds CuLuO3 and CuYO3 show outstanding conductivity and absorption. While, at lower incident photon energy intervals, they both exhibit transparency. Based on our electronic and optical properties investigations, we have found that CuLuO3 and CuYO3 are potential candidates for use in high-energy UV, and optoelectronic technologies.

The k-core in percolated dense graph sequences

Abstract We determine the order of the k-core in a large class of dense graph sequences. Let $G_n$ be a sequence of undirected, n-vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}$ that converges to a graphon $W\colon[0,1]^2 \to [0,+\infty)$ in the cut metric. Keeping an edge (i,j) of $G_n$ with probability ${a^n_{i,j}}/{n}$ independently, we obtain a sequence of random graphs $G_n({1}/{n})$ . Using a branching process and the theory of dense graph limits, under mild assumptions we obtain the order of the k-core of random graphs $G_n({1}/{n})$ . Our result can also be used to obtain the threshold of appearance of a k-core of order n.

Fast and Optimal Extraction for Sparse Equality Graphs

Equality graphs (e-graphs) are used to compactly represent equivalence classes of terms in symbolic reasoning systems. Beyond their original roots in automated theorem proving, e-graphs have been used in a variety of applications. They have become particularly important as the key ingredient in the popular technique of equality saturation, which has notable applications in compiler optimization, program synthesis, program verification, and symbolic execution, among others. In a typical equality saturation workflow, an e-graph is used to store a large number of equalities that are generated by local rewrites during a saturation phase, after which an optimal term is extracted from the e-graph as the output of the technique. However, despite its crucial role in equality saturation, e-graph extraction has received relatively little attention in the literature, which we seek to start addressing in this paper. Extraction is a challenging problem and is notably known to be NP-hard in general, so current equality saturation tools rely either on slow optimal extraction algorithms based on integer linear programming (ILP) or on heuristics that may not always produce the optimal result. In fact, in this paper, we show that e-graph extraction is hard to approximate within any constant ratio. Thus, any such heuristic will produce wildly suboptimal results in the worst case. Fortunately, we show that the problem becomes tractable when the e-graph is sparse, which is the case in many practical applications. We present a novel parameterized algorithm for extracting optimal terms from e-graphs with low treewidth, a measure of how “tree-like” a graph is, and prove its correctness. We also present an efficient Rust implementation of our algorithm and evaluate it against ILP on a number of benchmarks extracted from the Cranelift benchmark suite, a real-world compiler optimization library based on equality saturation. Our algorithm optimally extracts e-graphs with treewidths of up to 10 in a fraction of the time taken by ILP. These results suggest that our algorithm can be a valuable tool for equality saturation users who need to extract optimal terms from sparse e-graphs.

A Fast Algorithm for All-Pairs-Shortest-Paths Suitable for Neural Networks.

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: if the edges are given by the adjacency matrix Aij, then with a suitably small value of γ, the shortest path distances are Dij=ceil(logγ[(I-γA)-1]ij).We derive several graph-theoretic bounds on the value of γ and explore its useful range with numerics on different graph types. Even when the distance function is not globally accurate across the entire graph, it still works locally to instruct pursuit of the shortest path. In this mode, it also extends to weighted graphs with positive edge weights. For a wide range of dense graphs, this distance function is computationally faster than the best available alternative. Finally, we show that this method leads naturally to a neural network solution of the all-pairs-shortest-path problem.