Sparse Graphs Research Articles

Multi-hop path reasoning over sparse temporal knowledge graphs based on path completion and reward shaping

Multi-hop path reasoning plays a crucial role in temporal knowledge graph reasoning, aiming to infer deep complex relationships and obtain interpretable reasoning results. Previous reasoning models primarily focus on designing temporal knowledge graphs with rich paths between entities but struggle to handle path sparsity, known as sparse temporal knowledge graphs. Sparse temporal knowledge graphs store only essential knowledge information, resulting in missing connection paths between certain entities and encountering issues of sparse rewards and information scarcity. To tackle these challenges, this paper proposes a multi-hop path reasoning model over sparse temporal knowledge graph based on path completion and reward shaping (STKGR-PR). STKGR-PR dynamically completes missing paths using a temporal embedding model to alleviate path sparsity. To tackle the issue of sparse rewards caused by reduced hit rates, we propose semantic composition-based reasoning path embeddings derived from relation embeddings and timestamp embeddings for reward shaping. Considering the limited information contained in sparse temporal knowledge graphs, we incorporate time vectors into the embedding and multi-hop path reasoning models to enhance the accuracy of reasoning paths and results. Experimental results conducted on six sparse temporal datasets sampled from ICEWS14 and ICEWS515–05 demonstrate that STKGR-PR outperforms state-of-the-art multi-hop path reasoning models over temporal knowledge graphs across all evaluation metrics, while ensuring interpretability.

On the intersection density of the Kneser graph [formula omitted

A set F⊂Sym(V) is intersecting if any two of its elements agree on some element of V. Given a finite transitive permutation group G≤Sym(V), the intersection densityρ(G) is the maximum ratio |F||V||G| where F runs through all intersecting sets of G. The intersection densityρ(X) of a vertex-transitive graph X=(V,E) is equal to maxρ(G):G≤Aut(X),G transitive. In this paper, we study the intersection density of the Kneser graph K(n,3), for n≥7. The intersection density of K(n,3) is determined whenever its automorphism group contains PSL2(q), with some exceptional cases depending on the congruence of q. We also briefly consider the intersection density of K(n,2) for values of n where PSL2(q) is a subgroup of its automorphism group.

Core microbiota play important roles in maintaining soil multi‐nutrient cycling in lakeshore wetland of plateau lake Caohai

AbstractMicroorganisms play important roles in soil biogeochemical processes, but the relative contributions of different microbial members in soil nutrient cycling and community maintenance are unclear especially in wetland soils with water‐level fluctuation. Here, soil samples, collected from severe inundation zone (SIZ), wet–dry cycling zone (WIZ), and arid zone (NIZ) of the lakeshore wetland of plateau lake Caohai, were used to investigate the relative contributions of core and rare taxa in maintaining nutrient cycling and their associations with microbial network. Results showed that WIZ exhibited higher extracellular enzyme activities including β‐1,4‐N‐acetylglucosaminidase, L‐leucine aminopeptidase, and acid phosphatase, the level of multi‐nutrient cycling and core microbial diversity compared with the NIZ and SIZ. The values of topological features (i.e., links, average degree, clustering coefficient, and graph density) were also higher in the WIZ compared with the NIZ and SIZ. Moreover, the core taxa, specifically their community structures, were the most important driver for multi‐nutrient cycles of wetland soil. Among these taxa, Sphingomonas, Bradyrhizobium, Mortierella, and Fusarium as the most abundant taxa in lakeshore wetlands were significantly positively correlated with most extracellular enzymes. By contrast, rare taxa showed higher degree and its subnetwork complexity than those of core taxa, which potentially serve as the species pool of core taxa to maintaining the microbial community stability. In conclusion, our study suggested that core taxa play dominant roles in soil nutrient cycles, while rare microbiota could greatly influence microbial interaction under hydrological changes.

DYS-SLAM: A real-time RGBD SLAM combined with optical flow and semantic information in a dynamic environment1

Traditional Simultaneous Localization and Mapping application in dynamic situations is constrained by static assumptions. However, the majority of well-known dynamic SLAM systems use deep learning to identify dynamic objects, which creates the issue of trade-offs between accuracy and real-time. To tackle this issue, this work suggests a unique dynamic semantics method(DYS-SLAM) for semantic simultaneous localization and mapping that strikes a trade-off between high accuracy and high real-time performance. We propose M-LK, an enhanced Lucas-Kanade(LK) optical flow method. This technique keeps the continuous motion and greyscale consistency assumptions from the original method while switching out the spatial consistency assumption for a motion consistency assumption, reducing sensitivity to image gradients to identify dynamic feature points and regions efficiently. In order to increase segmentation accuracy while maintaining real-time performance, we develop a segmentation refinement scheme that projects 3D point cloud segmentation results into 2D object detection zones. A dense semantic octree graph is built in the interim to expedite the high-level process. Compared to the four equivalent dynamic SLAM approaches, experiments on the publicly available TUM RGB-D dataset demonstrate that the DYS-SLAM method offers competitive localization accuracy and satisfactory real-time performance in both high and low-dynamic scenarios.

SGA-Net: A Sparse Graph Attention Network for Two-View Correspondence Learning

Establishing reliable correspondences between two images is a fundamental and important task in computer vision. This paper proposes a novel network called Sparse Graph Attention Network (SGA-Net), to capture rich contextual information of sparse graphs for feature matching task. Specifically, a graph attention block is proposed to enhance the representational ability of graph-structured features. The proposed block introduces a novel normalization technique for graph-structured features to embed global information into each edge feature, and it adopts the squeeze-and-excitation mechanism to capture graph-wise contextual information. Meanwhile, to further obtain interesting structural information of sparse graphs, a novel sparse graph transformer is developed based on multi-headed self-attention mechanism, while maintaining permutation-equivariance. Additionally, considering that the graph contexts in shallow layers are not fully exploited, a simple graph-context fusion block is introduced to adaptively capture topological information from different layers by implicitly modeling the interdependence between these graph contexts. The proposed SGA-Net can search dependable candidates among the putative correspondences and simultaneously estimate accurate camera poses for two-view geometry estimation. Extensive experiments on outlier removal and camera pose estimation tasks have demonstrated that the proposed SGA-Net outperforms state-of-the-art methods on both outdoor and indoor benchmarks (i.e., YFCC100M and SUN3D). SGA-Net achieves a mAP5° of 58.88% without RANSAC on the outdoor dataset, and it achieves a precision increase of 13.45% and 7.34% compared with the state-of-the-art result on outdoor and indoor datasets, respectively.

Sparse graph neural network aided efficient decoder for polar codes under bursty interference

In this paper, a sparse graph neural network-aided (SGNN-aided) decoder is proposed for improving the decoding performance of polar codes under bursty interference. Firstly, a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding. To further improve the decoding performance, a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network. This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks. Finally, predictions are generated by feeding the embedding vectors into a readout module. Simulation results are shown that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.

CoGNN: An Algorithm-Hardware Co-Design Approach to Accelerate GNN Inference With Minibatch Sampling

As a new algorithm of graph embedding, Graph Neural Networks (GNNs) have been widely used in many fields. However, GNN computing has the characteristics of both sparse graph processing and dense neural network, which make it difficult to be deployed efficiently on the existing graph processing accelerators or neural network accelerators. Recently, some GNN accelerators have been proposed, but the following challenges have not been fully solved: 1) The mini-batch GNN inference scenario has the potential of software and hardware co-design, which can bring 30% computation amount reduction, and this is not well utilized. Besides, the cost of Message Flow Graph construction is large and may account for more than 50% of the total delay. 2) The feature aggregation has a large amount of data access and relatively small amount of computation, which leads to low on-chip data reuse, only 10% of dense computing. 3) Without the optimization of sparse computing units, simple memory bank and cross bar architecture can easily lead to bank access conflict and load imbalance, reducing the utilization of computing units to less than 60%. In order to solve the above problems, we propose a algorithm-hardware co-design scheme to accelerate GNN inference, which includes three technologies: 1) A reuse-aware sampling method is proposed for mini-batch inference scenarios, which reduces 30% of the calculation and improves the on-chip reusability of local data. 2) Through the node-wise parallelism-aware quantization, the features and weights are quantized to integers with eight or four bits, which reduces the amount of memory access by at least four times. 3) An accelerator supporting the above technologies is designed and evaluated, and different operations are supported by the sampling-inference integration architecture. The multi-bank on-chip memory pool is designed to support data reuse, and edge stream reordering is used to reduce data access conflicts, improving the utilization of computing units by 1.5x. Combined with the above technologies, the experiments show that our design achieves 9.2× speedup and 29× energy efficiency improvement compared with Deep Graph Library framework running on servers equiped with CPU and GPU.

Weisfeiler-Leman Indistinguishability of Graphons

The color refinement algorithm is mainly known as a heuristic method for graph isomorphism testing. It has surprising but natural characterizations in terms of, for example, homomorphism counts from trees and solutions to a system of linear equations. Grebík and Rocha (2022) have recently shown how color refinement and notions that characterize it generalize to graphons, which emerged as limit objects in the theory of dense graph limits. In particular, they show that these characterizations are still equivalent in the graphon case. The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a more powerful variant of color refinement that colors $k$-tuples instead of single vertices, where the terms $1$-WL and color refinement are often used interchangeably since they compute equivalent colorings. We show how to adapt the result of Grebík and Rocha to $k$-WL or, in other words, how $k$-WL and its characterizations generalize to graphons. In particular, we obtain characterizations in terms of homomorphism densities from multigraphs of bounded treewidth and linear equations. We give a simple example that parallel edges make a difference in the more general case of graphons, which means that, there, the equivalence between $1$-WL and color refinement does not hold anymore. We also show how this equivalence can be recovered by defining a variant of $k$-WL that corresponds to homomorphism densities from simple graphs of bounded treewidth.

APOE ε4 and cognitive networks: Centrality of episodic memory nodes in patients with mild cognitive impairment

AbstractBackgroundThe literature based on univariate models does not lead to unequivocal conclusions on the effects of APOE variability on cognition. We thus hypothesised that the impact of APOE‐ε4 on cognitive functioning can be reliably captured by graph‐theory.MethodCognitive datasets were extracted from the National Alzheimer’s Coordinating Center’s database. After the application of stringent exclusion criteria, 16,173 participants with a known APOE ε3ε3/ε4ε3/ε4ε4 genotype were retained: 8,118 controls, 3,482 MCI patients and 4,573 AD‐dementia patients. ε3ε3 individuals were classified as “non‐carriers”, while ε4ε3/ε4ε4 individuals were tagged as “carriers”. Two independent sub‐cohorts were defined based on the version of the battery used to characterise cognitive profiles. Pairwise Markov random‐field models of cognitive functioning were constructed in “R” using the “qgraph” package, following published methodological guidelines. Nine cognitive nodes were established, and partial correlations were run to calculate the statistical strength of all node‐to‐node edges. This was regularised via the LASSO penalty‐imposing method, to control graph sparsity. Differences in global and nodal metrics between ε4 carriers and non‐carriers were tested via permutation‐based Network Invariance Tests. These analyses were run separately in each sub‐cohort and within each diagnostic status. “Expected Influence” was analysed as the centrality metric of interest, to assess how influential each node is within its network.ResultA significant APOE‐dependant effect emerged from the analysis of the Logical‐Memory nodes in MCI patients in both sub‐cohorts. While non‐carriers showed equal centrality in immediate and delayed recall, the latter was significantly less central among carriers. These findings were replicated in the sub‐groups of sole amnestic‐MCI patients (n = 2,971), were independent of differences in network communities, clinical severity or other demographic factors. No effects were found in the other diagnostic groups or in global network metrics.ConclusionAPOE‐ε4 influences nodal properties of cognitive networks when patients are clinically classified as MCI. Our findings expand this area of knowledge by characterising the statistical effect of the ε4 allele in terms of its differential impact on immediate and delayed recall, and how this results in specific network effects. The study of the wider cognitive network can complement univariate approaches in characterising the effects of risk factors.

Pliability and Approximating Max-CSPs

We identify a sufficient condition, treewidth-pliability , that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint graphs (with arbitrary constraints on an unbounded alphabet). Our result applies more generally to the maximum homomorphism problem between two rational-valued structures. The condition unifies the two main approaches for designing a polynomial-time approximation scheme. One is Baker’s layering technique, which applies to sparse graphs such as planar or excluded-minor graphs. The other is based on Szemerédi’s regularity lemma and applies to dense graphs. We extend the applicability of both techniques to new classes of Max-CSPs. However, we prove that the condition cannot be used to find solutions (as opposed to approximating the optimal value) in general. Treewidth-pliability turns out to be a robust notion that can be defined in several equivalent ways, including characterisations via size, treedepth, or the Hadwiger number. We show connections to the notions of fractional-treewidth-fragility from structural graph theory, hyperfiniteness from the area of property testing, and regularity partitions from the theory of dense graph limits. These may be of independent interest. In particular, we show that a monotone class of graphs is hyperfinite if and only if it is fractionally-treewidth-fragile and has bounded degree.

A multipopulation multitasking evolutionary scheme with adaptive knowledge transfer to solve the clustered minimum routing cost tree problem

The advancement in communication technology nowadays has increased the number of networked devices exponentially. Thus, network applications begin to cluster terminals to address scalability, privacy, and device connectivity with low routing costs. A recently introduced NP-hard problem called the Clustered Minimum Routing Cost Tree (CluMRCT) problem is assessed to be a fundamental key in designing an efficient network with low routing costs. Lately, some evolutionary multitasking meta-heuristics have been proposed to tackle multiple CluMRCT problems concurrently. However, these previous studies still have some limitations, such as only being applicable to complete graphs or there is no mechanism for effective knowledge transfer between problems when solving them simultaneously. To overcome these limitations, this paper proposes a novel multi-population multitasking evolutionary framework to address the problem. The individual representation is developed based on Network random key scheme and can be applied to both sparse and complete graphs. Moreover, our proposal can adaptively exploit positive knowledge transfer by adjusting the number of individuals migrating from other populations to a particular task. Then, the proposed algorithm is experimented on various data types and compared with other state-of-the-art algorithms. The experimental results show the proposal's effectiveness in most cases of the dataset, followed by detailed comparison, evaluation, and analysis.

Neurodegenerative diseases associated antibody repertoire signatures in mimotope arrays based on cyclic versus linear peptides

The role of peptide probes’ conformational flexibility in extracting immunosignatures has not been sufficiently studied. Immunosignatures profile the antibody diversity and prove promising for early cancer detection and multi-disease diagnostics. A novel tool for modeling antibody repertoires, the concept of antibody reactivity graphs, proved instrumental in this respect. Serum samples from patients with Alzheimer’s disease (AD), frontotemporal dementia (FTD), dementia of unknown etiology (DUE), and healthy controls were probed using a set of 130 7-mer peptides relevant to neurodegenerative diseases. Results show that linear peptides probed with IgM yielded higher graph density compared to IgG, indicating different levels of polyspecificities. Additionally, the impact of peptide topology and antibody isotype on feature selection was studied using recursive feature elimination. Findings reveal that IgM assays on linear peptides offer superior diagnostic differentiation of neurodegenerative diseases and define the degree of agreement between IgG and IgM immunosignatures with linear or cyclic peptides.

On vertex Ramsey graphs with forbidden subgraphs

A classical vertex Ramsey result due to Nešetřil and Rödl states that given a finite family of graphs F, a graph A and a positive integer r, if every graph B∈F has a 2-vertex-connected subgraph which is not a subgraph of A, then there exists an F-free graph which is vertex r-Ramsey with respect to A. We prove that this sufficient condition for the existence of an F-free graph which is vertex r-Ramsey with respect to A is also necessary for large enough number of colours r.We further show a generalisation of the result to a family of graphs and the typical existence of such a subgraph in a dense binomial random graph.

Injective chromatic index of sparse graphs

A k-injective-edge coloring of a graph G is an assignment of colors, i.e. integers in {1,2,…,k}, to the edges of G such that e1 and e3 receive distinct colors for any three consecutive edges e1, e2, e3 of a path or a 3-cycle. The smallest integer k such that G has an injective-edge coloring is called the injective chromatic index of G, denoted by χi′(G). In this paper,we consider the injective-edge coloring of sparse graph G with ΔG=5, and prove that χi′(G)≤10 (resp., 11, 12, 13) if madG<3714 (resp., 3914, 176, 3).

Global and item-by-item reasoning fusion-based multi-hop KGQA

Existing embedded multi-hop Question Answering over Knowledge Graph (KGQA) methods attempted to handle Knowledge Graph (KG) sparsity using Knowledge Graph Embedding (KGE) to improve KGQA. However, they almost ignore the intermediate path reasoning process of answer prediction, do not consider the information interaction between the question and the KG, and rarely consider the problem that the triple scoring reasoning mechanism is inadequate in extracting deep features. To address the above issues, this paper proposes Global and Item-by-item Reasoning Fusion-based Multi-hop KGQA (GIRFM-KGQA). In global reasoning, a convolutional attention reasoning mechanism is proposed and fused with the triple scoring reasoning mechanism to jointly implement global reasoning, thus enhancing the long-chain reasoning ability of the global reasoning model. In item-by-item reasoning, the reasoning path is formed by serially predicting relations, and then the answer is predicted, which effectively solves the problem that the embedded multi-hop KGQA method lacks the intermediate path reasoning ability. In addition, we introduce an information interaction method between the question and the KG to improve the accuracy of the answer prediction. Finally, we merge the global reasoning score with the item-by-item reasoning score to jointly predict the answer. Our model, compared to the baseline model (EmbedKGQA), achieves an accuracy improvement of 0.5% and 2.7% on two-hop questions, and 6.2% and 4.6% on three-hop questions for the MetaQA_Full and MetaQA_Half datasets, and 1.7% on the WebQuestionSP dataset, respectively. The experimental results show that the proposed model can effectively improve the accuracy of the multi-hop KGQA model and enhance the interpretability of the model. We have made our model’s source code available at github: https://github.com/feixiongfeixiong/GIRFM.

Hypergraph-based locality-enhancing methods for graph operations in Big Data applications

The need for speeding up data analytics increases inevitably due to the need for extracting valuable information from social media, data generated by smart devices with sensors, patterns of people’s communications over the web, items viewed and bought by global-scale customers, cloud applications, etc., all of which take part in the “Big Data.” Such kind of interaction data is very well represented as sparse graphs to enable the graph analytics, which requires efficient underlying kernels. The breadth-first search (BFS)-based traversal is a commonly used kernel in graph algorithms such as the betweenness centrality algorithm for centrality analysis. In this work, we focus on parallel BFS operations and propose hypergraph-based combinatorial models that aim at reducing cache misses and hence exploiting data locality during the parallel BFS operations. Our models are based on finding new vertex visit orders so that locality in accessing the data associated with vertices is exploited. Experiments on graphs arising in a wide range of applications show that our proposed models achieve on average 9% performance improvement in the CPU-based Ligra data analytics framework.

A regularized interior point method for sparse optimal transport on graphs

In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal–dual regularization, the authors propose to solve large scale OT problems on sparse graphs using a bespoke IPM algorithm able to suitably exploit primal–dual regularization in order to enforce scalability. Indeed, the authors prove that the introduction of the regularization allows to use sparsified versions of the normal Newton equations to inexpensively generate IPM search directions. A detailed theoretical analysis is carried out showing the polynomial convergence of the inner algorithm in the proposed computational framework. Moreover, the presented numerical results showcase the efficiency and robustness of the proposed approach when compared to network simplex solvers.

Optimal approaches to analyzing functional MRI data in glioma patients

BackgroundResting-state fMRI is increasingly used to study the effects of gliomas on the functional organization of the brain. A variety of preprocessing techniques and functional connectivity analyses are represented in the literature. However, there so far has been no systematic comparison of how alternative methods impact observed results. New methodWe first surveyed current literature and identified alternative analytical approaches commonly used in the field. Following, we systematically compared alternative approaches to atlas registration, parcellation scheme, and choice of graph-theoretical measure as regards differentiating glioma patients (N = 59) from age-matched reference subjects (N = 163). ResultsOur results suggest that non-linear, as opposed to affine registration, improves structural match to an atlas, as well as measures of functional connectivity. Functionally- as opposed to anatomically-derived parcellation schemes maximized the contrast between glioma patients and reference subjects. We also demonstrate that graph-theoretic measures strongly depend on parcellation granularity, parcellation scheme, and graph density. Comparison with existing methods and conclusionsOur current work primarily focuses on technical optimization of rs-fMRI analysis in glioma patients and, therefore, is fundamentally different from the bulk of papers discussing glioma-induced functional network changes. We report that the evaluation of glioma-induced alterations in the functional connectome strongly depends on analytical approaches including atlas registration, choice of parcellation scheme, and graph-theoretical measures.

An algebraic approach for counting DP-3-colorings of sparse graphs

DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in 2015. As the analogue of the chromatic polynomial of a graph G, P(G,m), and the list color function, Pℓ(G,m), the DP-color function of G, denoted by PDP(G,m), counts the minimum number of DP-colorings over all possible m-fold covers. It follows that PDP(G,m)≤Pℓ(G,m)≤P(G,m). A function f is chromatic-adherent if for every graph G, f(G,a)=P(G,a) for some a≥χ(G) implies that f(G,m)=P(G,m) for all m≥a. It is known that the DP-color function is not chromatic-adherent, but there are only two known graphs that demonstrate this. Suppose G is an n-vertex graph and H is a 3-fold cover of G. In this paper we associate with H a polynomial fG,H∈F3[x1,…,xn] so that the number of non-zeros of fG,H equals the number of H-colorings of G. We then use a well-known result of Alon and Füredi on the number of non-zeros of a polynomial to establish a non-trivial lower bound on PDP(G,3) when 2n>|E(G)|. An easy consequence of this is that PDP(G,3)≥3n/6 for every n-vertex planar graph G of girth at least 5, improving the previously known bounds on both PDP(G,3) and Pℓ(G,3). Finally, we use this bound to show that there are infinitely many graphs that demonstrate the non-chromatic-adherence of the DP-color function.

KGFlex: Efficient Recommendation with Sparse Feature Factorization and Knowledge Graphs

Collaborative filtering models have undoubtedly dominated the scene of recommender systems in recent years. However, due to the little use of content information, they narrowly focus on accuracy, disregarding a higher degree of personalization. Meanwhile, knowledge graphs are arousing considerable interest in recommendation models thanks to their ability to enrich the system with content features that captures subtle user-item relations. Nevertheless, with many high-quality features, the models become more complex and challenging to train. We extend KGFlex [ 16 ], a hybrid model that analyzes historical data to understand the semantic features the user decisions depend on. KGFlex represents item features as embeddings, and it models user-item interactions as a factorized entropy-driven combination of the item attributes relevant to the user, thus reducing the complexity and raising the degree of personalization. The method does not neglect long tail items, reducing the popularity bias and ensuring a high level of fairness. The user-item prediction is mediated by the user’s personal views of the embeddings that grant a high degree of expressiveness. This extension analyzes different entropy measurement strategies, an enhanced user negative decision modeling, and assesses the fairness of KGFlex and the impact of its hyperparameters. KGFlex is available at https://split.to/kgflex .