Sparse Graphs Research Articles

A note on the k-colored crossing ratio of dense geometric graphs

A geometric graph is a graph whose vertex set is a set of points in general position in the plane, and its edges are straight line segments joining these points. We show that for every integer k≥2, there exists a constant c>0 such that the following holds. The edges of every dense geometric graph, with sufficiently many vertices, can be colored with k colors, such that the number of pairs of edges of the same color that cross is at most (1/k−c) times the total number of pairs of edges that cross. The case when k=2 and G is a complete geometric graph, was proved by Aichholzer et al. (2019) [2].

MSGA-Net: Progressive Feature Matching via Multi-Layer Sparse Graph Attention

MSGA-Net: Progressive Feature Matching via Multi-Layer Sparse Graph Attention

Directed graphs with lower orientation Ramsey thresholds

We investigate the threshold p⃗H = p⃗H (n) for the Ramsey-type property G(n, p) → ⃗H, where G(n, p) is the binomial random graph and G → ⃗H indicates that every orientation of the graph G contains the oriented graph ⃗ H as a subdigraph. Similarly to the classical Ramsey setting, the upper bound p⃗H ⩽ Cn−1/m2(⃗ H) is known to hold for some constant C = C( ⃗ H), where m2(⃗H) denotes the maximum 2-density of the underlying graph H of ⃗ H. While this upper bound is indeed the threshold for some ⃗H, this is not always the case. We obtain examples arising from rooted products of orientations of sparse graphs (such as forests, cycles and, more generally, subcubic {K3, K3,3}-free graphs) and arbitrarily rooted transitive triangles.

CGKPN: Cross-Graph Knowledge Propagation Network with Adaptive Connection for Reasoning-Based Machine Reading Comprehension

The task of machine reading comprehension (MRC) is to enable machine to read and understand a piece of text and then answer the corresponding question correctly. This task requires machine to not only be able to perform semantic understanding but also possess logical reasoning capabilities. Just like human reading, it involves thinking about the text from two interacting perspectives of semantics and logic. However, previous methods based on reading comprehension either consider only the logical structure of the text or only the semantic structure of the text and cannot simultaneously balance semantic understanding and logical reasoning. This single form of reasoning cannot make the machine fully understand the meaning of the text. Additionally, the issue of sparsity in composition presents a significant challenge for models that rely on graph-based reasoning. To this end, a cross-graph knowledge propagation network (CGKPN) with adaptive connection is presented to address the above issues. The model first performs self-view node embedding on the constructed logical graph and semantic graph to update the representations of the graphs. Specifically, a relevance matrix between nodes is introduced to adaptively adjust node connections in response to the challenge posed by sparse graph. Subsequently, CGKPN conducts cross-graph knowledge propagation on nodes that are identical in both graphs, effectively resolving conflicts arising from identical nodes in different views, and enabling the model to better integrate the logical and semantic relationships of the text through efficient interaction. Experiments on the two MRC datasets ReClor and LogiQA indicate the superior performance of our proposed model CGKPN compared to other existing baselines.

A weighted multi-view clustering via sparse graph learning

A weighted multi-view clustering via sparse graph learning

Sparse dynamic graph learning for district heat load forecasting

Accurate heat load forecasting is crucial for the efficient operation and management of district heating systems. This study introduces a novel Sparse Dynamic Graph Neural Network (SDGNN) framework designed to address the complexities of forecasting heat load in district heating networks. The proposed model represents the district heating network as a dynamic graph, with nodes corresponding to consumers or heat sources and edges denoting temporal dependencies. The SDGNN framework comprises three key components: (1) a sparse graph learning module that identifies the most relevant nodes and edges, (2) a spatio-temporal memory enhancement module that captures both short-term and long-term dependencies, and (3) a temporal fusion module that integrates node representations into a comprehensive global forecast. Evaluated on a real-world district heating dataset from Denmark, the SDGNN model demonstrates superior accuracy and efficiency compared to existing methods. The results indicate that the SDGNN framework effectively captures intricate spatio-temporal patterns in historical heat load data, achieving up to 5.7% improvement in RMSE, 7.4% in MAE, and 5.7% in CVRMSE over baseline models. Additionally, incorporating meteorological factors into the model further enhances its predictive performance. These findings suggest that the SDGNN framework is a robust and scalable solution for district heat load forecasting, with potential applications in other domains involving spatio-temporal graph data.

Spatiotemporal Variations in Co-Occurrence Patterns of Planktonic Prokaryotic Microorganisms along the Yangtze River.

Bacteria and archaea are foundational life forms on Earth and play crucial roles in the development of our planet's biological hierarchy. Their interactions influence various aspects of life, including eukaryotic cell biology, molecular biology, and ecological dynamics. However, the coexistence network patterns of these microorganisms within natural river ecosystems, vital for nutrient cycling and environmental health, are not well understood. To address this knowledge gap, we systematically explored the non-random coexistence patterns of planktonic bacteria and archaea in the 6000-km stretch of the Yangtze River by using high-throughput sequencing technology. By analyzing the O/R ratio, representing the divergence between observed (O%) and random (R%) co-existence incidences, and the module composition, we found a preference of both bacteria and archaea for intradomain associations over interdomain associations. Seasons notably influenced the co-existence of bacteria and archaea, and archaea played a more crucial role in spring as evidenced by their predominant presence of interphyla co-existence and more species as keystone ones. The autumn network was characterized by a higher node or edge number, greater graph density, node degree, degree centralization, and nearest neighbor degree, indicating a more complex and interconnected structure. Landforms markedly affected microbial associations, with more complex networks and more core species found in plain and non-source areas. Distance-decay analysis suggested the importance of geographical distance in shaping bacteria and archaea co-existence patterns (more pronounced in spring). Natural, nutrient, and metal factors, including water temperature, NH4+-N, Fe, Al, and Ni were identified as crucial determinants shaping the co-occurrence patterns. Overall, these findings revealed the dynamics of prokaryotic taxa coexistence patterns in response to varying environmental conditions and further contributed to a broader understanding of microbial ecology in freshwater biogeochemical cycling.

SymNOM-GED: Symmetric neighbor outlier mining in gene expression datasets

The accurate detection of outliers in gene expression datasets plays a crucial role in the unraveling of intricate biological processes. This research introduces "SymNOM-GED," an innovative algorithm for outlier mining in gene expression datasets, with a focus on Esophageal Squamous Cell Carcinoma (ESCC). SymNOM-GED leverages symmetric neighbor to effectively identify outliers by considering local and global gene expression patterns. Extensive experiments demonstrate that SymNOM-GED outperforms existing algorithms in terms of accuracy, robustness, and scalability. The algorithm's performance is validated using clustering coefficient, graph density, and modularity, confirming its superiority. SymNOM-GED's precise and reliable outlier detection capabilities contribute significantly to bioinformatics research, offering insights into gene expression patterns in diverse biological contexts.

Low-depth Clifford circuits approximately solve MaxCut

We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, ADAPT-Clifford, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an N-vertex graph by building a depth O(N) Clifford circuit. The algorithm has runtime complexity O(N2) and O(N3) for sparse and dense graphs, respectively, and space complexity O(N2), with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to ∼94% of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW. Published by the American Physical Society 2024

Some Remarks on Linear-Quadratic Closed-Loop Games with Many Players

AbstractWe identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a sparse graph, both short-time and long-time existence of a classical solution for the Nash system set in infinitely many dimensions are addressed, as well as convergence to the solution to the respective ergodic problem as the time horizon goes to infinity; in addition, equilibria for the infinite-dimensional game are shown to provide $$\epsilon $$ ϵ -Nash closed-loop equilibria for the N-player game. In a setting of generalized mean-field type (where the number of interactions is large but not necessarily symmetric), directly from the N-player Nash system estimates on the value functions are deduced on an arbitrary large time horizon, which should pave the way for a convergence result as N goes to infinity.

Multi kernel cross sparse graph attention convolutional neural network for brain magnetic resonance imaging super-resolution

High-resolution Magnetic Resonance Imaging (MRI) is pivotal in both diagnosing and treating brain tumors, assisting physicians in diagnosis and treatment by displaying anatomical structures. Utilizing convolutional neural network-based super-resolution methods enables the efficient acquisition of high-resolution MRI images.However, Convolutional neural networks are limited by their kernel size, which restricts their ability to capture a wider field of view, potentially leading to feature omission and difficulties in establishing global and local feature relationships. To overcome these shortcomings, We have designed a novel network architecture that highlights three main modules: (i) Multiple Convolutional Feature (MCF)extraction module, which diversifies convolution operations for extracting image features, achieving comprehensive feature representation. (ii) Multiple Groupss of Cross-Iterative Feature(MGCIF) modules, promoting inter-channel feature interactions and emphasizing crucial features needed for subsequent learning. (iii) A Graph Neural Network Module based on a sparse attention mechanism, capable of connecting distant pixel features and identifying influential neighboring pixels for target pixel inpainting. To evaluate the accuracy of our proposed network, we conducted tests on four datasets, comprising two sets of brain tumor data and two sets of healthy head MRI data, all of which underwent varying degrees of degradation. We conducted experiments using nineteen super-resolution (SR) models. Our experiments were carried out on four datasets, and the results demonstrate that our method outperforms the current leading-edge methods. In the four datasets, our model showed improvements in Peak Signal-to-Noise Ratio (PSNR) scores compared to the second-place model,with increase of 1.16 %,1.08 %,0.19 % and 0.53 % for ×2,and 2.26 %,1.67 %,0.13 % and 0.45 % for × 4,respectively.

On some algorithms for estimation in Gaussian graphical models

Abstract In Gaussian graphical models, the likelihood equations must typically be solved iteratively. This paper investigates two algorithms: a version of iterative proportional scaling, which avoids inversion of large matrices, and an algorithm based on convex duality and operating on the covariance matrix by neighbourhood coordinate descent, which corresponds to the graphical lasso with zero penalty. For large, sparse graphs, the iterative proportional scaling algorithm appears feasible and has simple convergence properties. The algorithm based on neighbourhood coordinate descent is extremely fast and less dependent on sparsity, but needs a positive-definite starting value to converge. We provide an algorithm for finding such a starting value for graphs with low colouring number. As a consequence, we also obtain a simplified proof of existence of the maximum likelihood estimator in such cases.

A complex-network-based estimation of the representative elementary volume and equivalent permeability coefficient for fractured rock masses

The determination of the representative elementary volume (REV) and equivalent permeability coefficient (EPC) of fractured rock masses is crucial for studying the hydraulic behaviors of engineering rock masses. The complex network originated from graph theory and represents a rapidly developing interdisciplinary field in the 21st century. In this paper, we propose a novel method that utilizes complex-network-based metrics to estimate the REV and EPC of fractured rock masses. In this method, fractures and their intersections are treated as nodes and edges of a complex network, respectively. We propose a transformation procedure of a discrete fracture network (DFN) into a complex network, and the corresponding algorithms are conducted in MATLAB. Subsequently, we obtain a complex network, and several complex-network-based metrics, such as average degree, average clustering coefficient, and graph density, are calculated using Gephi software. We employ the average degree to estimate the REV size of DFN models, while the coefficient of variation is used to quantitatively assess changes in the average degree of multiple random models. Furthermore, we establish an empirical formula utilizing the average degree, average clustering coefficient, and graph density to estimate the EPC of a large-scale DFN model based on the EPC of a small-scale DFN model. To verify the developed method, we conduct numerical experiments using the MAFIC (Matrix/Fracture Interaction Code) solver within the FracMan software. This enabled us to calculate the EPC, which was then used to determine the REV. The results demonstrate that: (a) the REV size estimated by the average degree aligns with the REV size obtained through numerical simulations for both isotropic and anisotropic DFN models, and (b) the error rates between the average EPC calculated by the empirical formula and that obtained by numerical simulations are within 10%. Thus, the proposed seepage parameter estimation methods are deemed valid.

On the rank, Kernel, and core of sparse random graphs

AbstractWe study the rank of the adjacency matrix of a random Erdős‐Rényi graph . It is well known that when , with high probability, is singular. We prove that when , with high probability, the corank of is equal to the number of isolated vertices remaining in after the Karp‐Sipser leaf‐removal process, which removes vertices of degree one and their unique neighbor. We prove a similar result for the random matrix , where all entries are independent Bernoulli random variables with parameter . Namely, we show that if is the bipartite graph with bi‐adjacency matrix , then the corank of is with high probability equal to the max of the number of left isolated vertices and the number of right isolated vertices remaining after the Karp‐Sipser leaf‐removal process on . Additionally, we show that with high probability, the ‐core of is full rank for any and . This partially resolves a conjecture of Van Vu for . Finally, we give an application of the techniques in this paper to gradient coding, a problem in distributed computing.

Conditional room layout generation based on graph neural networks

In this paper, we present a novel end-to-end variational generative model that utilizes graph-based latent representations for indoor scene synthesis at one time. In contrast to prior research, our method deviates from the practice of gradually introducing and arranging furniture in an empty room using autoregression. Instead, it focuses on acquiring a comprehensive implicit representation of the room’s original architectural structure and the placement of furniture. We initially transform the 3D room scene into a dense scene graph, where nodes correspond to the objects present in the room while edges reflect the spatial location links and functional correlations between objects. Then, a neural network is trained to acquire the graph-based latent representation of the room scene through iterative message passing, ultimately resulting in the acquisition of the data distribution on the latent space of the room layout. Given the architectural structure of an empty room as a prerequisite for scene synthesis, the generative model has the ability to sample from the prior distribution of the room’s latent representation. This allows the model to then decode and generate a variety of room layouts. We evaluate our method with the state-of-the-art 3D indoor scene dataset and generation methods. The experimental results demonstrate that our method achieves more rational and diverse outcomes in the context of generating scenes under specific conditions.

Geometric localized graph convolutional network for multi-view semi-supervised classification

Multi-view learning has received increasing attention in recent years due to its ability to leverage valuable patterns hidden in heterogeneous data sources. While existing studies have achieved encouraging results, especially those based on graph convolutional networks, they are still limited in their ability to fully exploit the connectivity relationships between samples and are susceptible to noise. To address the aforementioned limitations, we propose a framework called geometric localized graph convolutional network for multi-view semi-supervised classification. This framework utilizes a diffusion map to obtain the geometric structure of the feature space of multiple views and constructs a stable distance matrix that considers the local connectivity of nodes on the geometric structure. Additionally, we propose a truncated diffusion correlation function that maps the distance matrix of each view into correlations between samples to obtain a reliable sparse graph. To fuse the features, we use learnable weights to concatenate the coordinates of the geometric structure. Finally, we obtain a graph embedding of the fused feature and topology by using graph convolutional networks. Comprehensive experiments demonstrate the superiority of the proposed method over other state-of-the-art methods.

A Spectral Clustering Algorithm for Non-Linear Graph Embedding in Information Networks

With the development of network technology, information networks have become one of the most important means for people to understand society. As the scale of information networks expands, the construction of network graphs and high-dimensional feature representation will become major factors affecting the performance of spectral clustering algorithms. To address this issue, in this paper, we propose a spectral clustering algorithm based on similarity graphs and non-linear deep embedding, named SEG_SC. This algorithm introduces a new spectral clustering model that explores the underlying structure of graphs through sparse similarity graphs and deep graph representation learning, thereby enhancing graph clustering performance. Experimental analysis with multiple types of real datasets shows that the performance of this model surpasses several advanced benchmark algorithms and performs well in clustering on medium- to large-scale information networks.

CS-ViG-UNet: Infrared small and dim target detection based on cycle shift vision graph convolution network

Infrared small and dim target detection benefits from the exploration of correlations among targets, neighboring regions, and the background. However, existing methods that rely on convolutional neural networks and vision transformers cannot effectively capture long-range information correlations within images. To overcome this limitation, this paper proposes CS-ViG-UNet, a framework that introduces vision graph convolution for infrared small and dim target detection. Our framework employs a cyclic shift sparse graph attention mechanism to address the issue of reduced expressive power. Meanwhile, the CS-ViG module is designed to construct an effective graph structure using image patches, thereby capturing feature information relevant to target recognition. On the public datasets Sirst AUG and IRSTD-1K, our method obtained F1 scores of 0.8561 and 0.745, respectively, showing an improvement of 3.15 % and 4.1 % compared to the state-of-the-art methods. On the RTX3090 with TensorRT acceleration, CS-ViG-UNet can process approximately 357 images of size 256 × 256 pixels per second at FP16 precision. For detailed information, please visit our homepage: https://linaom1214.github.io/CSViG-UNet.

Typical structure of sparse exponential random graph models

Typical structure of sparse exponential random graph models

Seizure onset zone (SOZ) identification using effective brain connectivity of epileptogenic networks

Objective. To demonstrate the capability of utilizing graph feature-based supervised machine learning (ML) algorithm on intracranial electroencephalogram recordings for the identification of seizure onset zones (SOZs) in individuals with drug-resistant epilepsy. Approach. Utilizing three model-free measures of effective connectivity (EC)-directed information, mutual information-guided Granger causality index (MI-GCI), and frequency-domain convergent cross-mapping (FD-CCM) - directed graphs are generated. Graph centrality measures at different sparsity are used as the classifier’s features. Main results. The centrality features achieve high accuracies exceeding 90% in distinguishing SOZ electrodes from non-SOZ electrodes. Notably, a sparse graph representation with just ten features and simple ML models effectively achieves such performance. The study identifies FD-CCM centrality measures as particularly significant, with a mean AUC of 0.93, outperforming prior literature. The FD-CCM-based graph modeling also highlights elevated centrality measures among SOZ electrodes, emphasizing heightened activity relative to non-SOZ electrodes during ictogenesis. Significance. This research not only underscores the efficacy of automated SOZ identification but also illuminates the potential of specific EC measures in enhancing discriminative power within the context of epilepsy research.