Complex Graph Research Articles

Integrating Graph Structures into Kernel Regression Models

Kernel methods are highly flexible and powerful tools for capturing complex, nonlinear relationships in data. In this paper, we propose a substantial extension of existing network-based regression models by integrating kernel methods with graph-theoretic constraints. Our approach builds upon the foundational work of Li et al. [1], who incorporated network cohesion into generalized linear models (GLMs). We extend their framework by introducing a kernelized regression model that allows for the modeling of nonlinear interactions while leveraging network data. This kernelized framework relaxes the linearity constraints of GLMs, making the model more versatile and capable of capturing complex patterns in high-dimensional spaces. We demonstrate the effectiveness of our approach using simulated and real-world datasets, such as the Teenage Friends and Lifestyle Study. Results show that our kernelized network regression model not only outperforms traditional linear and generalized linear models in predictive accuracy but also scales efficiently to larger datasets. Our work represents a significant advancement in the modeling of network-linked data, providing a robust, scalable, and interpretable framework that extends the application of kernel methods beyond their traditional constraints. Future directions include exploring more complex graph structures, such as weighted and directed graphs, and developing optimized algorithms for even larger datasets.

Decreasing graph complexity with transitive reduction to improve temporal graph classification

Decreasing graph complexity with transitive reduction to improve temporal graph classification

Multi-particle quantum walks on 3D integrated photonic chip

Quantum walks provide a speed-up in computational power for various quantum algorithms and serve as inspiration for the construction of complex graph representations. Many pioneering works have been dedicated to expanding the experimental state space and the complexity of graphs. However, these experiments are mostly limited to small experimental scale, which do not reach a many-body level and fail to reflect the multi-particle quantum interference effects among non-adjacent modes. Here, we present a quantum walk with three photons on a two-dimensional triangular lattice, which is mapped to a 19 × 19 × 19 high-dimensional state space and constructs a complex graph with 6859 nodes and 45,486 edges. By utilizing the statistical signatures of the output combinations and incorporating machine learning techniques, we successfully validate the nonclassical properties of the experiment. Our implementation provides a paradigm for exponentially expanding the state space and graph complexity of quantum walks, paving the way for surmounting the classical regime in large-scale quantum simulations.

Advancing Session-Based Recommendations with Atten-Mixer+: Dynamic and Adaptive Multi-Level Intent Mining

Session-based recommendation (SBR) systems, traditionally reliant on complex graph neural networks (GNNs), often face challenges with marginal performance improvements despite increased model complexity. In this paper, we dissect the classical GNN-based SBR models and empirically find that the sophisticated GNN propagations might be redundant, given the readout module plays a significant role in GNN-based models. Based on this observation, we introduce Atten-Mixer+, an advanced iteration of our previously developed Multi-Level Attention Mixture Network (Atten-Mixer). Atten-Mixer+ forgoes GNN propagation in favor of a dynamic and adaptive readout process, tailored to the unique characteristics of each session. Different from the vanilla version, Atten-Mixer+ features the Adaptive Intent Scaler (AIS) layer, which dynamically determines the depth of multi-level user intent analysis, and a soft allocation approach for generating user intent queries across entire user interaction sequences. This innovative design allows Atten-Mixer+ to capture a nuanced and comprehensive understanding of user behaviors, overcoming the limitations of fixed-length analysis. Empirical evaluations on benchmark datasets highlight Atten-Mixer+'s superior efficiency and effectiveness, marking a significant step forward in the predictive accuracy of session-based recommendation systems.

PolyJuice: Detecting Mis-compilation Bugs in Tensor Compilers with Equality Saturation Based Rewriting

Tensor compilers are essential for deploying deep learning applications across various hardware platforms. While powerful, they are inherently complex and present significant challenges in ensuring correctness. This paper introduces PolyJuice, an automatic detection tool for identifying mis-compilation bugs in tensor compilers. Its basic idea is to construct semantically-equivalent computation graphs to validate the correctness of tensor compilers. The main challenge is to construct equivalent graphs capable of efficiently exploring the diverse optimization logic during compilation. We approach it from two dimensions. First, we propose arithmetic and structural equivalent rewrite rules to modify the dataflow of a tensor program. Second, we design an efficient equality saturation based rewriting framework to identify the most simplified and the most complex equivalent computation graphs for an input graph. After that, the outcome computation graphs have different dataflow and will likely experience different optimization processes during compilation. We applied it to five well-tested industrial tensor compilers, namely PyTorch Inductor, OnnxRuntime, TVM, TensorRT, and XLA, as well as two well-maintained academic tensor compilers, EinNet and Hidet. In total, PolyJuice detected 84 non-crash mis-compilation bugs, out of which 49 were confirmed with 20 fixed.

Generative AI-based knowledge graphs for the illustration and development of mHealth self-management content.

Digital therapeutics (DTx) in the form of mobile health (mHealth) self-management programs have demonstrated effectiveness in reducing disease activity across various diseases, including fibromyalgia and arthritis. However, the content of online self-management programs varies widely, making them difficult to compare. This study aims to employ generative artificial intelligence (AI)-based knowledge graphs and network analysis to categorize and structure mHealth content at the example of a fibromyalgia self-management program. A multimodal mHealth online self-management program targeting fibromyalgia and post-viral fibromyalgia-like syndromes was developed. In addition to general content, the program was customized to address specific features and digital personas identified through hierarchical agglomerative clustering applied to a cohort of 202 patients with chronic musculoskeletal pain syndromes undergoing multimodal assessment. Text files consisting of 22,150 words divided into 24 modules were used as the input data. Two generative AI web applications, ChatGPT-4 (OpenAI) and Infranodus (Nodus Labs), were used to create knowledge graphs and perform text network analysis, including 3D visualization. A sentiment analysis of 129 patient feedback entries was performed. The ChatGPT-generated knowledge graph model provided a simple visual overview with five primary edges: "Mental health challenges", "Stress and its impact", "Immune system function", "Long COVID and fibromyalgia" and "Pain management and therapeutic approaches". The 3D visualization provided a more complex knowledge graph, with the term "pain" appearing as the central edge, closely connecting with "sleep", "body", and "stress". Topical cluster analysis identified categories such as "chronic pain management", "sleep hygiene", "immune system function", "cognitive therapy", "healthy eating", "emotional development", "fibromyalgia causes", and "deep relaxation". Gap analysis highlighted missing links, such as between "negative behavior" and "systemic inflammation". Retro-engineering of the self-management program showed significant conceptual similarities between the knowledge graph and the original text analysis. Sentiment analysis of free text patient comments revealed that most relevant topics were addressed by the online program, with the exception of social contacts. Generative AI tools for text network analysis can effectively structure and illustrate DTx content. Knowledge graphs are valuable for increasing the transparency of self-management programs, developing new conceptual frameworks, and incorporating feedback loops.

Graph Convolution Network Combining Spatiotemporal Self-Attention and Mutual Information for Pedestrian-Trajectory Prediction

Accurate pedestrian-trajectory prediction is significant and challenging for intelligent driving. There are two challenges in this field: most existing methods ignore pedestrian–vehicle interaction in the multiple pedestrian and vehicle scenario; and research on interaction modes and objects during the interaction process remains relatively limited in depth and scope. To tackle these challenges, a novel graph convolution network combining spatiotemporal self-attention and mutual information (STSAMI-GCN) is designed for predicting pedestrian trajectories. First, to model the spatiotemporal interaction between pedestrians and vehicles, we build a spatiotemporal graph interaction module that integrates graph convolutional networks and self-attention mechanisms. Second, to filter redundant interactions and optimize feature extraction in the spatiotemporal graph interaction module, a mutual information graph network module is designed as an auxiliary network, which can reduce information redundancy and simplify graph complexity. In addition, to address the problem of propagation and accumulation of prediction errors, we design a trajectory decoder to generate future trajectories. Finally, a suitable dataset for our research scenario is built to validate the proposed model. We also evaluate it on two publicly available datasets. Experimental results show that, in the multiple pedestrian and vehicle scenario, STSAMI-GCN can be used to predict the future trajectories of multiple pedestrians, and to predict socially acceptable future trajectories. Specifically, STSAMI-GCN achieves 0.25 and 0.27 average and final deviation error, respectively, and outperforms various mainstream methods. Furthermore, ablation studies demonstrate the effectiveness of the spatiotemporal dual self-attention mechanism and mutual information graph network in improving pedestrian-trajectory prediction accuracy.

AGNN: Alternating Graph-Regularized Neural Networks to Alleviate Over-Smoothing.

Graph convolutional network (GCN) with the powerful capacity to explore graph-structural data has gained noticeable success in recent years. Nonetheless, most of the existing GCN-based models suffer from the notorious over-smoothing issue, owing to which shallow networks are extensively adopted. This may be problematic for complex graph datasets because a deeper GCN should be beneficial to propagating information across remote neighbors. Recent works have devoted effort to addressing over-smoothing problems, including establishing residual connection structure or fusing predictions from multilayer models. Because of the indistinguishable embeddings from deep layers, it is reasonable to generate more reliable predictions before conducting the combination of outputs from various layers. In light of this, we propose an alternating graph-regularized neural network (AGNN) composed of graph convolutional layer (GCL) and graph embedding layer (GEL). GEL is derived from the graph-regularized optimization containing Laplacian embedding term, which can alleviate the over-smoothing problem by periodic projection from the low-order feature space onto the high-order space. With more distinguishable features of distinct layers, an improved Adaboost strategy is utilized to aggregate outputs from each layer, which explores integrated embeddings of multi-hop neighbors. The proposed model is evaluated via a large number of experiments including performance comparison with some multilayer or multi-order graph neural networks, which reveals the superior performance improvement of AGNN compared with the state-of-the-art models.

Accurate Sampling-Based Cardinality Estimation for Complex Graph Queries

Accurately estimating the cardinality (i.e., the number of answers) of complex queries plays a central role in database systems. This problem is particularly difficult in graph databases, where queries often involve a large number of joins and self-joins. Recently, Park et al. [ 55 ] surveyed seven state-of-the-art cardinality estimation approaches for graph queries. The results of their extensive empirical evaluation show that a sampling method based on the WanderJoin online aggregation algorithm [ 47 ] consistently offers superior accuracy. We extended the framework by Park et al. [ 55 ] with three additional datasets and repeated their experiments. Our results showed that WanderJoin is indeed very accurate, but it can often take a large number of samples and thus be very slow. Moreover, when queries are complex and data distributions are skewed, it often fails to find valid samples and estimates the cardinality as zero. Finally, complex graph queries often go beyond simple graph matching and involve arbitrary nesting of relational operators such as disjunction, difference, and duplicate elimination. Neither of the methods considered by Park et al. [ 55 ] is applicable to such queries. In this article, we present a novel approach for estimating the cardinality of complex graph queries. Our approach is inspired by WanderJoin, but, unlike all approaches known to us, it can process complex queries with arbitrary operator nesting. Our estimator is strongly consistent, meaning that the average of repeated estimates converges with probability one to the actual cardinality. We present optimisations of the basic algorithm that aim to reduce the chance of producing zero estimates and improve accuracy. We show empirically that our approach is both accurate and quick on complex queries and large datasets. Finally, we discuss how to integrate our approach into a simple dynamic programming query planner, and we confirm empirically that our planner produces high-quality plans that can significantly reduce end-to-end query evaluation times.

Enhancing Knowledge-Aware Recommendation with Dual-Graph Contrastive Learning

Incorporating knowledge graphs as auxiliary information to enhance recommendation systems can improve the representations learning of users and items. Recommendation methods based on knowledge graphs can introduce user–item interaction learning into the item graph, focusing only on learning the node vector representations within a single graph; alternatively, they can treat user–item interactions and item graphs as two separate graphs and learn from each graph individually. Learning from two graphs has natural advantages in exploring original information and interaction information, but faces two main challenges: (1) in complex graph connection scenarios, how to adequately mine the self-information of each graph, and (2) how to merge interaction information from the two graphs while ensuring that user–item interaction information predominates. Existing methods do not thoroughly explore the simultaneous mining of self-information from both graphs and effective interaction information, leading to the loss of valuable insights. Considering the success of contrastive learning in mining self-information and auxiliary information, this paper proposes a dual-graph contrastive learning recommendation method based on knowledge graphs (KGDC) to explore a more accurate representations of users and items in recommendation systems based on external knowledge graphs. In the learning process within the self-graph, KGDC strengthens and represents the information of different connecting edges in both graphs, and extracts the existing information more fully. In interactive information learning, KGDC reinforces the interaction relationship between users and items in the external knowledge graph, realizing the leading role of the main task. We conducted a series of experiments on three standard datasets, and the results show that the proposed method can achieve better results.

Are All Pictures Worth 1,000 Words? An Investigation of Fit Between Graph Type and Performance on Accounting Data Analytics Tasks

ABSTRACT Despite the increasing prevalence of the use of data analytics and visualizations in accounting settings, little is known about the relative effectiveness of different visualization formats for tasks such as those involving comparisons over time and those involving evaluations of whole-part compositions. In this study, we examine if there is a difference in decision efficiency and effectiveness between bar and line graphs for a comparison task and between pie and stacked column graphs for a compositional task. We also examine if the component complexity of graphs affects performance. We find that line graphs result in significantly greater decision sensitivity (ability to identify true positives) than bar graphs on comparison tasks regardless of the degree of component complexity. We also find that bar graphs result in significantly greater decision specificity (ability to identify true negatives) and overall accuracy.

Complex Graph Analysis and Representation Learning: Problems, Techniques, and Applications

Complex Graph Analysis and Representation Learning: Problems, Techniques, and Applications

SPORT: A Subgraph Perspective on Graph Classification with Label Noise

Graph neural networks (GNNs) have achieved great success recently on graph classification tasks using supervised end-to-end training. Unfortunately, extensive noisy graph labels could exist in the real world because of the complicated processes of manual graph data annotations, which may significantly degrade the performance of GNNs. Therefore, we investigate the problem of graph classification with label noise, which is demanding because of the complex graph representation learning issue and serious memorization of noisy samples. In this work, we present a novel approach called S ubgra p h Set Netw or k with Sample Selection and Consis t ency Learning (SPORT) for this problem. To release the overfitting of GNNs, SPORT proposes to characterize each graph as a set of subgraphs generated by certain predefined stratagems, which can be viewed as samples from its underlying semantic distribution in graph space. Then we develop an equivariant network to encode the subgraph set with the consideration of the symmetry group. To further release the influences of noisy examples, we leverage the predictions of subgraphs to measure the likelihood of a sample being clean or noisy, followed by effective label updating. In addition, we propose a joint loss to advance the model generalizability by introducing consistency regularization. Comprehensive experiments on a wide range of graph classification datasets demonstrate the effectiveness of our SPORT. Specifically, SPORT outperforms the most competing baseline by up to 6.4%.

Contributions to the characterization of the Schema using APOS theory: Graphing with derivative

This study contributes to Action, Process, Object, Schema (APOS) theory research by showing two approaches used by advanced mathematics students to construct relations between higher-order derivatives to solve complex problems. We show evidence of students’ ability to perform Actions on their graphing derivative Schema, that is, of its thematization. It also contributes to the literature on the learning of differential calculus by showing how advanced students use their knowledge to construct relations between concepts when facing complex situations. The work of three graduate students on transforming complex graphs and determining their properties and their relation to the domain structure is analyzed to determine their solution approaches. Their graphing derivative Schema is analyzed in depth in terms of the construction of relations among the Schema structures and assimilation and accommodation mechanisms involved in thematization in APOS theory. These findings are important in informing and developing didactic strategies to foster university students’ understanding of derivatives, which can smoothe the transition to the study of advanced mathematics courses.

ERT-GFAN: A multimodal drug–target interaction prediction model based on molecular biology and knowledge-enhanced attention mechanism

In drug discovery, precisely identifying drug–target interactions is crucial for finding new drugs and understanding drug mechanisms. Evolving drug/target heterogeneous data presents challenges in obtaining multimodal representation in drug–target prediction(DTI). To deal with this, we propose ‘ERT-GFAN’, a multimodal drug–target interaction prediction model inspired by molecular biology. Firstly, it integrates bio-inspired principles to obtain structure feature of drugs and targets using Extended Connectivity Fingerprints(ECFP). Simultaneously, the knowledge graph embedding model RotatE is employed to discover the interaction feature of drug–target pairs. Subsequently, Transformer is utilized to refine the contextual neighborhood features from the obtained structure feature and interaction features, and multi-modal high-dimensional fusion features of the three-modal information constructed. Finally, the final DTI prediction results are outputted by integrating the multimodal fusion features into a graphical high-dimensional fusion feature attention network (GFAN) using our innovative multimodal high-dimensional fusion feature attention. This multimodal approach offers a comprehensive understanding of drug–target interactions, addressing challenges in complex knowledge graphs. By combining structure feature, interaction feature, and contextual neighborhood features, ‘ERT-GFAN’ excels in predicting DTI. Empirical evaluations on three datasets demonstrate our method’s superior performance, with AUC of 0.9739, 0.9862, and 0.9667, AUPR of 0.9598, 0.9789, and 0.9750, and Mean Reciprocal Rank(MRR) of 0.7386, 0.7035, and 0.7133. Ablation studies show over a 5% improvement in predictive performance compared to baseline unimodal and bimodal models. These results, along with detailed case studies, highlight the efficacy and robustness of our approach.

Cross-attention based two-branch networks for document image forgery localization in the Metaverse

In recent years, the Metaverse has garnered significant attention in social and Metahuman realms, showcasing substantial value and immense developmental potential through its integration of virtual and real worlds. However, this integration has also raised security concerns. For instance, in digital image forensics, the malicious dissemination of false images by wrongdoers could result in serious consequences and the propagation of misinformation. This paper presented a novel two-branch network (abbreviated as CAFTB-Net) to detect and localize the forged regions of document images in the Metaverse. One branch extracts manipulation trace directly from spatial information, e.g., unnatural smears, anomalies between pixels, etc. The other branch employs an SRM filter to transform the input image from the color domain into the noise domain, effectively extracting anomalies, such as global noise inconsistencies from the noise domain. Compared to spatial domain features, the discontinuity of forgery traces within the noise domain aids the network in authenticating the document image. The two branches extract local and global features in the forged document images. Finally, we propose a cross-attention module to fuse local spatial features and global noise features. Extensive experimental results demonstrate that the proposed network achieves F1 scores of 0.819 and 0.948 on the SACP and ICDAR datasets, respectively, with AUC scores of 0.933 and 0.764, outperforming some of the state-of-the-art algorithms.

MolGC: molecular geometry comparator algorithm for bond length mean absolute error computation on molecules.

Density Functional Theory (DFT) is extensively used in theoretical and computational chemistry to study molecular and crystal properties across diverse fields, including quantum chemistry, materials physics, catalysis, biochemistry, and surface science. Despite advances in DFT hardware and software for optimized geometries, achieving consensus in molecular structure comparisons with experimental counterparts remains a challenge. This difficulty is exacerbated by the lack of automated bond length comparison tools, resulting in labor-intensive and error-prone manual processes. To address these challenges, we propose MolGC, a Molecular Geometry Comparator algorithm that automates the comparison of optimized geometries from different theoretical levels. MolGC calculates the mean absolute error (MAE) of bond lengths by integrating data from various DFT software. It provides interactive and customizable visualization of geometries, enabling users to explore different views for enhanced analysis. In addition, it saves MAE computations for further analysis and offers a comprehensive statistical summary of the results. MolGC effectively addresses complex graph labeling challenges, ensuring accurate identification and categorization of bonds in diverse chemical structures. It achieves a 98.91% average rate in correct bond label assignments on an antibiotics dataset, showcasing its effectiveness for comparing molecular bond lengths across geometries of varying complexity and size. The executable file and software resources for running MolGC can be downloaded from https://github.com/AbimaelGP/MolGC/tree/main .

The Complexity of Octopus Graph, Friendship Graph, and Snail Graph

Graphs are basic structures that represent objects with nodes and relationships between objects with edges. Trees are one of the parts studied in graph theory along with finding the number of spanning trees of a graph such as octopus graph, friendship graph, and snail graph. The complexity of an octopus graph is strongly dependent on the number and length of tentacles, the complexity of a friendship graph is dependent on the number of triangle cycles, and the complexity of a snail graph is dependent on the number of edges and vertices located in the shell-like part of the snail. To calculate the number of spanning trees (τ(G)) of a graph, various calculations can be used, such as the extension of Kirchhoff's formula. The extension of Kirchhoff's formula uses the determinant of the adjacency matrix and degree matrix of the graph complement of a graph. Therefore, this research applies the extension of Kirchhoff's formula to obtain the complexity of octopus graph, friendship graph, and snail graph. From the analysis, it is obtained that for any n≥2, the number of spanning trees of octopus graph and friendship graph are τ(On )=1/5 √5 [((3+√5)/2)^n-((3-√5)/2)^n ] and τ(Fn )=3^n and the number of spanning trees of snail graph is τ(SIn )=2^(n+2)+3n∙2^(n-1) for n≥1.

Semantic Code Clone Detection Based on Community Detection

Semantic code clone detection is to find code snippets that are structurally or syntactically different, but semantically identical. It plays an important role in software reuse, code compression. Many existing studies have achieved good performance in non-semantic clone, but semantic clone is still a challenging task. Recently, several works have used tree or graph, such as Abstract Syntax Tree (AST), Control Flow Graph (CFG) or Program Dependency Graph (PDG) to extract semantic information from source codes. In order to reduce the complexity of tree and graph, some studies transform them into node sequences. However, this transformation will lose some semantic information. To address this issue, we propose a novel high-performance method that utilizes community detection to extract features of AST while preserving its semantic information. First, based on the AST of source code, we exploit community detection to split AST into different subtrees to extract the underlying semantics information of different code blocks, and use centrality analysis to quantify the semantic information as the weight of AST nodes. Then, the AST is converted into a sequence of tokens with weights, and a Siamese neural network model is used to detect the similarity of token sequences for semantic code clone detection. Finally, to evaluate our approach, we conduct experiments on two standard benchmark datasets, Google Code Jam (GCJ) and BigCloneBench (BCB). Experimental results show that our model outperforms the eight publicly available state-of-the-art methods in detecting code clones. It is five times faster than the tree-based method (ASTNN) in terms of time complexity.

OH and H2O Maser Activities Among Long-period Variables

The distribution within an infrared color–magnitude diagram of variable red giants known to have circumstellar masers is reported. Stars with H2O-maser sources occur within a color and period domain of (J − K s ) > 1.15 and P > 199 days, respectively, often in the absence of OH masers. By contrast, OH masers are mostly detected among cooler red giants with (J − K s ) > 1.35 and P > 316 days, and can coexist with H2O-maser sources. The results suggest that red giants must evolve to absolute magnitudes brighter than MKs=−6.8 prior to enabling H2O-maser emission, and possibly expand beyond a certain size before triggering OH masers.