Multiple Graphs Research Articles

Predicting Ride-Hailing Demand with Consideration of Social Equity: A Case Study of Chengdu

In the realm of shared autonomous vehicle ride-sharing, precise demand prediction is vital for optimizing resource allocation, improving travel efficiency, and promoting sustainable transport solutions. However, existing studies tend to overlook social attributes and demographic characteristics across various regions, resulting in disparities in prediction fairness between areas with plentiful and limited transportation resources. In order to achieve more accurate and fair prediction, an innovative Social Graph Convolution Long Short-Term Memory framework is proposed, incorporating demographic, spatial, and transportation accessibility information into multiple functional graphs, including functional similarity, population structure, and historical demand graphs. Furthermore, Mean Percentage Error indicators are employed in the loss function to balance prediction accuracy and fairness. The findings indicate that there is an enhancement in both prediction accuracy and fairness by at least 8.9% and 12.9%, respectively, compared to base models. Additionally, the predictions for rush hours in both privileged and underprivileged regions exhibit greater precision and rationality, supporting sustainable transport practices. The proposed framework effectively captures the demands of diverse social groups, thereby contributing to the advancement of social equity and long-term sustainability in urban mobility.

Towards Integrating Federated Learning with Split Learning via Spatio-temporal Graph Framework for Brain Disease Prediction.

Functional Magnetic Resonance Imaging (fMRI) is used for extracting blood oxygen signals from brain regions to map brain functional connectivity for brain disease prediction. Despite its effectiveness, fMRI has not been widely used: on the one hand, collecting and labeling the data is time-consuming and costly, which limits the amount of valid data collected at a single healthcare site; on the other hand, integrating data from multiple sites is challenging due to data privacy restrictions. To address these issues, we propose a novel, integrated Federated learning and Split learning Spatio-temporal Graph framework (FS2G). Specifically, we introduce federated learning and split learning techniques to split a spatio-temporal model into a client temporal model and a server spatial model. In the client temporal model, we propose a time-aware mechanism to focus on changes in brain functional states and use an InceptionTime model to extract information about changes in the brain states of each subject. In the server spatial model, we propose a united graph convolutional network to integrate multiple graph convolutional networks. Integrating federated learning and split learning, FS2G can utilize multi-site fMRI data without violating data privacy protection and reduce the risk of overfitting as it is capable of learning from limited training data sets. Moreover, it boosts the extraction of spatio-temporal features of fMRI using spatio-temporal graph networks. Experiments on ABIDE and ADHD200 datasets demonstrate that our proposed method outperforms state-of-the-art methods. In addition, we explore biomarkers associated with brain disease prediction using community discovery algorithms using intermediate results of FS2G. The source code is available at https://github.com/yutian0315/FS2G.

Application of the Nirmala Index in Nanotechnology: Optimizing Molecular Structures for Advanced Nanomaterials

Abstract Chemical graph theory has played a key role in advancing our understanding of molecular structure by producing degree-based topological indices that forecast crucial physical and chemical properties. In this paper we attempt to investigate this recently defined Nirmala index as an invariant from different topological angles and applications on multiple molecular graph structures such as triangular, double, and alternate quadrilateral snake structures. This index offers a more profound comprehension of the connections between molecular structures and attributes. The next generation of ground breaking developments in nanotechnology, where the creation of devices and functional nanomaterials hinges on molecular interaction at the nanoscale, may also be greatly influenced by this index. These indices have potential applications in drug delivery systems and in molecular structure optimization related to nanotechnological fields like nanophotonics and nanoelectronics. Consequently, the Nirmala index will pave the way for the development of more sophisticated tools for the production of high-performing nanoscale materials.

Counting spanning trees of multiple complete split-like graph containing a given spanning forest

The multiple complete split-like graph MCSb,sa is the join of an empty graph K‾a and s copies of complete graph Kb. In this article, we obtain the formulas for the number of spanning trees of MCSb,sa containing a given spanning forest when s=1 and 2. Particularly, when s=1, our result derives the number of spanning trees of complete split graph containing a given spanning forest, thereby extending Moon's result [19].

Ensemble-Enhanced Semi-Supervised Learning with Optimized Graph Construction for High-Dimensional Data.

Graph-based methods have demonstrated exceptional performance in semi-supervised classification. However, existing graph-based methods typically construct either a predefined graph in the original space or an adaptive graph within the output space, which often limits their ability to fully utilize prior information and capture the optimal intrinsic data distribution, particularly in high-dimensional data with abundant redundant and noisy features. This paper introduces a novel approach: Semi-Supervised Classification with Optimized Graph Construction (SSC-OGC). SSC-OGC leverages both predefined and adaptive graphs to explore intrinsic data distribution and effectively employ prior information. Additionally, a graph constraint regularization term (GCR) and a collaborative constraint regularization term (CCR) are incorporated to further enhance the quality of the adaptive graph structure and the learned subspace, respectively. To eliminate the negative effect of constructing a predefined graph in the original data space, we further propose a Hybrid Subspace Ensemble-enhanced framework based on the proposed Optimized Graph Construction method (HSE-OGC). Specifically, we construct multiple hybrid subspaces, which consist of meticulously chosen features from the original data to achieve high-quality and diverse space representations. Then, HSE-OGC constructs multiple predefined graphs within hybrid subspaces and trains multiple SSC-OGC classifiers to complement each other, significantly improving the overall performance. Experimental results conducted on various high-dimensional datasets demonstrate that HSE-OGC exhibits outstanding performance.

Backdoor Attacks in Peer-to-Peer Federated Learning

Most machine learning applications rely on centralized learning processes, opening up the risk of exposure of their training datasets. While federated learning (FL) mitigates to some extent these privacy risks, it relies on a trusted aggregation server for training a shared global model. Recently, new distributed learning architectures based on Peer-to-Peer Federated Learning (P2PFL) offer advantages in terms of both privacy and reliability. Still, their resilience to poisoning attacks during training has not been investigated. In this paper, we propose new backdoor attacks for P2PFL that leverage structural graph properties to select the malicious nodes, and achieve high attack success, while remaining stealthy. We evaluate our attacks under various realistic conditions, including multiple graph topologies, limited adversarial visibility of the network, and clients with non-IID data. Finally, we show the limitations of existing defenses adapted from FL and design a new defense that successfully mitigates the backdoor attacks, without an impact on model accuracy.

Action recognition algorithm based on skeleton graph with multiple features and improved adjacency matrix

AbstractAlthough graph convolutional networks have achieved good performances in skeleton‐graph‐based action recognition, there are still some problems which include the incomplete utilization of skeleton graph features and the lacking of logical adjacency information between nodes in adjacency matrix. In this article, a human action recognition algorithm is proposed based on multiple features from the skeleton graph to solve these problems. More specifically, an improved adjacency matrix is constructed to make full use of the multiple skeleton graph features. These features include local differential features, multi‐scale edge features, features of the original skeleton graph, nodal features, and nodal motion features. Extensive results are conducted on four standard datasets (NTU RGB‐D 60, NTU RGB‐D 120, Kinetics, and Northwestern‐UCLA). The experimental results show that the proposed algorithm outperforms the SOTA action recognition algorithms.

Node classification based on Attribute Fuse Edge Features and Label Adaptive Adjustment

Most of existing graph representation learning methods only extract information from nodes and ignore the hidden information of edges. Nodes carry weak structural information thus affecting the specificity of node embeddings.To solve these problems, this paper proposes a node classification algorithm based on Attribute Fuse Edge Features and Label Adaptive Adjustment (AFEF_LAA).Firstly, Intimate-Relationship-Attribute of node is designed based on edge embeddings.Rz-Cos rule is constructed to perform the similarity metric between nodes and their neighbors to select intimate neighbor nodes.After that Reverse-TransE is constructed to encode embedding vectors of the edges connected to intimate neighborhood nodes.Secondly, a multi-fusion method based on smoothed neighborhood information is constructed.Each node in the original graph is smoothed together with its neighbor nodes.The smoothed original graph is multi-fused with multiple twin graphs. Finally, a strategy of label adaptive adjustment is proposed to select the label embedding vectors for input to the next-generation trainer by comparing accuracy.This strategy can improve the quality of graph embeddings while effectively avoiding the overfitting problem when processing high-dimensional data.AFEF_LAA is compared with the state-of-the-art algorithms on six graph datasets.Experimental results show that AFEF_LAA can achieve higher node classification accuracy.

GCNPMDA: Human microbe-disease association prediction by hierarchical graph convolutional network with layer attention

Microorganisms play a crucial role in various physiological processes, including metabolism, immune defense, nutrition absorption, defense against cancer, and protection against pathogen colonization. Changes in microbial communities serve as potential biomarkers for diseases, offering significant insights into disease treatment and diagnosis. However, the association between microorganisms and diseases is still unclear, and more computational methods are needed to predict potential associations. In this paper, we introduce a novel computational model, the Graph Convolutional Network to Predict Microbe-Disease Associations (GCNPMDA), which employs layer attention mechanisms (see Figure 1). GCNPMDA integrates known microbe-disease associations, microbe–microbe similarities, and disease–disease similarities into a heterogeneous network. The model utilizes a Graph Convolutional Network (GCN) to learn embeddings for diseases and microbes. To enhance attribute information, microbe–microbe similarities are computed using Cosine similarity, Jaccard similarity, Gaussian kernel, and functional information, while disease–disease similarities are computed using Cosine similarity, Jaccard similarity, Gaussian kernel, and symptom information. Additionally, attention mechanisms are applied to combine embeddings from multiple graph convolution layers. The model’s predictive effectiveness is evaluated on Human Microbe-Disease Association Database (HMDAD). Leave-one-out cross-validation (LOOCV) was conducted. The Area Under ROC Curve (AUC) of LOOCV is 0.98. The 5-fold cross-validation (5-fold CV) on HMDAD yields average AUC of 0.98 ± 0.009. Furthermore, we carried out a case study of type 2 diabetes (T2D), inflammatory bowel disease (IBD), and rheumatoid arthritis. Based on existing literature evidence, it was confirmed that 6, 7, and 7 of the top-10 inferred microbes have established associations with T2D, IBD, and rheumatoid arthritis, respectively. GCNPMDA demonstrates potential efficacy in identifying disease-related microbes, offering a promising tool to uncover the intricate relationship between microorganisms and their human hosts.

Transfer graph feature alignment guided multi-source domain adaptation network for machinery fault diagnosis

In recent years, the application of unsupervised multi-source domain adaptation (MSDA) techniques for fault diagnosis has gained significant traction. Current research typically overlooks or fails to effectively capture critical data structure information during feature extraction. Another challenge is optimising the integration of information from multiple source domains to diagnose the target domain while avoiding negative transfer. To address these challenges, this study proposes a transfer graph feature alignment guided multi-source domain adaptation network (MDTGAL). In the proposed method, a transfer graph sample generator module (GSG) is constructed to model the data structure between source and target domains, and multiple graph feature extractors are employed to learn the data structure information from different domain combinations. A regularisation technique is introduced to extract the domain-invariant features by aligning the parameters across multiple independent graph feature extractors. In addition, a weighted soft-voting mechanism based on the polynomial kernel-induced maximum mean difference metric (PK-MMD) is designed to fuse the outputs from multiple classifiers, to comprehensively account for the influence of each source domain. The proposed method was tested on multi-source domain transfer tasks involving various operating conditions of rotating machinery. The experimental results demonstrate that the MDTGAL exhibits superior cross-domain diagnostic performance, outperforming existing mainstream methods. In addition, this study explored the impact of varying numbers of source domains on the diagnostic accuracy of the target domain, providing insights into selecting the correct number of source domains for specific MSDA tasks.

Adaptive multi-graph contrastive learning for bundle recommendation

Recently, recommending bundles - sets of items that complement each other - instead of individual items to users has drawn much attention in both academia and industry. Models based on Graph Neural Networks (GNNs) for bundle recommendation have achieved great success in capturing users’ preferences by modeling pairwise correlations among users, bundles, and items via information propagation on graphs. However, a notable limitation lies in their insufficient focus on explicitly modeling intricate ternary relationships. Additionally, the loose combination of node embeddings from different graphs tends to introduce noise, as it fails to consider disparities among the graphs. To this end, we propose a novel approach called Adaptive Multi-Graph Contrastive Learning for Bundle Recommendation (AMCBR). Specifically, AMCBR models ternary interactions by constructing multiple graphs, including a bundle preference graph based on direct user-bundle interactions, a collaborative neighborhoods graph featuring user-level and bundle-level subgraphs, and an item-level preference hypergraph capturing indirect user-bundle relationships through items. Then, (hyper)graph convolution is applied to each (hyper)graph to encode diverse potential preferences into node embeddings. To enhance the model’s robustness, an adaptive aggregation module is employed to assign varying weights to node embeddings from different graphs during the fusion process, which enriches the semantic and comprehensive information in the embeddings while mitigating potential noise. Finally, a contrastive learning strategy is proposed to jointly optimize the model, strengthening collaborative links between individual graphs. Extensive experiments on three real datasets demonstrate that AMCBR can outperform the state-of-the-art baselines on the Top-K recommendations.

Spatio-temporal Dual Graph Neural Networks for Travel Time Estimation

Travel time estimation is one of the core tasks for the development of intelligent transportation systems. Most previous works model the road segments or intersections separately by learning their spatio-temporal characteristics to estimate travel time. However, due to the continuous alternations of the road segments and intersections in a path, the dynamic features are supposed to be coupled and interactive. Therefore, modeling one of them limits further improvement in accuracy of estimating travel time. To address the above problems, a novel graph-based deep learning framework for travel time estimation is proposed in this article, namely, Spatio-temporal Dual Graph Neural Networks (STDGNN). Specifically, we first establish the node-wise and edge-wise graphs to, respectively, characterize the adjacency relations of intersections and that of road segments. To extract the joint spatio-temporal correlations of the intersections and road segments, we adopt the spatio-temporal dual graph learning approach that incorporates multiple spatial-temporal dual graph learning modules with multi-scale network architectures for capturing multi-level spatial-temporal information from the dual graph. Finally, we employ the multi-task learning approach to estimate the travel time of a given whole route, each road segment and intersection simultaneously. We conduct extensive experiments to evaluate our proposed model on three real-world trajectory datasets, and the experimental results show that STDGNN significantly outperforms several state-of-art baselines.

FuseLinker: Leveraging LLM’s pre-trained text embeddings and domain knowledge to enhance GNN-based link prediction on biomedical knowledge graphs

ObjectiveTo develop the FuseLinker, a novel link prediction framework for biomedical knowledge graphs (BKGs), which fully exploits the graph’s structural, textual and domain knowledge information. We evaluated the utility of FuseLinker in the graph-based drug repurposing task through detailed case studies. MethodsFuseLinker leverages fused pre-trained text embedding and domain knowledge embedding to enhance the graph neural network (GNN)-based link prediction model tailored for BKGs. This framework includes three parts: a) obtain text embeddings for BKGs using embedding-visible large language models (LLMs), b) learn the representations of medical ontology as domain knowledge information by employing the Poincaré graph embedding method, and c) fuse these embeddings and further learn the graph structure representations of BKGs by applying a GNN-based link prediction model. We evaluated FuseLinker against traditional knowledge graph embedding models and a conventional GNN-based link prediction model across four public BKG datasets. Additionally, we examined the impact of using different embedding-visible LLMs on FuseLinker’s performance. Finally, we investigated FuseLinker’s ability to generate medical hypotheses through two drug repurposing case studies for Sorafenib and Parkinson’s disease. ResultsBy comparing FuseLinker with baseline models on four BKGs, our method demonstrates superior performance. The Mean Reciprocal Rank (MRR) and Area Under receiver operating characteristic Curve (AUROC) for KEGG50k, Hetionet, SuppKG and ADInt are 0.969 and 0.987, 0.548 and 0.903, 0.739 and 0.928, and 0.831 and 0.890, respectively. ConclusionOur study demonstrates that FuseLinker is an effective novel link prediction framework that integrates multiple graph information and shows significant potential for practical applications in biomedical and clinical tasks. Source code and data are available at https://github.com/YKXia0/FuseLinker.

Asymmetric augmented paradigm-based graph neural architecture search

In most scenarios of graph-based tasks, graph neural networks (GNNs) are trained end-to-end with labeled samples. Labeling graph samples, a time-consuming and expert-dependent process, leads to huge costs. Graph data augmentations can provide a promising method to expand labeled samples cheaply. However, graph data augmentations will damage the capacity of GNNs to distinguish non-isomorphic graphs during the supervised graph representation learning process. How to utilize graph data augmentations to expand labeled samples while preserving the capacity of GNNs to distinguish non-isomorphic graphs is a challenging research problem. To address the above problem, we abstract a novel asymmetric augmented paradigm in this paper and theoretically prove that it offers a principled approach. The asymmetric augmented paradigm can preserve the capacity of GNNs to distinguish non-isomorphic graphs while utilizing augmented labeled samples to improve the generalization capacity of GNNs. To be specific, the asymmetric augmented paradigm will utilize similar yet distinct asymmetric weights to classify the real sample and augmented sample, respectively. To systemically explore the benefits of asymmetric augmented paradigm under different GNN architectures, rather than studying individual asymmetric augmented GNN (A2GNN) instance, we then develop an auto-search engine called Asymmetric Augmented Graph Neural Architecture Search (A2GNAS) to save human efforts. We empirically validate our asymmetric augmented paradigm on multiple graph classification benchmarks, and demonstrate that representative A2GNN instances automatically discovered by our A2GNAS method achieve state-of-the-art performance compared with competitive baselines. Our codes are available at: https://github.com/csubigdata-Organization/A2GNAS.

Collaborative graph neural networks for augmented graphs: A local-to-global perspective

In the field of graph neural networks (GNNs) for representation learning, a noteworthy highlight is the potential of embedding fusion architectures for augmented graphs. However, prevalent GNN embedding fusion architectures mainly focus on handling graph combinations from a global perspective, often ignoring their collaboration with the information of local graph combinations. This inherent limitation constrains the ability of the constructed models to handle multiple input graphs, particularly when dealing with noisy input graphs collected from error-prone sources or those resulting from deficiencies in graph augmentation methods. In this paper, we propose an effective and robust embedding fusion architecture from a local-to-global perspective termed collaborative graph neural networks for augmented graphs (LoGo-GNN). Essentially, LoGo-GNN leverages a pairwise graph combination scheme to generate local perspective inputs. Together with the global graph combination, this serves as the basis to generate a local-to-global perspective. Specifically, LoGo-GNN employs a perturbation augmentation strategy to generate multiple augmentation graphs, thereby facilitating collaboration and embedding fusion from a local-to-global perspective through the use of graph combinations. In addition, LoGo-GNN incorporates a novel loss function for learning complementary information between different perspectives. We also conduct theoretical analysis to assess its expressive power under ideal conditions, demonstrating the effectiveness of LoGo-GNN. Our experiments, focusing on node classification and clustering tasks, highlight the superior performance of LoGo-GNN compared to state-of-the-art methods. Additionally, robustness analysis further confirms its effectiveness in addressing uncertainty challenges.

Joint consensus kernel learning and adaptive hypergraph regularization for graph-based clustering

Recent advancements in multiple kernel learning-based graph clustering methods have demonstrated significant promise in effectively learning a consensus kernel matrix from various candidate kernel matrices. This approach enables the creation of a low-dimensional representation in the kernel space of high-dimensional data through self-expressiveness. However, a key challenge remains in capturing the latent geometric properties embedded within different kernel matrices to enhance data representation. In this paper, we propose a novel method called joint consensus kernel learning and adaptive hypergraph regularization for graph-based clustering (JKHR). Our approach integrates an innovative adaptive hypergraph Laplacian regularizer, which is characterized by the fusion of multiple nearest neighbor kernel graphs, into the multiple kernel learning-based graph clustering framework. JKHR jointly and adaptively optimizes both the consensus kernel matrix and the hypergraph Laplacian regularizer to achieve a low-dimensional representation that effectively preserves the intrinsic geometry of the data. Experimental results on both synthetic and real benchmark datasets demonstrate that JKHR outperforms state-of-the-art self-expressiveness-based graph clustering methods as well as traditional clustering techniques.

ES-GNN: Generalizing Graph Neural Networks Beyond Homophily With Edge Splitting.

While Graph Neural Networks (GNNs) have achieved enormous success in multiple graph analytical tasks, modern variants mostly rely on the strong inductive bias of homophily. However, real-world networks typically exhibit both homophilic and heterophilic linking patterns, wherein adjacent nodes may share dissimilar attributes and distinct labels. Therefore, GNNs smoothing node proximity holistically may aggregate both task-relevant and irrelevant (even harmful) information, limiting their ability to generalize to heterophilic graphs and potentially causing non-robustness. In this work, we propose a novel Edge Splitting GNN (ES-GNN) framework to adaptively distinguish between graph edges either relevant or irrelevant to learning tasks. This essentially transfers the original graph into two subgraphs with the same node set but complementary edge sets dynamically. Given that, information propagation separately on these subgraphs and edge splitting are alternatively conducted, thus disentangling the task-relevant and irrelevant features. Theoretically, we show that our ES-GNN can be regarded as a solution to a disentangled graph denoising problem, which further illustrates our motivations and interprets the improved generalization beyond homophily. Extensive experiments over 11 benchmark and 1 synthetic datasets not only demonstrate the effective performance of ES-GNN but also highlight its robustness to adversarial graphs and mitigation of the over-smoothing problem.

Visual Analysis of Multi-outcome Causal Graphs.

We introduce a visual analysis method for multiple causal graphs with different outcome variables, namely, multi-outcome causal graphs. Multi-outcome causal graphs are important in healthcare for understanding multimorbidity and comorbidity. To support the visual analysis, we collaborated with medical experts to devise two comparative visualization techniques at different stages of the analysis process. First, a progressive visualization method is proposed for comparing multiple state-of-the-art causal discovery algorithms. The method can handle mixed-type datasets comprising both continuous and categorical variables and assist in the creation of a fine-tuned causal graph of a single outcome. Second, a comparative graph layout technique and specialized visual encodings are devised for the quick comparison of multiple causal graphs. In our visual analysis approach, analysts start by building individual causal graphs for each outcome variable, and then, multi-outcome causal graphs are generated and visualized with our comparative technique for analyzing differences and commonalities of these causal graphs. Evaluation includes quantitative measurements on benchmark datasets, a case study with a medical expert, and expert user studies with real-world health research data.

Entropy optimization in Casson tetra-hybrid nanofluid flow over a rotating disk with nonlinear thermal radiation: a Levenberg–Marquardt neural network approach

Abstract This research employs a neural network, specifically the Levenberg–Marquardt algorithm, to characterize the entropy optimization performance in the electro-magneto-hydrodynamic flow of a Casson tetra-hybrid nanofluid over a rotating disk. The problem was formulated mathematically using equations for momentum, continuity, and temperature. This study converts ordinary differential equations (ODEs) into partial differential equations (PDEs) by a self-similarity transformation. The equations are resolved via the fourth-order Runge-Kutta method in combination with a shooting technique for obtaining the required datasets. Using the Levenberg-Marquardt algorithm (LMA), these datasets are characterised as training, testing, and validation. The proposed outcomes are presented in multiple tables and graphs. This trained neural network is then utilized to predict the heat flow velocity and Nusselt number of the rotating disk. The developed model was evaluated using mean square error, error analysis, and regression analysis, thereby confirming the consistency, accuracy, and reliability of the designed technique. The best validation performance for skin friction and the Nusselt number for the Casson tetra-hybrid nanofluid flow across a rotating disk is 8752e-05 at epoch 95 and 0.00033239 at epoch 37. Training, validation, testing, and all performance metrics of the artificial neural network model are close to unity. As magnetic field strength increases, temperature profiles rise in di-hybrid, ternary-hybrid, and tetra-hybrid nanoparticle scenarios. Tetra-hybrid nanofluids are considered superior fluids when compared to di-hybrid, ternary-hybrid, and tetra-hybrid nanofluids. This optimization method holds promise for diverse applications in biotechnology, microbiology, and medicine, offering significant potential for various fields.

Grapher: A Reconfigurable Graph Computing Accelerator with Optimized Processing Elements

In recent years, various graph computing architectures have been proposed to process graph data that represent complex dependencies between different objects in the world. The designs of the processing element (PE) in traditional graph computing accelerators are often optimized for specific graph algorithms or tasks, which limits their flexibility in processing different types of graph algorithms, or the parallel configuration that can be supported by their PE arrays is inefficient. To achieve both flexibility and efficiency, this paper proposes Grapher, a reconfigurable graph computing accelerator based on an optimized PE array, efficiently supporting multiple graph algorithms, enhancing parallel computation, and improving adaptability and system performance through dynamic hardware resource configuration. To verify the performance of Grapher, this paper selected six datasets from the Stanford Network Analysis Project (SNAP) database for testing. Compared with the existing typical graph frameworks Ligra, Gemini, and GraphBIG, the processing time for the six datasets using the BFS, CC, and PR algorithms was reduced by up to 39.31%, 35.43%, and 27.67%, respectively. The energy efficiency has also been improved by 1.8× compared to Hitgraph and 4.7× compared to ThunderGP.