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SGCN: A Scalable Graph Convolutional Network with Graph-Shaped Kernels and Multi-Channels

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SSRN

SSRN 2023年

作者： Huang, Zhenhua Zhou, Wenhao Li, Kunhao Jia, Zhaohong School of Internet Anhui University Feixi Road Hefei230039 China Key Lab of Intelligent Computing and Signal Processing of Ministry of Education Hefei China

Graph neural networks (GNNs) have shown great success in graph processing. However, current message-passing-based GNNs have limitations in feature aggregations and update mechanisms that rely on a fixed mode, resulting in inadequate representations of the neighborhood structure's richness. Furthermore, the convolution layer in most GNNs lacks flexibility and multi-channels compared to convolutional neural networks (CNNs). CNNs employ multiple channels, where different kernels capture shared patterns of images. To address the limitations, we propose a novel scalable graph convolution network (SGCN). SGCN enhances structural information learning by introducing an expressive feature aggregation mechanism. Drawing inspiration from the design of CNNs, SGCN designs graph-shaped kernels to perform multi-channel convolutions on the subgraph structure. A sampler based on degree centrality is employed to simplify the computation costs. Extensive experiments demonstrate that SGCN achieved state-of-the-art performances on various scales of graph datasets (accuracy improved up to 5.38%). © 2023, The Authors. All rights reserved.

关键词： Convolution

Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions

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arXiv 2022年

作者： Zheng, Wenjie Wang, Wenxue Zhao, Shu Qian, Fulan Nanjing University of Science and Technology China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University China

Knowledge graph embeddings (KGE) have been validated as powerful methods for inferring missing links in knowledge graphs (KGs) that they typically map entities into Euclidean space and treat relations as transformations of entities. Recently, some Euclidean KGE methods have been enhanced to model semantic hierarchies commonly found in KGs, improving the performance of link prediction. To embed hierarchical data, hyperbolic space has emerged as a promising alternative to traditional Euclidean space, offering high fidelity and lower memory consumption. Unlike Euclidean, hyperbolic space provides countless curvatures to choose from. However, it is difficult for existing hyperbolic KGE methods to obtain the optimal curvature settings manually, thereby limiting their ability to effectively model semantic hierarchies. To address this limitation, we propose a novel KGE model called Hyperbolic Hierarchical KGE (HypHKGE). This model introduces attention-based learnable curvatures for hyperbolic space, which helps preserve rich semantic hierarchies. Furthermore, to utilize the preserved hierarchies for inferring missing links, we define hyperbolic hierarchical transformations based on the theory of hyperbolic geometry, including both inter-level and intra-level modeling. Experiments demonstrate the effectiveness of the proposed HypHKGE model on the three benchmark datasets (WN18RR, FB15K-237, and YAGO3-10). The source code will be publicly released at https://***/wjzheng96/HypHKGE. Copyright © 2022, The Authors. All rights reserved.

关键词： Knowledge graph

Gray Images of Cyclic Codes over p2 and pp2

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arXiv 2022年

作者： Wang, Xuan Shi, Minjia Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China

In the paper, we firstly study the algebraic structures of ppk-additive cyclic codes and give the generator polynomials and the minimal spanning set of these codes. Secondly, a necessary and sufficient condition for the pp2-additive cyclic code whose Gray image is linear (not necessarily cyclic) over p is given. Moreover, as for some special families of cyclic codes over p2 and pp2, the linearity of the Gray images is *** Codes 94B05 © 2022, CC0.

关键词： Additives

Equivalence and Duality of Polycyclic Codes Associated with Trinomials over Finite Fields

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arXiv 2022年

作者： Shi, Minjia Lu, Haodong Zhou, Shuang Xu, Jiarui Zhu, Yuhang The Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China

In this paper, several conjectures proposed in [2] are studied, involving the equivalence and duality of polycyclic codes associated with trinomials. According to the results, we give methods to construct isodual and self-dual polycyclic codes, and study the self-orthogonal and dual-containing polycyclic codes over F2MSC Codes 94B05, 05E30 © 2022, CC0.

关键词： Algebra

An Efficient Saddle Search Method for Ordered Phase Transitions Involving Translational Invariance

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SSRN

SSRN 2024年

作者： Cui, Gang Jiang, Kai Zhou, Tiejun Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states efficiently. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS method. © 2024, The Authors. All rights reserved.

关键词： Free energy

Near-field Source DOA Estimation Algorithm Based on De-impact Function under Impulse Noise

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Near-field Source DOA Estimation Algorithm Based on De-impac...

IEEE International Conference on Electronic Information and Communication Technology (ICEICT)

作者： Xingchao Xu Baohe Pang Yingsong Li Liping Li Dingcheng Zou Nikola Zlatanov College of Information and Communication Engineering Harbin Engineering University Harbin China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University China Faculty of Computer and Engineering Sciences Innopolis University Innopolis Russia

ISBN: (数字)9798350384437

ISBN: (纸本)9798350384444

In addressing the issue of localizing near-field source signals in the presence of impulse noise, this manuscript introduces a novel de-impact function designed for preprocessing received signals to alleviate the interference caused by impulse noise. Simulation experiments verify the effectiveness of the proposed de-impact function in effectively suppressing impulse noise. Furthermore, to augment estimation precision, a novel algorithm for near-field source localization is proposed. Building upon the framework of correlation entropy theory, a new correntropy covariance matrix is formulated to replace the original signal covariance matrix for signal processing. Through a succession of low-bias approximations between near-field and far-field scenarios, the algorithm converts the original 2-D search into 1-D operations. Additionally, the conventional spectral peak search is replaced by polynomial solving to further mitigate the computational complexity of the algorithm.

关键词： Location awareness Direction-of-arrival estimation Noise signal processing algorithms Estimation Interference Approximation algorithms

A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs

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arXiv 2024年

作者： Cui, Chen Jiang, Kai Liu, Yun Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Recently, deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM combine the smoothing effect of simple iterative methods with the spectral bias of neural networks, which allows them to effectively eliminate both high-frequency and low-frequency error components. However, their efficiency may decrease if simple iterative methods can not provide effective smoothing, making it difficult for the neural network to learn mid-frequency and high-frequency components. This paper first conducts a convergence analysis for general DL-HIM from a spectral viewpoint, concluding that under reasonable assumptions, DL-HIM exhibit a convergence rate independent of grid size h and physical parameters µ. To meet these assumptions, we design a neural network from an eigen perspective, focusing on learning the eigenvalues and eigenvectors corresponding to error components that simple iterative methods struggle to eliminate. Specifically, the eigenvalues are learned by a meta subnet, while the eigenvectors are approximated using Fourier modes with a transition matrix provided by another meta subnet. The resulting DL-HIM, termed the Fourier Neural Solver (FNS), can be trained to achieve a convergence rate independent of grid size and PDE parameters by designing a loss function that ensures the neural network complements the smoothing effect of Jacobi iterative methods. We verify the performance of FNS on six types of linear parametric *** Codes 65F10, 65F08, 68T07, 65N22, 90C06 Copyright © 2024, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

PianoPal: A Robotic Multimedia System for Interactive Piano Instruction Based on Q-Learning and Real-Time Feedback 31st

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PianoPal: A Robotic Multimedia System for Interactive Piano...

31st International Conference on Multimedia Modeling, MMM 2025

作者： Wang, Yufei Yao, Junfeng Wang, Zefeng Xiamen University Xiamen China Center for Digital Media Computing School of Film Xiamen University Xiamen China Institute of Artificial Intelligence Xiamen University Xiamen China School of Informatics Xiamen University Xiamen China Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan Ministry of Culture and Tourism Xiamen China

ISBN: (纸本)9789819620630

Traditional piano learning often requires significant equipment and skill, which can be intimidating for novices. This paper introduces PianoPal, a multimedia piano instruction system based on robotic interaction, designed for novices. The system includes three modules: intelligent performance, piano interaction, and real-time feedback. To test PianoPal’s effectiveness, we conducted two experiments. The first evaluated the fingering planning function using Q-Learning, showing it outperformed alternatives across all metrics. The second experiment involved 24 novice users, with pre- and post-experience questionnaires and interviews indicating that PianoPal improved one- and two-handed performances and was effective in the short term. Overall, PianoPal proves effective in aiding novice piano learning and has been successfully integrated into our robotic piano device, laying a solid foundation for future piano tutoring robot developments. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Musical instruments

Exploring Invariance Matters for Domain Generalization

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IEEE Transactions on Image processing 2025年 34卷 3336-3351页

作者： Wang, Shanshan He, Houmeng Yang, Xun Liu, Zhipu Zhong, Yuanhong Zhang, Xingyi Wang, Meng Anhui University National Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology Institutes of Physical Science and Information Technology Hefei230601 China University of Science and Technology of China School of Information Science and Technology Department of Electronic Engineering and Information Science Hefei230026 China Chongqing University of Technology School of Computer Science and Engineering Chongqing400054 China Chongqing University School of Microelectronics and Communication Engineering Chongqing400030 China Anhui University Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Computer Science and Technology Hefei230601 China Hefei University of Technology School of Computer Science and Information Engineering Hefei230009 China

Domain generalization (DG) aims to solve the problem of significant performance degradation when target domain data collected from the Out-Of-Distribution (O.O.D). Previous efforts try to exploit invariant features in the source domain through CNN networks. However, inspired by causal mechanisms, we find that the complex spurious-invariant information is still hidden in this view invariant features, and the impact of domain and class discrepancies on extracting invariance has not been effectively mitigated. To alleviate these issues, we propose a self-weighted multi-view mining invariance domain generalization framework (SMIDG). On the one hand, to make up for the insufficiency of traditional single-view convolutional feature extraction networks, we propose to mine features from another frequency view and use the self-adaptive adversarial masks to eliminate some spurious correlations, ensuring causal invariance in the coarse-grained generalization. However, due to inconsistencies in discriminative information between interdomain and intra-domain samples, as well as inter-class and intra-class samples, the coarse-grained elimination of spurious associations does not fully resolve this issue. On the other hand, we also consider the fine-grained generalization from two aspects. Firstly, to better tackle the domain discrepancies, we propose a novel progressive contrastive learning strategy that learns the underlying specific features of samples while gradually mitigating domain discrepancies, thereby ensuring domain invariance in fine-grained generalization. Secondly, due to the issue of feature inconsistency, we adopt a self-adaptive hard sample mining method with information gain to ensure that the model pays more attention on hard disentangled samples, thus maintaining feature invariance. Extensive experiments on five benchmark datasets demonstrate that our method outperforms state-of-the-art approaches. © 1992-2012 IEEE.

关键词： Contrastive learning Feature extraction Frequency-domain analysis Training Data models Data mining Correlation Data augmentation Convolutional neural networks Computer science