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SSRN 2024年

作者： Li, Xuetong Zhang, Xiao-Dong Funded Key Lab of Scientific and Engineering Computing Shanghai Center for Applied Mathematics Shanghai Jiao Tong University Shanghai200240 China

Constructing the similarity matrix is a pivotal step in multi-view clustering, serving as the foundation for subsequent clustering processes. Most multi-view clustering algorithms focus on computing similarity matrices based solely on attribute information, often overlooking the significance of inter-node interaction structures. This paper introduces a novel multi-view clustering algorithm, abbreviated as AAS. This algorithm not only integrates information across multiple views but also combines the attribute information of nodes with their structural interactions, thereby enabling the similarity matrix to more accurately reflect actual classifications. Furthermore, the complexity of the algorithm is simplified through the utilization of anchor method, and a more flexible and representative method for selecting anchors is proposed. Ultimately, the process of solving the similarity matrix and clustering is integrated into a unified optimization framework. Experiments conducted on datasets generated by the improved Attribute SBM method, and comparative analyses with eight other algorithms, demonstrate the effectiveness and superiority of the proposed method. © 2024, The Authors. All rights reserved.

关键词： Clustering algorithms

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Multi-View Clustering Integrating Anchor Attribute and Structural Information

SSRN

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SSRN 2024年

作者： Li, Xuetong Zhang, Xiao-Dong Funded Key Lab of Scientific and Engineering Computing Shanghai Center for Applied Mathematics Shanghai Jiao Tong University Shanghai200240 China

Multisource data has encouraged the development of advanced clustering algorithms, such as multi-view clustering, which critically relies on constructing similarity matrices. Traditional algorithms typically generate these matrices from node attributes alone. However, real-world networks often include pairwise directed topological structures critical for clustering. This paper introduces a novel multi-view clustering algorithm, AAS. It proposes a two-step proximity approach via anchors in each view, integrating attribute and directed structural information. This approach enhances the clarity of class features in the similarity matrices. The construction of the anchor structural similarity matrix leverages strongly connected components of directed graphs. The entire process—from similarity matrices construction to clustering—is consolidated into a unified optimization framework. Comparative experiments on the modified Attribute SBM dataset against eight algorithms affirm the effectiveness and superiority of AAS. © 2024, The Authors. All rights reserved.

关键词： Data fusion

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Multi-view clustering integrating anchor attribute and structural information

arXiv

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arXiv 2024年

作者： Li, Xuetong Zhang, Xiao-Dong Funded Key Lab of Scientific and Engineering Computing Shanghai Center for Applied Mathematics Shanghai Jiao Tong University Shanghai200240 China

Multisource data has driven the development of advanced clustering algorithms, such as multi-view clustering, which critically rely on the construction of similarity matrices. Traditional algorithms typically generate these matrices based solely on node attributes. However, for certain directed real-world networks, neglecting the asymmetric structural relationships between nodes may compromise the accuracy of clustering results. This paper introduces a novel multiview clustering algorithm, AAS, which employs a two-step proximity approach using anchors in each view, effectively integrating both attribute and directed structural information. This method enhances the clarity of cluster features within the similarity matrices. The construction of the anchor structural similarity matrix utilizes strongly connected components of directed graphs. The entire process—from the construction of similarity matrices to clustering—is formulated within a unified optimization framework. Comparative experiments conducted on the modified Attribute SBM dataset, benchmarked against seven other algorithms, demonstrate the effectiveness and superiority of AAS. Copyright © 2024, The Authors. All rights reserved.

关键词： Data fusion

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Derimorphisms over Algebras and Applications

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Algebra Colloquium 2023年第2期30卷 193-204页

作者： X.Cao S.H.Liu X.S.Lu Z.J.Ye Z.R.Yu Y.H.Zhang School of Mathematical Sciences Shanghai Jiao Tong University 800 Dongchuan RoadShanghai 200240China MoE Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University 800 Dongchuan RoadShanghai 200240China

The new concept"derimorphism"generalizing both derivation and homomor-phism is *** a derimorphism is invertible,its inverse is a Rota-Baxter *** general theory of derimorphism is *** classification of all derimorphisms over an associative unital algebra is *** to the nonexistence of nontriv-ial positive derivations,it is shown that nontrivial positive derimorphisms do exist over any pair of opposite orderings over R[x],the lattice-ordered full matrix algebra and upper triangular matrix algebra over a totally ordered field.

关键词： derimorphism Rota-Baxter operator opposite orderings positive derimor-phism

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Adaptive energy-preserving algorithms for guiding center system

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Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

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Fundamental Patterns of Signal Propagation in Complex Networks

arXiv

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arXiv 2023年

作者： Hu, Qitong Zhang, Xiao-Dong School of Mathematical Sciences Shanghai Jiao Tong University Shanghai China Funded Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai China Shanghai Jiao Tong University Shanghai China

Various disasters stem from minor perturbations, such as the spread of infectious diseases, cascading failure in power grids, etc. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have proposed basic propagation patterns for perturbation and explored the impact of basic network motifs on the collective response to these perturbations, However, the current framework is limited in its ability to decouple interactions, and therefore cannot analyze more complex structures. In this article, we establish an effective, robust and powerful propagation framework under a general dynamic model. This framework reveals common and dense network motifs that exert a critical influence on signal propagation, often spanning orders of magnitude compared with conclusions generated by previous work. Moreover, our framework provides a new approach to understand the fundamental principles of complex systems and the negative feedback mechanism, which is of great significance for research of system controlling and network *** Codes 05C82, 82C26 Copyright © 2023, The Authors. All rights reserved.

关键词： Complex networks

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STk: A Scalable Module for Solving Top-k Problems 38

STk: A Scalable Module for Solving Top-k Problems

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Xia, Hanchen Liu, Weidong Mao, Xiaojun School of Mathematical Sciences Shanghai Jiao Tong University Shanghai China Ministry of Education Key Lab of Artificial Intelligence Shanghai Jiao Tong University Shanghai China Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai China RoyalFlush AI Research Institute Hangzhou China

The cost of ranking becomes significant in the new stage of deep learning. We propose STk, a fully differentiable module with a single trainable parameter, designed to solve the Top-k problem without requiring additional time or GPU memory. Due to its fully differentiable nature, STk can be embedded end-to-end into neural networks and optimize the Top-k problems within a unified computational graph. We apply STk to the Average Top-k Loss (ATk), which inherently faces a Top-k problem. The proposed STk Loss outperforms ATk Loss and achieves the best average performance on multiple benchmarks, with the lowest standard deviation. With the assistance of STk Loss, we surpass the state-of-the-art (SOTA) on both CIFAR-100-LT and Places-LT leaderboards. © 2024 Neural information processing systems foundation. All rights reserved.

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key Motifs Searching in Complex Dynamical Systems

arXiv

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arXiv 2024年

作者： Hu, Qitong Zhang, Xiao-Dong School of Mathematical Sciences Shanghai Jiao Tong University Shanghai Shanghai200240 China Funded Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai Shanghai200240 China Shanghai Jiao Tong University Shanghai Shanghai200240 China

key network motifs searching in complex networks is one of the crucial aspects of network analysis. There has been a series of insightful findings and valuable applications for various scenarios through the analysis of network structures. However, in dynamic systems, slight changes in the choice of dynamic equations and parameters can alter the significance of motifs. The known methods are insufficient to address this issue effectively. In this paper, we introduce a concept of perturbation energy based on the system’s Jacobian matrix, and define motif centrality for dynamic systems by seamlessly integrating network topology with dynamic equations. Through simulations, we observe that the key motifs obtained by the proposed energy method present better effective and accurate than them by integrating network topology methods, without significantly increasing algorithm complexity. The finding of key motifs can be used to apply for system control, such as formulating containment policies for the spread of epidemics and protecting fragile ecosystems. Additionally, it makes substantial contribution to a deeper understanding of concepts in physics, such as signal propagation and system’s stability. Copyright © 2024, The Authors. All rights reserved.

关键词： Network topology

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key Motifs Searching in Complex Dynamical Systems

SSRN

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SSRN 2024年

关键词： Dynamical systems

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Statistical Multiplexing Gain Analysis of Centralized Open Radio Access Networks with Limited Cells and Heterogeneous Traffics

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IEEE Transactions on Vehicular Technology 2025年

作者： Wang, Lu Zhou, Yiqing Liu, Ya-Feng Liu, Ling Shi, Ningzhe Tian, Lin Shi, Jinglin National Key Laboratory of Transient Impact Beijing102202 China 208 Research Institute of China Ordnance Industries Beijing102202 China Chinese Academy of Sciences State Key Lab of Processors Institute of Computing Technology Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Beijing Key Laboratory of Mobile Computing and Pervasive Device Beijing100190 China Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Chinese Academy of Sciences Institute of Computing Technology Beijing100190 China Nanjing Institute of InforSuperBahn Nanjing211100 China

Centralized open radio access networks (O-RANs) aggregate computing resources of multiple cells to improve resource utilization and achieve statistical multiplexing gain (SMG), i.e., the ratio of the number of deployed resources (DepR) for distributed radio access network (D-RAN) to that for O-RAN. SMG of O-RAN has been investigated with infinite number of cells with homogeneous bursty-temporal traffic features. However, in practice, the number of cells is limited, and in the era of Internet of Things (IoT), cells with heterogeneous bursty-temporal traffics (het-traffics), should be considered. This paper analyzes the SMG of O-RAN with limited het-traffic cells. First of all, given traffic models of het-traffic cells following different bursty lognormal distribution and periodic time-varying features, required resources (ReqR) for D-RAN can be derived. Then, to obtain the distribution of ReqR for O-RAN with limited het-traffic cells, a Gaussian mixture model (GMM) based resource distribution approximation (GMM-RDA) is proposed. Thus SMG can be obtained for any given service rate. In simulations, the effectiveness of GMM-RDA is verified by Kolmogorov-Smirnov (K-S) test, and the accuracy of achieved SMG can be up to 99.7%, which is about 33% higher than that obtained by the law of large numbers (LLN) for infinite cells. Moreover, het-traffic cells resulting from service diversification can enhance SMG in O-RAN by 34.7%. © 1967-2012 IEEE.

关键词： Radio access networks

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