Detecting overlapping communities in attributed networks remains a significant challenge due to the complexity of jointly modeling topological structure and node attributes,the unknown number of communities,and the ne...Detecting overlapping communities in attributed networks remains a significant challenge due to the complexity of jointly modeling topological structure and node attributes,the unknown number of communities,and the need to capture nodes with multiple memberships.To address these issues,we propose a novel framework named density peaks clustering with neutrosophic C-means.First,we construct a consensus embedding by aligning structure-based and attribute-based representations using spectral decomposition and canonical correlation analysis.Then,an improved density peaks algorithm automatically estimates the number of communities and selects initial cluster centers based on a newly designed cluster strength metric.Finally,a neutrosophic C-means algorithm refines the community assignments,modeling uncertainty and overlap explicitly.Experimental results on synthetic and real-world networks demonstrate that the proposed method achieves superior performance in terms of detection accuracy,stability,and its ability to identify overlapping structures.展开更多
Attributed graph clustering plays a vital role in uncovering hidden network structures,but it presents significant challenges.In recent years,various models have been proposed to identify meaningful clusters by integr...Attributed graph clustering plays a vital role in uncovering hidden network structures,but it presents significant challenges.In recent years,various models have been proposed to identify meaningful clusters by integrating both structural and attribute-based information.However,these models often emphasize node proximities without adequately balancing the efficiency of clustering based on both structural and attribute data.Furthermore,they tend to neglect the critical fuzzy information inherent in attributed graph clusters.To address these issues,we introduce a new framework,Markov lumpability optimization,for efficient clustering of large-scale attributed graphs.Specifically,we define a lumped Markov chain on an attribute-augmented graph and introduce a new metric,Markov lumpability,to quantify the differences between the original and lumped Markov transition probability matrices.To minimize this measure,we propose a conjugate gradient projectionbased approach that ensures the partitioning closely aligns with the intrinsic structure of fuzzy clusters through conditional optimization.Extensive experiments on both synthetic and real-world datasets demonstrate the superior performance of the proposed framework compared to existing clustering algorithms.This framework has many potential applications,including dynamic community analysis of social networks,user profiling in recommendation systems,functional module identification in biological molecular networks,and financial risk control,offering a new paradigm for mining complex patterns in high-dimensional attributed graph data.展开更多
The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrodinger and Klein-Gordon equations.These theories encompass both local and global well-posed...The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrodinger and Klein-Gordon equations.These theories encompass both local and global well-posedness,as well as the existence of blowing-up solutions for large and irregular initial data.The main results presented in this paper can be summarized as follows:(1)Discrete Nonlinear Schrodinger Equation:Global well-posedness in l^(p) spaces for all1≤p≤∞,regardless of whether it is in the defocusing or focusing cases.(2)Discrete Klein-Gordon Equation:Local well-posedness in l^(p) spaces for all 1≤p≤∞.Furthermore,in the defocusing case,we establish global well-posedness in l^(p) spaces for any2≤p≤2σ+2(σ>0).In contrast,in the focusing case,we show that solutions with negative energy blow up within a finite time.These conclusions reveal the distinct dynamic behaviors exhibited by the solutions of the equations in discrete settings compared to their continuous setting.Additionally,they illuminate the significant role that discretization plays in preventing ill-posedness,and collapse for the nonlinear Schrodinger equation.展开更多
This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an ...This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.展开更多
基金supported by the Natural Science Foundation of China(Grant No.72571150)。
文摘Detecting overlapping communities in attributed networks remains a significant challenge due to the complexity of jointly modeling topological structure and node attributes,the unknown number of communities,and the need to capture nodes with multiple memberships.To address these issues,we propose a novel framework named density peaks clustering with neutrosophic C-means.First,we construct a consensus embedding by aligning structure-based and attribute-based representations using spectral decomposition and canonical correlation analysis.Then,an improved density peaks algorithm automatically estimates the number of communities and selects initial cluster centers based on a newly designed cluster strength metric.Finally,a neutrosophic C-means algorithm refines the community assignments,modeling uncertainty and overlap explicitly.Experimental results on synthetic and real-world networks demonstrate that the proposed method achieves superior performance in terms of detection accuracy,stability,and its ability to identify overlapping structures.
基金supported by the National Natural Science Foundation of China(Grant No.72571150)Beijing Natural Science Foundation(Grant No.9182015)。
文摘Attributed graph clustering plays a vital role in uncovering hidden network structures,but it presents significant challenges.In recent years,various models have been proposed to identify meaningful clusters by integrating both structural and attribute-based information.However,these models often emphasize node proximities without adequately balancing the efficiency of clustering based on both structural and attribute data.Furthermore,they tend to neglect the critical fuzzy information inherent in attributed graph clusters.To address these issues,we introduce a new framework,Markov lumpability optimization,for efficient clustering of large-scale attributed graphs.Specifically,we define a lumped Markov chain on an attribute-augmented graph and introduce a new metric,Markov lumpability,to quantify the differences between the original and lumped Markov transition probability matrices.To minimize this measure,we propose a conjugate gradient projectionbased approach that ensures the partitioning closely aligns with the intrinsic structure of fuzzy clusters through conditional optimization.Extensive experiments on both synthetic and real-world datasets demonstrate the superior performance of the proposed framework compared to existing clustering algorithms.This framework has many potential applications,including dynamic community analysis of social networks,user profiling in recommendation systems,functional module identification in biological molecular networks,and financial risk control,offering a new paradigm for mining complex patterns in high-dimensional attributed graph data.
基金in part supported by the NSFC(12171356,12494544)supported by the National Key R&D Program of China(2020 YFA0713300)+1 种基金the NSFC(12531006)the Nankai Zhide Foundation。
文摘The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrodinger and Klein-Gordon equations.These theories encompass both local and global well-posedness,as well as the existence of blowing-up solutions for large and irregular initial data.The main results presented in this paper can be summarized as follows:(1)Discrete Nonlinear Schrodinger Equation:Global well-posedness in l^(p) spaces for all1≤p≤∞,regardless of whether it is in the defocusing or focusing cases.(2)Discrete Klein-Gordon Equation:Local well-posedness in l^(p) spaces for all 1≤p≤∞.Furthermore,in the defocusing case,we establish global well-posedness in l^(p) spaces for any2≤p≤2σ+2(σ>0).In contrast,in the focusing case,we show that solutions with negative energy blow up within a finite time.These conclusions reveal the distinct dynamic behaviors exhibited by the solutions of the equations in discrete settings compared to their continuous setting.Additionally,they illuminate the significant role that discretization plays in preventing ill-posedness,and collapse for the nonlinear Schrodinger equation.
基金supported by the National Natural Science Foundation of China(Grant No.12171253).
文摘This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.
