In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified i...In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion,which share and fuse local measurements and posterior densities between sensors,respectively.Important properties of each fusion rule including the optimality and sub-optimality are presented.In particulax,two robust multitarget density-averaging approaches,arithmetic-and geometric-average fusion,are addressed in detail for various RFSs.Relevant research topics and remaining challenges are highlighted.展开更多
网络安全态势要素提取是开展网络安全态势感知的前提性基础工作,同时也是直接影响网络安全态势感知系统性能的关键性工作之一。文章针对在复杂异构的网络环境下网络安全态势要素难以提取的问题,提出了一种基于粗糙集属性约简(Rough Set ...网络安全态势要素提取是开展网络安全态势感知的前提性基础工作,同时也是直接影响网络安全态势感知系统性能的关键性工作之一。文章针对在复杂异构的网络环境下网络安全态势要素难以提取的问题,提出了一种基于粗糙集属性约简(Rough Set Attribute Reduction, RSAR )的随机森林网络安全态势要素提取方法。在该提取方法中,首先通过粗糙集理论确定数据集中每个属性的重要性,对重要程度低的属性进行约简,删除冗余属性;然后,使用随机森林分类器对约简后的数据集进行分类训练。为验证提出方法的有效性,文章使用入侵检测数据集对提出方法进行实验测试,实验结果表明,通过与传统提取方法相比,该方法有效地提高了态势要素提取的准确性,实现了高效提取网络安全态势要素。展开更多
针对传统K-均值聚类方法不能有效处理大规模数据聚类的问题,提出一种基于随机抽样的加速K-均值聚类(Kmeans Clustering Algorithm Based on Random Sampling,Kmeans_RS)方法,以提高传统K-均值聚类方法的效率。首先从大规模的聚类数据集...针对传统K-均值聚类方法不能有效处理大规模数据聚类的问题,提出一种基于随机抽样的加速K-均值聚类(Kmeans Clustering Algorithm Based on Random Sampling,Kmeans_RS)方法,以提高传统K-均值聚类方法的效率。首先从大规模的聚类数据集中进行随机抽样,得到规模较小的工作集,在工作集上进行传统K-均值聚类,得到聚类中心和半径,并得到抽样结果;然后通过衡量剩下的聚类样本与已得到的抽样结果之间的关系,对剩余的样本进行归类。该方法通过随机抽样大大地减小了参与K-均值聚类的问题规模,从而有效提高了聚类效率,可解决大规模数据的聚类问题。实验结果表明,Kmeans_RS方法在大规模数据集中在保持聚类效果的同时大幅度提高了聚类效率。展开更多
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounde... The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.展开更多
The authors consider the random iteration of serval functions.Denote byJ(R)the Julia set for the random iteration dynamical system formed by a set of complex functionsR={R 1,R 2,…,R M}.Some sufficient conditions are ...The authors consider the random iteration of serval functions.Denote byJ(R)the Julia set for the random iteration dynamical system formed by a set of complex functionsR={R 1,R 2,…,R M}.Some sufficient conditions are given forJ(R)to have no interior points.Also some conditions are given forJ(R)to have interior points but fail to be the extended plane.In addition,J(az n,bz n)(n≥2,ab≠0)andJ(z 2+c 1,z 2+c 2)are investigated and some interesting results are obtained.展开更多
The character and an algorithm about DRVIP（ discrete random variable with interval probability） and the secured kind DRVFP （discrete random variable with crisp event-fuzzy probability） are researched. Using the fu...The character and an algorithm about DRVIP（ discrete random variable with interval probability） and the secured kind DRVFP （discrete random variable with crisp event-fuzzy probability） are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is a typical linear programming problem. A very functional calculating formula for solving mathematical expectation of DRVIP was obtained by using the Dantzig＇s simplex method. The example indicates that the result obtained by using the functional calculating formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.展开更多
For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ο ? ο fc1 are considered. The Fatou set F(Cn) is defined as the set of all $z \in \hat {\ma...For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ο ? ο fc1 are considered. The Fatou set F(Cn) is defined as the set of all $z \in \hat {\mathbb{C}}: = {\mathbb{C}} \cup \left\{ \infty \right\}$ such that (Fn) is normal in some neighbourhood of z, while the complement J(Cn) of F(cn) (in $\hat {\mathbb{C}}$ ) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(Cn) in the case where (cn) is bounded. A problem put forward by Brück is solved.展开更多
The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally diffi...The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.展开更多
基金Project supported by the Key Laboratory Foundation of National Defence Technology,China(No.61424010306)the Joint Fund of Equipment Development and Aerospace Science and Technology,China(No.6141B0624050101)the National Natural Science Foundation of China(Nos.61901489 and 62071389)。
文摘In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion,which share and fuse local measurements and posterior densities between sensors,respectively.Important properties of each fusion rule including the optimality and sub-optimality are presented.In particulax,two robust multitarget density-averaging approaches,arithmetic-and geometric-average fusion,are addressed in detail for various RFSs.Relevant research topics and remaining challenges are highlighted.
文摘针对传统K-均值聚类方法不能有效处理大规模数据聚类的问题,提出一种基于随机抽样的加速K-均值聚类(Kmeans Clustering Algorithm Based on Random Sampling,Kmeans_RS)方法,以提高传统K-均值聚类方法的效率。首先从大规模的聚类数据集中进行随机抽样,得到规模较小的工作集,在工作集上进行传统K-均值聚类,得到聚类中心和半径,并得到抽样结果;然后通过衡量剩下的聚类样本与已得到的抽样结果之间的关系,对剩余的样本进行归类。该方法通过随机抽样大大地减小了参与K-均值聚类的问题规模,从而有效提高了聚类效率,可解决大规模数据的聚类问题。实验结果表明,Kmeans_RS方法在大规模数据集中在保持聚类效果的同时大幅度提高了聚类效率。
基金the the Morningside Center of Mathematics of the Chinese Academy of Sciencesthe Program of "One Hundred Distinguished Chinese Scientists" of the Chinese Academy of Sciences.
文摘 The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.
文摘The authors consider the random iteration of serval functions.Denote byJ(R)the Julia set for the random iteration dynamical system formed by a set of complex functionsR={R 1,R 2,…,R M}.Some sufficient conditions are given forJ(R)to have no interior points.Also some conditions are given forJ(R)to have interior points but fail to be the extended plane.In addition,J(az n,bz n)(n≥2,ab≠0)andJ(z 2+c 1,z 2+c 2)are investigated and some interesting results are obtained.
文摘The character and an algorithm about DRVIP（ discrete random variable with interval probability） and the secured kind DRVFP （discrete random variable with crisp event-fuzzy probability） are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is a typical linear programming problem. A very functional calculating formula for solving mathematical expectation of DRVIP was obtained by using the Dantzig＇s simplex method. The example indicates that the result obtained by using the functional calculating formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.
文摘For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ο ? ο fc1 are considered. The Fatou set F(Cn) is defined as the set of all $z \in \hat {\mathbb{C}}: = {\mathbb{C}} \cup \left\{ \infty \right\}$ such that (Fn) is normal in some neighbourhood of z, while the complement J(Cn) of F(cn) (in $\hat {\mathbb{C}}$ ) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(Cn) in the case where (cn) is bounded. A problem put forward by Brück is solved.
基金supported by the National Natural Science Foundation of China(No.61871301)。
文摘The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.
