代数商空间的同余结构研究

商空间理论是粒计算最为重要的模型之一,现有的商空间模型的结构一般为拓扑结构.当论域结构是代数结构时,拓扑结构中的等价关系已经不再适用,所以使用比等价关系约束更为严格的同余关系.当给定关系是非同余等价关系时,则引入同余闭包和同余内核的概念来逼近非同余等价关系.本文系统的论证了同余闭包和同余内核的求法以及一些相关性质与结论.以此为基础,对代数商空间模型合成进行系统的研究,为使用商空间理论解决代数结构的复杂问题提供了理论基础.     

超K-代数上的模糊正则商结构

给出超K-代数上的模糊正则同余关系的定义,构建了商超K-代数,运用模糊同余关系,研究了一些相关的性质,证明商结构是BCK-代数。     

基于无线信号不规则性的无线传感网层次型拓扑控制算法

构建层次型拓扑结构是延长网络生存时间的有效方法。该文将拓扑构建过程分为由簇成员组成的感知层和由簇头组成的平面数据转发层,建立了基于无线信号不规则性的网络能耗模型以及节点成簇稳定性模型,提出了基于无线信号不规则性的层次型拓扑控制(WSIBTC)算法。WSIBTC算法根据节点平均有效传输距离将监测区域划分为多个子区域,由成簇稳定性和节点在簇中的位置决定最终簇头,簇头间形成平面拓扑结构,延长网络生存时间。分析和仿真结果表明由WSIBTC算法得到的网络拓扑大幅度地提升了网络生存时间。     

混合维定性空间查询语言MQS-SQL

定性空间推理的RCC理论能够比较全面地表达空间对象的拓扑关系.但由于不支持混合维空间对象,RCC不能直接用于空间查询.本文扩展了RCC,建立了能表达混合维空间关系,更适合于空间查询的空间关系模型MRCC.该模型采用GIS中常用的数据结构,支持混合维空间对象的全拓扑(mereotopology)关系,并根据混合维对象的特点建立了与维数无关的统一的方向、距离关系.利用该模型扩充了标准SQL语言的关系代数,实现了混合维定性空间查询语言MQS-SQL.     

知识论域，知识拓扑与映射的性质

定义了知识论域和知识拓扑,组建了4种拓扑空间,并分析了它们之间的联系,为介绍拓扑与映射的联系做了铺垫;讨论了Z.PAWLAK 粗糙集模型上映射的拓扑性质,指出了粗糙集模型与一个有限集之间的映射.可以诱导出在此有限集上的等价关系,从而得到了两个粗集拓扑空间的映射.这个映射是连续的,如果是双射则此映射是开的且把粗集映成粗集,粗集的原像还是粗集.本文研究了Z.PAWLAK粗糙集模型上的映射的性质和映射的关系,具有一定的理论价值,从而为使用拓扑学的方法来研究粗糙集的理论成为了可能.     

基于商空间的层次式数据网格资源调度算法

为了解决传统数据网格调度算法在对层次式数据网格调度过程中出现的极易陷入局部最优值和收敛速度过慢的问题,将粒计算的思想引入到网格调度中,提出了一种基于商空间的层次式数据网格资源调度QSHDGRA (quotient space theory based hierarchical data grid resource allocation)算法。首先分析了层次式数据网格的特点,接着提出一种基于业务请求平均等待时间和网络与节点资源利用均衡度的调和函数的调度问题模型,随后设计了基于商空间的层次式最优资源调度算法。该算法的特点是可以在不同粒度上由粗至细地对网格业务进行调度,从而保证不同业务的QoS,并实现系统全局最优资源分配。仿真实验表明,算法可以显著地提升系统整体的吞吐率,具有更快的收敛速度,并具备线性扩展能力。     

一种不确定区域的扩展蛋黄模型

空间区域的拓扑关系建模是空间推理、地理信息系统(GIS)和计算机视觉等领域一个重要的研究内容,近年来不确定区域间的拓扑关系建模受到相关领域研究者的极大关注.基于三元组谓词给出了一种不确定区域的扩展蛋黄模型,该模型具有较高的认知合理性,将分明区域作为特例统一处理,分别基于RCC5和RCC8关系进行了扩展,能够实现多层次上的拓扑关系分析.     

基于区间值模糊集的模糊区域拓扑关系模型

在GIS实际应用领域中,采样点的属性数据往往不是精确的数值,而是一个区间范围,对此类空间数据的建模、分析和推理越来越受到相关领域研究者的重视.利用区间值模糊集描述由不确定属性数据所圈定的模糊区域,基于区间值和区间值模糊集的运算性质,给出了模糊区域间拓扑关系的分析模型.该模型改进了基于经典模糊集及其截集的拓扑关系模型,对模糊区域拓扑关系的分析结果更符合人们的认知习惯,可以利用区间值结果进行推理和决策,能够有效地分析由区间值属性所确定的模糊区域间的拓扑关系,在地理信息系统和空间数据库等领域具有实际应用价值.     

基于联盟图博弈的地下空间无人机应急通信网络拓扑控制算法

地下空间灾害事故对极端环境下应急通信网络快速重组与灾情信息实时回传提出了严峻挑战,亟需构建具备按需动态重构、快速响应能力的无人机(UAV)应急通信网络。针对拓扑快变等动态不确定性造成的网络连通性频繁失效等问题,该文利用图论对时变拓扑的关键信息提取简化后,将联盟博弈（CG）引入时变拓扑图,提出一种基于联盟图博弈的自适应拓扑控制算法（CGG-ATC）,通过协同决策建立远程传输链路（LLs）维护拓扑连通性。仿真结果表明,与其他现有算法相比,该算法能更好地实现拓扑连通性、平均传输时延与链路损耗3种性能之间的权衡优化。此外,该算法具有较快的收敛速度,能支持灾后动态不确定场景下组网决策随拓扑快变弹性适变。     

网络传输态势感知的研究与实现

将态势感知的先进思想引入网络传输领域,以空间流量聚类为基本思想,建立网络传输态势感知(NTSA)模型;围绕模型关键技术,依据信息增益和互信息的等价性执行态势因子选择,提出了一种面向传输模式划分的高维数据流聚类算法,并且基于图论进行拓扑重要性分析;设计并且实现了NTSA原型系统.基于真实数据集的实验验证了系统的时效性、准确性以及可扩展性.     

The Models of Granular System and Algebraic Quotient Space in Granular Computing

Granular computing (GrC) is an emerging computing paradigm,and it is an umbrella term exploring multilevel granularity,we present a generic abstract mathematical model of the granular system.Supposing the inter-granule structure as an algebra,we propose the algebraic quotient space model.In this model,the granulation is based on a congruence relation and all the congruence relations on a granular system form a complete semi-order lattice,which is the theoretical basis for transformation,composition and decomposition among different granularities.The different granulation rules between the topological quotient space model and the algebraic quotient space model lead to the dissimilarity while composing granularities.A real-world case study is presented that demonstrates how the algebraic quotient space model works in the network transmission by error-correcting code.These work shows that the granular system model and the algebraic quotient space model are powerful conceptual modeling and functional specification methodologies for GrC.     

Topology preserving non-negative matrix factorization for face recognition.

In this paper, a novel topology preserving non-negative matrix factorization (TPNMF) method is proposed for face recognition. We derive the TPNMF model from original NMF algorithm by preserving local topology structure. The TPNMF is based on minimizing the constraint gradient distance in the high-dimensional space. Compared with L(2) distance, the gradient distance is able to reveal latent manifold structure of face patterns. By using TPNMF decomposition, the high-dimensional face space is transformed into a local topology preserving subspace for face recognition. In comparison with PCA, LDA, and original NMF, which search only the Euclidean structure of face space, the proposed TPNMF finds an embedding that preserves local topology information, such as edges and texture. Theoretical analysis and derivation given also validate the property of TPNMF. Experimental results on three different databases, containing more than 12,000 face images under varying in lighting, facial expression, and pose, show that the proposed TPNMF approach provides a better representation of face patterns and achieves higher recognition rates than NMF.     

基于代数连通度优化的空间信息网络分布式拓扑控制方法

针对空间信息网络中节点高速运动导致的网络拓扑结构难以长期稳定的问题,本文提出了基于代数连通度优化的网络动态拓扑控制方法,通过少量链路调整来维持网络拓扑的稳定性.为减小空间信息网络节点持续相对运动对网络拓扑结构稳定性造成的不利影响,针对网络初始化和网络重构场景,采用图论中的拉普拉斯矩阵特征值优化思想,构建了星上资源约束条件下的加权代数连通度最大化模型.为降低计算复杂度来实现网络拓扑的捷变控制,提出了基于连通矩阵弱摄动的动态网络拓扑控制策略.研究结果表明,提出的算法能够通过内点法,可高效地得到次优解,且次优解与全局最优解十分接近.     

Vector space framework for unification of one- and multidimensionalfilter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parseval's relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem     

一种基于最小化广义Rayleigh商的无源定位算法研究

 为改善只测角无源定位的性能,提出了一种基于最小化广义Rayleigh商的无源定位算法.该算法利用扰动观测矩阵和扰动观测向量的乘性结构,将约束总体最小二乘问题转化为最小化广义Rayleigh商问题,从而只需对一对矩阵束进行广义特征值分解即可求得全局最优定位解.仿真结果表明所提算法性能稳健且计算量较小,定位收敛精度逼近克拉美罗限(CRLB),远优于最小二乘(LS)算法和总体最小二乘(TLS)算法,实用性强.     

A bumpless hybrid supervisory control algorithm for the formation of unmanned helicopters

This paper presents a bumpless hybrid supervisory control scheme for the formation of unmanned helicopters. The approach is based on the polar partitioning of the space, from which a finite bisimilar quotient transition system of the original continuous variable control system is obtained. Then, to implement the designed hybrid supervisory control algorithm, a hierarchical control structure is introduced with a discrete supervisor on the top layer that is connected to the regulation layer via an interface layer. Transiting over the partitioned space may cause jumps on the generated control signal which is harmful for a real flight system. Hence, a smooth control mechanism is introduced that has no jump when the system’s trajectory transits from one region to its adjacent region while preserving the bisimulation relation between the abstract model and the original partitioned system. Several actual flight tests have been conducted to verify the algorithm and the control performance.     

On Analytic Properties of Entropy Rate

Entropy rate is a real valued functional on the space of discrete random sources for which it exists. However, it lacks existence proofs and/or closed formulas even for classes of random sources which have intuitive parameterizations. A good way to overcome this problem is to examine its analytic properties relative to some reasonable topology. A canonical choice of a topology is that of the norm of total variation as it immediately arises with the idea of a discrete random source as a probability measure on sequence space. It is shown that both upper and lower entropy rate, hence entropy rate itself if it exists, are Lipschitzian relative to this topology, which, by well known facts, is close to differentiability. An application of this theorem leads to a simple and elementary proof of the existence of entropy rate of random sources with finite evolution dimension. This class of sources encompasses arbitrary hidden Markov sources and quantum random walks.     

Model of three-way decision based on the space of set pair information granule and its application

Through the analysis of the existing theory and method of three-way decision,model of three-way decision based on the space of set pair information granule was proposed,which was to explain the intension and extension of three-way decision on the view of unity of opposites.Firstly the space structure of set pair information granule can be di-vided into positive granule,negative granule,different granule,which were similar and slightly different with three re-gions of generalized three-way decision.The three kinds of information granules in set pair information granule space were built based on certain positive degree,negative degree and different degree.Secondly,according to the given threshold,set pair information granule is divided into mutually disjointing positive region,negative region and different region.Based on these three regions,the computing method of decision loss function is put forward,and the process of decision-making algorithm is obtained use the three-way decision method of set pair information granule space to evalu-ate and make decision on risk investment,then good decision results have been achieved.