Random Sampling of Euler Tours

We define a Markov chain on the set of Euler tours of a given Eulerian graph based on transformations first defined by Kotzig in 1966. We prove that the chain is rapidly mixing if the maximum degree in the given graph is 6, thus obtaining an efficient algorithm for sampling and counting the set of Euler tours for such an Eulerian graph. Received October 30, 1997; revised March 12, 1999, and April 17, 2000.     

The solutions of two star-height problems for regular trees

Regular trees can be defined by two types of rational expressions. For these two types we solve the star-height problem, i.e., we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e., the analogue of the minimal deterministic automation for regular languages). In one case, the minimal starheight is the rank (in the sense of Eggan) of the minimal graph. There corresponds a characterization of the star-height of a prefix-free regular language w.r.t. rational expressions of a special kind (called deterministic) as the rank of its minimal deterministic automaton considered as a graph.     

Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging.     

基于状态-动作图测地高斯基的策略迭代强化学习

在策略迭代强化学习中,基函数构造是影响动作值函数逼近精度的一个重要因素.为了给动作值函数逼近提供合适的基函数,提出一种基于状态-动作图测地高斯基的策略迭代强化学习方法.首先,根据离策略方法建立马尔可夫决策过程的状态-动作图论描述;然后,在状态-动作图上定义测地高斯核函数,利用基于近似线性相关的核稀疏方法自动选择测地高斯...     

RDF（S）三元组的推理控制算法

为实现资源描述框架（RDF）数据的访问控制,提出一种RDF（S）三元组的推理控制算法,通过计算推理依赖图得到三元组的逻辑表达式,对敏感三元组的逻辑表达式求析取范式进而得到推理控制问题的候选解和最优解。实验表明,该算法能够有效地阻止非法推理,合理控制语义信息的丢失。     

Generalizing Swendsen-Wang to sampling arbitrary posterior probabilities

Many vision tasks can be formulated as graph partition problems that minimize energy functions. For such problems, the Gibbs sampler provides a general solution but is very slow, while other methods, such as Ncut and graph cuts are computationally effective but only work for specific energy forms and are not generally applicable. In this paper, we present a new inference algorithm that generalizes the Swendsen-Wang method to arbitrary probabilities defined on graph partitions. We begin by computing graph edge weights, based on local image features. Then, the algorithm iterates two steps: (1) graph clustering - it forms connected components by cutting the edges probabilistically based on their weights; (2) graph relabeling - it selects one connected component and flips probabilistically, the coloring of all vertices in the component simultaneously. Thus, it realizes the split, merge, and regrouping of a "chunk" of the graph, in contrast to Gibbs sampler that flips a single vertex. We prove that this algorithm simulates ergodic and reversible Markov chain jumps in the space of graph partitions and is applicable to arbitrary posterior probabilities or energy functions defined on graphs. We demonstrate the algorithm on two typical problems in computer vision-image segmentation and stereo vision. Experimentally, we show that it is 100-400 times faster in CPU time than the classical Gibbs sampler and 20-40 times faster then the DDMCMC segmentation algorithm. For stereo, we compare performance with graph cuts and belief propagation. We also show that our algorithm can automatically infer generative models and obtain satisfactory results (better than the graphic cuts or belief propagation) in the same amount of time.     

Dynamic transition embedding for image feature extraction and recognition

In this paper, we propose a novel method called dynamic transition embedding (DTE) for linear dimensionality reduction. Differing from the recently proposed manifold learning-based methods, DTE introduces the dynamic transition information into the objective function by characterizing the Markov transition processes of the data set in time t(t?>?0). In the DTE framework, running the Markov chain forward in time, or equivalently, taking the larger powers of Markov transition matrices integrates the local geometry and, therefore, reveals relevant geometric structures of the data set at different timescales. Since the Markov transition matrices defined by the connectivity on a graph contain the intrinsic geometry information of the data points, the elements of the Markov transition matrices can be viewed as the probabilities or the similarities between two points. Thus, minimizing the errors of the probability reconstruction or similarity reconstruction instead of the least-square reconstruction in the well-known manifold learning algorithms will obtain the optimal linear projections with respect to preserving the intrinsic Markov processes of the data set. Comprehensive comparisons and extensive experiments show that DTE achieves higher recognition rates than some well-known linear dimensionality reduction techniques.     

Context-free graph grammars and concatenation of graphs

An operation of concatenation is defined for graphs. This allows strings to be viewed as expressions denoting graphs, and string languages to be interpreted as graph languages. For a class of string languages, is the class of all graph languages that are interpretations of languages from . For the classes REG and LIN of regular and linear context-free languages, respectively, . is the smallest class of graph languages containing all singletons and closed under union, concatenation and star (of graph languages). equals the class of graph languages generated by linear HR (= Hyperedge Replacement) grammars, and is generated by the corresponding -controlled grammars. Two characterizations are given of the largest class such that . For the class CF of context-free languages, lies properly inbetween and the class of graph languages generated by HR grammars. The concatenation operation on graphs combines nicely with the sum operation on graphs. The class of context-free (or equational) graph languages, with respect to these two operations, is the class of graph languages generated by HR grammars. Received 16 October 1995 / 18 September 1996     

一种HRG模型初始化算法及在链路预测中的应用

在利用层次随机图(HRG)模型对真实网络进行链路预测的过程中,需要构造一个初始层次随机图来初始化马尔科夫链以运行马尔科夫链蒙特卡洛抽样算法。针对现有的层次随机图初始化方案效率不高的问题,本文对初始层次随机图模型进行重建,提出一种新的层次随机图模型初始化算法。该算法分为2个阶段,第一阶段引入相似性指标(LHN-I指标)为网络中的边进行排序;第二阶段利用排序好的边对层次随机图模型进行构造。在该过程中,设计一种将网络顶点插入到层次随机图模型中的方法。通过3个实例网络对提出的算法与现有算法的性能进行比较,实验结果表明,利用提出的初始化算法构造出的初始层次随机图不仅有着较高的似然值,而且使得马尔科夫链蒙特卡洛算法能够更快地收敛,进而降低链路预测的时间消耗。除此之外,在链路预测实验中,改进的基于层次随机图模型的链路预测算法相比一些基于相似性指标的链路预测算法有着较好的预测精度。     

Web服务组合的马氏策略规划

针对Web服务存在的业务逻辑与服务质量的不确定性,以及时序、时间窗约束,本文提出了利用马尔可夫决策理论来解决Web服务组合中最优策略规划问题的方法。该方法首先将Web服务组合描述为有向无环图表示的任务网络,网络中每个节点代表一个任务。任务是由相应的Web服务来实现,任务之间的弧线代表任务间时序的约束,任务执行应满足时间窗的约束。在此基础上,建立Web服务组合的马尔可夫决策模型,从而获得Web服务组合的最优策略。     

由Markov网到Bayesian网

Markov网（马尔可夫网）是类似于Bayesian网（贝叶斯网）的另一种进行不确定性揄的有力工具，Markov网是一个无向图，而Bayesian网是一个有向无环图，发现Markov网不需要发现边的方向，因此要比发现Bayesian网容易得多，提出了一种通过发现Markov网得到等价的Bayesian网的方法，首先利用信息论中验证信息独立的一个重要结论，提出了一个基于依赖分析的边删除算法发现Markov网，该算法需O（n^2)次CI（条件独立）测试，CI测试的时间复杂度取决于由样本数据得到的联合概率函数表的大小，经证明，假如由样本数据得到的联合概率函数严格为正，则该算法发现的Markov网一定是样本的最小L图，由发现Markov网，根据表示的联合概率函数相等，得到与其等价的Bayesian网。     

Gibbs and Markov properties of graphs

Directed acyclic graphs (DAG's) and, more generally, chain graphs have in recent years been widely used for statistical modelling. Their Gibbs and Markov properties are now well understood and are exploited, e.g., in reducing the complexity encountered in estimating the joint distribution of many random variables. The scope of the models has been restricted to acyclic or recursive processes and this restriction was long considered imperative, due to the supposed fundamentally different nature of processes involving reciprocal interactions between variables. Recently however it was shown independently by Spirtes (Spirtes, 1995) and Koster (Koster, 1996) that graphs containing directed cycles may be given a proper Markov interpretation. This paper further generalizes the scope of graphical models. It studies a class of conditional independence (CI) probability models determined by a general graph which may have directed and undirected edges, and may contain directed cycles. This class of graphical models strictly includes the well-known class of graphical chain models studied by Frydenberg et al., and the class of probability models determined by a directed cyclic graph or a reciprocal graph, studied recently by Spirtes and Koster. It is shown that the Markov property determined by a graph is equivalent to the existence of a Gibbs-factorization of the density (assumed positive). To better understand the structural aspects of the Gibbs and Markov properties embodied by graphs the notion of lattice conditional independence (LCI), introduced by Andersson and Perlman (Andersson and Perlman, 1993), is needed. The Gibbs-factorization has an outer ‘skeleton’ which is determined by the ring of all anterior sets of the graph. This revised version was published online in June 2006 with corrections to the Cover Date.     

Behavioral Refinement of Graph Transformation-Based Models

Model-driven software engineering requires the refinement of abstract models into more concrete, platform-specific ones. To create and verify such refinements, behavioral models capturing recon- figuration or communication scenarios are presented as instances of a dynamic meta-model, i.e., a typed graph transformation system specifying the concepts and basic operations scenarios may be composed of. Possible refinement relations between models can now be described based on the corresponding meta-models.In contrast to previous approaches, refinement relations on graph transformation systems are not defined as fixed syntactic mappings between abstract transformation rules and, e.g., concrete rule expressions, but allow for a more loose, semantically defined relation between the transformation systems, resulting in a more flexible notion of refinement.     

Mapping the forms of meaning in small worlds

Prox is a stochastic method to map the local and global structures of real‐world complex networks, which are called small worlds. Prox transforms a graph into a Markov chain; the states of which are the nodes of the graph in question. Particles wander from one node to another within the graph by following the graph's edges. It is the dynamics of the particles' trajectories that map the structural properties of the graphs that are studied. Concrete examples are presented in a graph of synonyms to illustrate this approach. © 2008 Wiley Periodicals, Inc.     

基于概率超图的视频事件语义检测

视频事件类别的归属具有模糊性和不确定性,将超图的点边射入矩阵拓展成概率形式的软超图进行关联关系分析和语义分析,将会更有利于提高多事件检索检测的精准率和召回率。提出基于概率超图模型的视频事件语义检测算法（PHVESD）。 该方法首先将颜色、灰度共生矩阵、Tchebichef矩、局部二值模式（LBP）等四种底层视觉特征进行融合; 然后定义视频段的亲密度函数并利用亲密度的信息构建概率超图模型,其中每条超边对应一种事件语义;采用随机游走过程来预测视频段属于每条超边的概率;最后结合阈值采用条件概率模型对视频段进行事件语义分类。将该方法用于交通突发事件多语义检测中并与其他的识别算法相比较,实验结果表明,与基于超图模型的多标签随机游走算法（MLRW）相比,PHVESD的算法使多语义事件检测的准确率提高了10%,召回率提高了8%。     

Enumerating the decomposable neighbors of a decomposable graph under a simple perturbation scheme

Given a decomposable graph, we characterize and enumerate the set of pairs of vertices whose connection or disconnection results in a new graph that is also decomposable. We discuss the relevance of these results to Markov chain Monte Carlo methods that sample or optimize over the space of decomposable graphical models according to probabilities determined by a posterior distribution given observed multivariate data.     

随机拓扑结构下多智能体系统的平均一致性*

利用马尔可夫收敛准则、图的Laplace矩阵谱特性和欧氏度量的极值,对一类具有随机拓扑结构的离散时间多智能体系统平均一致性问题进行了深入讨论。引入完好概率矩阵的概念,建立随机拓扑结构下离散时间系统的一致性算法,应用马尔可夫过程收敛相关结论及伴随算子,从欧氏度量极值的角度证明了系统可达到渐近平均一致,并得出了所需满足的条件,该条件放宽了对系统连通性的要求。最后,采用六个智能体组成的多智能体系统进行计算机仿真,对理论的正确性进行了验证。     

基于图像内容层次表征的遥感图像 分割方法

提出基于图像内容层次表征的高分辨率遥感图像快速多精度分割方法。首先根据初始分割结果建立区域邻接图(RAG),并将其定义为马尔可夫随机场(MRF);然后引入光谱、形状和边缘等图像特征进行层次合并,通过记录层次合并过程获得图像内容的层次表征;最后根据层次表征中不同层级对象之间的关系快速生成任意不同精度的分割结果,以满足不同应用的需求。利用QuickBird卫星图像进行实验和评价的结果表明,本文方法具有较高的精度和效率。     

一种基于多层次MRF的多源图象融合算法

图象融合技术的主要目的是将多种图象传感器数据中的互补信息组合起来 ,使形成的新图象更适合于计算机处理 (如分割、特征提取和目标识别 )等 .在多层次 MRF模型的基础上 ,提出了一种应用于多源图象分类的图象融合算法 .该融合算法将定义在多层次图结构上的非线性因果 Markov模型与贝叶斯 SMAP(sequential m axi-mum a posteriori)最优化准则结合起来 ,克服了 MAP(maximum a posteriori)准则在多层次图结构上计算不合理的缺陷 .该算法可应用于多源遥感图象中的信息融合 ,使像素分类更精确 ,并解决多源海量数据的富集表示 .另外还利用合成图象与自然图象分别针对多层次 MRF模型的改进及算法中可最优化准则的不同进行了对比实验 ,结果表明 ,该算法具有许多优越性