Semi-supervised clustering via multi-level random walk

A key issue of semi-supervised clustering is how to utilize the limited but informative pairwise constraints. In this paper, we propose a new graph-based constrained clustering algorithm, named SCRAWL. It is composed of two random walks with different granularities. In the lower-level random walk, SCRAWL partitions the vertices (i.e., data points) into constrained and unconstrained ones, according to whether they are in the pairwise constraints. For every constrained vertex, its influence range, or the degrees of influence it exerts on the unconstrained vertices, is encapsulated in an intermediate structure called component. The edge set between each pair of components determines the affecting scope of the pairwise constraints. In the higher-level random walk, SCRAWL enforces the pairwise constraints on the components, so that the constraint influence can be propagated to the unconstrained edges. At last, we combine the cluster membership of all the components to obtain the cluster assignment for each vertex. The promising experimental results on both synthetic and real-world data sets demonstrate the effectiveness of our method.     

The compass rose and random walk tests

The recent discovery of the compass rose pattern (Crack and Ledoit J. Finance 51(2) (1996) 751) has sparked considerable interest among researchers. This paper explores the significance of the effect of the compass rose pattern on random walk tests and measures to what extent its influence may limit the performance of test statistics. We show that in general, the asymptotic theory of test statistics is invalid for transactions data. However, Monte Carlo simulations indicate that the impact of the pattern, measured by the empirical size, is visible for moderate size samples only when the tick/volatility ratio is above some threshold, a condition that is readily met with intraday but not daily or weekly returns.     

Periodic sensor switching and the random walk

Assume the random walk system is subjected to periodic sensor switching between a low-quality sensor with no delay, and a high-quality sensor with a delay. The low-quality sensor is utilized N−1$N-1$ consecutive times followed by one utilization of the high-quality sensor. A periodic Kalman filter is employed. Necessary and sufficient conditions are derived for the existence of scheduling sizes N$N$ such that the resulting periodic system has a steady state error covariance strictly smaller than both the steady state error covariances of the systems obtained with each sensor applied individually. The relationship between this result and recent developments in event driven scheduling is also provided.     

基于染色随机游走的可重叠社区发现

社区发现是一个基础性的且被广泛研究的问题。现有的社区发现方法大多聚焦于网络拓扑结构,然而随着真实网络中实体可用属性的激增,捕获图中结构和属性的丰富交互关系来进行社区发现变得尤为必要。据此面向属性图提出了一种基于染色随机游走的可重叠社区发现算法OCDC,该算法解决了传统的基于随机游走的社区发现算法利用结构转移矩阵造成社区发现效果不佳的问题。具体地,首先利用经典的初始种子策略选出网络中差异度较大的节点,在此基础上设计种子替换策略,挖掘网络中质量更佳的种子替换路径集合对初始种子集合进行替换;其次构建结构-属性交互节点转移矩阵并执行染色随机游走过程得到高质量种子节点的染色分布向量;最后基于融合结构和属性的并行电导值对社区进行扩展。在人工网络和现实网络上的实验表明,本文提出的算法能够准确地识别属性社区并显著优于基准算法。     

Exponential bounds for the random walk algorithm on random planted 3-SAT

Random walk algorithm （RWalkSAT） is one of the simplest and oldest heuristics for satisfiability problems. In contrast to many experimental results, relatively few rigorous analyses of RWalkSAT are available. Up to now, runtime results of small density random 3-SAT have been achieved showing RWalkSAT terminates successfully in linear time up to clause density 1.63. This paper presents a rigorous runtime analysis of RWalkSAT for 3-CNF formulas generated under the planted assignment distribution. It proves that with overwhelming probability, when starting from any initial assignment ｜x｜ 0.9999n, the expected number of steps until RWalkSAT on random planted formulas with a large constant density finds the planted assignment （1, . . . ,1） is at least Ω（1.1514n） and at most O（n21.1517n）.     

A random walk based multi-kernel graph learning framework

Graph learning is an important approach for machine learning. Kernel method is efficient for constructing similarity graph. Single kernel isn’t sufficient for complex problems. In this paper we propose a framework for multi-kernel learning. We give a brief introduction of Gaussian kernel, LLE and sparse representation. Then we analyze the advantages and disadvantages of these methods and give the reason why the combine of these methods with random walk is efficient. We compare our method with baseline methods on real-world data sets. The results show the efficiency of our method.

     

一种基于随机游走的歌曲推荐算法

推荐系统可以帮助人们在海量的数据中发现所需的有价值的信息。传统的协同过滤推荐算法根据历史数据中用户对项目的各种行为操作构建用户-项目评分矩阵,进而计算相似度,从而预测用户对项目的偏好程度进行推荐。但因为评分数据通常较为稀疏,使得推荐的准确性不高,从而不能很好地对用户进行推荐。针对这个问题,提出一种结合场论理论的随机游走歌曲推荐算法,融合歌曲评分相似度和歌曲基本信息相似度,降低歌曲间综合相似度矩阵的稀疏性,并将物理学中的场论理论和歌曲的重要度结合,构造转移概率矩阵,从而实现歌曲推荐。实验表明,该算法较协同过滤算法的推荐准确性更佳。     

基于随机游走的改进标签传播算法

社区发现是挖掘社交网络隐藏信息的一个有用的工具，而标签传播算法（LPA）是社区发现算法中的一种常见算法，不需要任何的先验知识，且运行速度快。针对标签传播算法有很强的随机性而导致的社区发现算法结果不稳定的问题，提出了一种基于随机游走的改进标签传播算法（LPARW）。首先，根据在网络上进行随机游走确定了节点重要性的排序，从而得到节点的更新顺序；然后，遍历节点的更新序列，对每个节点将其与排序在其之前的节点进行相似性计算，若该节点与排序在其之前的节点是邻居节点且它们之间的相似性大于阈值，则将排序在其之前的节点选为种子节点；最后，将种子节点的标签传播给其余的节点，得到社区的最终划分结果。将所提算法与一些经典的标签传播算法在4个有标签的网络和5个无标签的真实网络上进行比较分析，实验结果表明所提算法在标准互信息（NMI）、调整兰德系数（ARI）和模块度等经典的评价指标上的性能均优于其余对比算法，可见该算法具有很好的社区划分效果。     

基于重启随机游走的图自编码器

针对现有的图自编码器无法捕捉图中节点之间的上下文信息的问题,提出基于重启随机游走的图自编码器.首先,构造两层图卷积网络编码图的拓扑结构和特征,同时进行重启随机游走捕捉节点之间的上下文信息;其次,为了聚合重启随机游走和图卷积网络获得的表示,设计自适应学习策略,根据两种表示的重要性自适应地分配权重.为了证明该方法的有效性,将图最终的表示应用于节点聚类和链路预测任务.实验结果表明,与基线方法相比,提出的方法实现了更先进的性能.     

改进的随机游走模型节点排序方法

复杂网络节点重要性排序是研究复杂网络特性的重要方面之一,被广泛应用于数据挖掘、Web搜索、社会网络分析等众多研究领域。基于物理学场论模型,提出改进的随机游走模式的节点重要性排序算法,即通过节点之间相互作用的场力来确定随机游走模型中的Markov转移矩阵,这样可以对节点重要性排序作出更加准确真实的评估。实验结果表明,所采用的节点重要性评估方法能更合理地解释节点重要性的意义,并且可以给出更加真实精确的节点重要性的评估结果。     

基于随机行走时间的步态识别方法

为了在多视角条件下进行步态识别,提出了一种基于随机行走时间的步态识别方法.通过求解定义在步态轮廓上的泊松方程得到轮廓内任一点到轮廓边界的平均随机行走时间,以该时间给轮廓内的每个点重新赋值;统计该轮廓内等角度间隔的扇形区域内所有点的均值和方差,用其构造整体特征向量W;利用SVM算法在多视角的条件下进行步态分类.在CASIA步态数据库上进行了大量的实验,其结果表明了该方法的有效性和鲁棒性.     

Global random walk modelling of transport in complex systems

The Global random walk algorithm performs simultaneously the tracking of large collections of particles and permits massive simulations at reasonable costs. Applications were developed for transport in systems with anisotropic, non-homogeneous, and randomly distributed parameters. As a first illustration we present simulations for diffusion in human skin. Further, a case study for contaminant transport in groundwater shows that the realizations of the transport process converge in mean square limit to a Gaussian diffusion. This investigation also indicates that the use of the Kraichnan routine, based on periodic random fields, yields reliable simulations of transport in Gaussian velocity fields.     

基于超像素和随机游走的交互式分割算法

交互式图像分割通过先验信息指导获取图像中人们感兴趣的部分,但是现有算法无法在效率和精度上实现平衡。为了解决此问题,提出了一种基于超像素和随机游走的快速交互式分割算法(random walk on superpixel, SPRW)。首先,将图像预分割为具有局部相似性的超像素区域,使用像素颜色均值对超像素区域表示;其次,根据人工标记的先验信息建立F-B图结构,扩展随机游走的范围,并使用随机游走的方法求解,获得硬分割结果;最后,针对分割结果的边界不光滑问题,提出改进的抠图算法(fast robust matting, FRB)进行二次处理,得到软分割结果。在BSD500和MSRC数据集上的实验证实,所提出的硬分割方法与其他算法在时间和平均交并比等指标上有较大优势;在Alpha Matting数据集上的实验充分证实所提出的软算法在提高效率的同时精度也有一定的提升;此外,在生活照更换背景的实验上展现了该算法的应用价值。     

An improved spectral clustering algorithm based on random walk

The construction process for a similarity matrix has an important impact on the performance of spectral clustering algorithms. In this paper, we propose a random walk based approach to process the Gaussian kernel similarity matrix. In this method, the pair-wise similarity between two data points is not only related to the two points, but also related to their neighbors. As a result, the new similarity matrix is closer to the ideal matrix which can provide the best clustering result. We give a theoretical analysis of the similarity matrix and apply this similarity matrix to spectral clustering. We also propose a method to handle noisy items which may cause deterioration of clustering performance. Experimental results on real-world data sets show that the proposed spectral clustering algorithm significantly outperforms existing algorithms.     

基于随机行走的群机器人二维地图构建

机器人在未知环境自主探索时,需要快速准确地获取环境地图信息。针对高效探索和未知环境的地图构建问题,将随机行走算法应用于群机器人的探索中,机器人模拟布朗运动,对搜索区域建图。然后,改进了布朗运动算法,通过设置机器人随机行走时的最大旋转角度,来避免机器人重复性地搜索一个区域,使机器人在相同时间内探索更多的区域,提高机器人的搜索效率。最后,通过搭载激光雷达的多个移动机器人进行了仿真实验,实验分析了最大转角增量、机器人数量以及机器人运动步数对搜索区域的影响。     

Error and complexity of random walk Monte Carlo radiosity

The author studies the error and complexity of the discrete random walk Monte Carlo technique for radiosity, using both the shooting and gathering methods. The author shows that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an O(n log n) complexity. The author gives and compares three unbiased estimators for each method, and obtains closed forms and bounds for their variances. The author also bounds the expected value of the mean square error (MSE). Some of the results obtained are also shown to be valid for the nondiscrete gathering case. The author also gives bounds for the variances and MSE for the infinite path length estimators; these bounds might be useful in the study of biased estimators resulting from cutting off the infinite path     

基于改进随机游走的网络表示学习算法

现有的基于Word2vec的网络表示学习（NRL）算法使用随机游走（RW）来生成节点序列,针对随机游走倾向于选择具有较大度的节点,生成的节点序列不能很好地反映网络结构信息,从而影响表示学习性能的问题,提出了基于改进随机游走的网络表示学习算法。首先,使用RLP-MHRW算法生成节点序列,它在生成节点序列时不会偏向大度节点,得到的节点序列能更好地反映网络结构信息;然后,将节点序列投入到Skip-gram模型得到节点表示向量;最后,利用链路预测任务来测度表示学习性能。在4个真实网络数据集上进行了实验。在论文合作网络arXiv ASTRO-PH上与LINE和node2vec算法相比,链路预测的AUC值分别提升了8.9%和3.5%,其他数据集上也均有提升。实验结果表明,RLP-MHRW能有效提高基于Word2vec的网络表示学习算法的性能。     

基于用户偏好的信任网络随机游走推荐模型

为了提高推荐算法评分预测的准确度,解决冷启动用户推荐问题,在TrustWalker模型基础上提出一种基于用户偏好的随机游走模型——PtTrustWalker。首先,利用矩阵分解法对社会网络中的用户、项目相似度进行计算;其次,将项目进行聚类,通过用户评分计算用户对项目类的偏好和不同项目类下的用户相似度;最后,利用权威度和用户偏好将信任细化为不同类别下用户的信任,并在游走过程中利用信任用户最高偏好类中与目标物品相似的项目评分进行评分预测。该模型降低了噪声数据的影响,从而提高了推荐结果的稳定性。实验结果表明,PtTrustWalker模型在推荐质量和推荐速度方面相比现有随机游走模型有所提高。     

A model of finite-step random walk with absorbent boundaries

This paper proposes a model of finite-step lattice random walk with absorbent boundaries. We address a problem of optimal stop for this model, which is defined as the absorbent boundary value with maximum profit. Compared with many existing optimal stop investigations in the random process, our study only considers the small-sample behaviour (i.e., small number of steps behaviour) and does not consider the limit behaviour of the walk. The optimal stop time is given based on classical probability computation. Since the small-sample is more practical and common than the large-sample in many real world problems, the result obtained in this paper may provide some useful guidelines for real applications associated with the finite-step random walk such as the stock market and gambling games.