Interactive clustering and merging with a new fuzzy expected value

Major problems exist in both crisp and fuzzy clustering algorithms. The fuzzy c-means type of algorithms use weights determined by a power m of inverse distances that remains fixed over all iterations and over all clusters, even though smaller clusters should have a larger m. Our method uses a different “distance” for each cluster that changes over the early iterations to fit the clusters. Comparisons show improved results. We also address other perplexing problems in clustering: (i) find the optimal number K of clusters; (ii) assess the validity of a given clustering; (iii) prevent the selection of seed vectors as initial prototypes from affecting the clustering; (iv) prevent the order of merging from affecting the clustering; and (v) permit the clusters to form more natural shapes rather than forcing them into normed balls of the distance function. We employ a relatively large number K of uniformly randomly distributed seeds and then thin them to leave fewer uniformly distributed seeds. Next, the main loop iterates by assigning the feature vectors and computing new fuzzy prototypes. Our fuzzy merging then merges any clusters that are too close to each other. We use a modified Xie-Bene validity measure as the goodness of clustering measure for multiple values of K in a user-interaction approach where the user selects two parameters (for eliminating clusters and merging clusters after viewing the results thus far). The algorithm is compared with the fuzzy c-means on the iris data and on the Wisconsin breast cancer data.     

Linear regression analysis for fuzzy input and output data using the extension principle

The method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed. The membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators. In order to obtain the membership value of any given value taken from the fuzzy least squares estimator, optimization problems have to be solved. We also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data.     

多源网络安全事件的准确评估算法研究

研究网络安全事件的评估,由于恶意攻击严重影响网络安全,要求提高报警准确率。针对网络中各类安全设备的增多,产生了大量的安全事件,当安全事件评估结果不一致时,传统的统计方法的评估算法无法处理多源安全事件的不一致,造成漏警率较高的问题。提出了一种加权均值的评估算法,通过模糊聚类方法对多源安全事件融合,设定每个安全事件的权值并计算其加权平均作为评估指标,进行仿真,结果解决了多源安全事件评估不一致的问题。实验证明,改进方法能够有效融合多源安全事件并准确报警,保证了网络的安全,取得了满意的结果。     

等价闭包矩阵及其算法

1 引言在模糊聚类分析的研究与应用中,基于模糊关系等价闭包的模糊聚类算法,又称等价闭包法是一种重要的方法。等价闭包法即是利用样本间的模糊相似关系矩阵进行模糊矩阵相乘得到模糊等价矩阵进而得到等价闭包矩阵,选取适当的阈值对闭包矩阵截取得到一定的分类。该算法的关键问题就是计算出等价闭包矩阵。设R为模糊相似矩阵,其等价闭包矩阵由下式计算:     

一种改进的最小二乘回归子空间分割方法

最小二乘回归(LSR)算法是一种常见的子空间分割方法,由于LSR具有解析解,因此它的聚类性能较高。然而LSR算法是应用谱聚类方法聚类数据,谱聚类方法初始化聚类中心是随机的,会影响后面的聚类效果。针对这一问题,提出一种基于聚类中心局部密度和距离这2个特点的改进的LSR算法(LSR-DC)。在Extended Yale B数据集上进行实验,结果表明,该算法有较高的聚类精度,具有一定的鲁棒性,优于现有LSR等子空间分割方法。     

图像测量中平行线的自适应拟合

对于图像测量中平行线边缘点的拟合问题,本文通过聚类分析法中的 算法去除边缘点图像中的噪声数据,并结合最小二乘法对平行线边缘点进行分类拟合,解决了传统算法中根据图像特点人为划分区域进行分别拟合的问题,达到了机器对图像进行自动处理的目的.     

Point cloud surfaces using geometric proximity graphs

We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least-squares approach. It can be evaluated very fast, but artifacts are significantly reduced.

We propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG), for which we propose several extensions.

The proximity graph also allows us to estimate the local sampling density, which we utilize to automatically adapt the bandwidth of the kernel and to detect boundaries. Consequently, our method is able to handle point clouds of varying sampling density without manual tuning.

Our method can be integrated into other surface definitions, such as moving least squares, so that these benefits carry over.     

Spatial dependence-based fuzzy regression clustering

Fuzzy clustering based regression analysis is a novel hybrid approach to capture the linear structure while considering the classification structure of the measurement. Using the concept that weights provided via the fuzzy degree of clustering, some regression models have been proposed in literature. In these models, membership values derived from clustering or some weights obtained from geometrical functions are employed as the weights of regression system. This paper addresses a weighted fuzzy regression analysis based on spatial dependence measure of the memberships. By the methodology presented in this paper, the relative weights are used in fuzzy regression models instead of direct membership values or their geometrical transforms. The experimental studies indicate that the spatial dependence based analyses yield more reliable results to show the correlation of the independent variables into the dependent variable. In addition, it has been observed that spatial dependence based models have high estimation and generalization capacities.     

Adaptive tracking and recursive identification for Hammerstein systems

A weighted least squares (WLS) based adaptive tracker is designed for a class of Hammerstein systems. It is proved that the tracking error is asymptotically minimized. Incorporating with the diminishing excitation technique, the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved. Numerical examples are given and the simulation results are consistent with the theoretical analysis.     

基于空间距离的快速模糊C均值聚类算法

针对传统的模糊C均值聚类算法在进行图像分割时对孤立点、噪声点敏感性较强,聚类耗时随图像变大而快速增长等缺陷,基于临近元素空间距离的模糊C均值聚类算法即SFGFCM算法,采用核化的空间距离公式,计算出空间临近像素与考察像素的相似度Sij,然后用邻近像素灰度加权和计算出邻近信息制约图像,并进一步在邻近信息制约图像的灰度级统计的基础上进行聚类。该算法考察了临近像素灰度和位置等信息,并且它们之间取得了很好的平衡;不仅表现出较强的鲁棒性且很好地保留了原图像边缘等细节信息,提高了聚类精度,同时大大缩短了大幅图像的聚类时间。通过在合成图像、医学图像及自然图像上的大量实验,与传统算法对比该算法聚类性能明显提高,在图像分割上体现出了较好的分割效果。     

面向云环境的集群资源模糊聚类划分算法的优化

传统的串行模糊聚类分析算法在应对高维矩阵运算时存在运算量大、运算效率低等问题,难以满足云环境中集群资源调度的时效性要求。为此,在基于等价关系的模糊聚类算法基础上对传递闭包法进行优化,提出一种基于多线程的云资源模糊聚类划分并发算法,并将其应用于Hadoop调度器的策略改进。仿真实验结果表明,优化策略有助于减少平方法求解模糊等价矩阵的计算量,所设计的并发算法能够有效解决中小规模云集群资源聚类的运算瓶颈问题,且具有较好的加速比。为了解决现有Hadoop调度器存在的异构性问题,对该优化并发算法进行了理论分析,结果表明它有助于解决异构性带来的调度难题。     

Geostatistics with the Matern semivariogram model: A library of computer programs for inference, kriging and simulation

In many modern applications of geostatistics in the earth sciences, the empirical information is abundant and with complete spatial coverage (e.g. satellite sensor images). In these cases, a critical characteristic of spatial variability is the continuity of the random field that better models the natural phenomenon of interest. Such continuity describes the smoothness of the process at very short distances and is related to the behaviour of the semivariogram near the origin. For this reason, a semivariogram model that is flexible enough to describe the spatial continuity is very convenient for applications. A model that provides such flexibility is the Matern model that controls continuity with a shape parameter. The shape parameter must be larger than zero; a value larger than 1 implies a random field that is m-times mean square differentiable if the shape parameter is larger than m. A package of computer programs is provided for performing the different steps of a geostatistical study using the Matern model and the performance and implementation are illustrated by an example.     

GPS和无线传感器网络融合定位算法研究

为了解决普适计算环境下室内外无缝定位问题,提出了一种卫星定位和无线传感器网络组合定位的算法.算法主要利用了GPS卫星定位系统伪距观测数据和无线传感器网络距离观测数据联合进行位置解算.仿真结果表明,算法与传统的GPS定位相比,增加定位的适应范围,实现少于4颗可用卫星情况下的定位;与无线传感器网络定位算法相比,提高了定位精度.     

Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization

The first stage of knowledge acquisition and reduction of complexity concerning a group of entities is to partition or divide the entities into groups or clusters based on their attributes or characteristics. Clustering algorithms normally require both a method of measuring proximity between patterns and prototypes and a method for aggregating patterns. However sometimes feature vectors or patterns may not be available for objects and only the proximities between the objects are known. Even if feature vectors are available some of the features may not be numeric and it may not be possible to find a satisfactory method of aggregating patterns for the purpose of determining prototypes. Clustering of objects however can be performed on the basis of data describing the objects in terms of feature vectors or on the basis of relational data. The relational data is in terms of proximities between objects. Clustering of objects on the basis of relational data rather than individual object data is called relational clustering. The premise of this paper is that the proximities between the membership vectors, which are obtained as the objective of clustering, should be proportional to the proximities between the objects. The values of the components of the membership vector corresponding to an object are the membership degrees of the object in the various clusters. The membership vector is just a type of feature vector. Based on this premise, this paper describes another fuzzy relational clustering method for finding a fuzzy membership matrix. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort, a Bayesian stopping criterion is used in combination with a multi-start strategy for the PSO. Other relational clustering methods generally find local optimum of their objective function.     

基于彩色编码技术的准种重建算法

求解病毒准种单体型有助于了解其基因结构特点,对疫苗的研制及抗病毒治疗具有重要意义。文中通过引入模糊距离,构造一种带权的片段冲突图,并提出了基于彩色编码技术的病毒准种单体型重建算法CWSS。CWSS算法先根据给定阈值对片段冲突图进行预处理;然后根据顶点的边权和及饱和度取值为图中顶点着色,着色遵循相邻顶点颜色相异的原则,直至所有顶点完成着色;最后将相同颜色的顶点片段进行组装,得到准种单体型。CWSS算法的时间复杂度为O(m^2n+mn) 。采用模拟测序片段数据进行实验测试,对CWSS算法和Dsatur算法的重建性能和质量进行对比分析。实验结果显示,相比于Dsatur算法,CWSS算法能获得更准确的准种单体型,具有更高的重建性能。     

Fuzzy systems design: direct and indirect approaches

A systematic classification of the data-driven approaches for design of fuzzy systems is given in the paper. The possible ways to solve this modelling and identification problem are classified on the basis of the optimisation techniques used for this purpose. One algorithm for each of the two basic categories of design methods is presented and its advantages and disadvantages are discussed. Both types of algorithms are self-learning and do not require interaction during the process of fuzzy model design. They perform adaptation of both the fuzzy model structure (rule-base) and the parameters. The indirect approach exploits the dual nature of Takagi-Sugeno (TS) models and is based on recently introduced recursive clustering combined with Kalman filtering-based procedure for recursive estimation of the parameter of the local sub-models. Both algorithms result in finding compact and transparent fuzzy models. The direct approach solves the optimisation problem directly, while the indirect one decomposes the original problem into on-line clustering and recursive estimation problems and finds a sub-optimal solution in real-time. The later one is computationally very efficient and has a range of potential applications in real-time process control, moving images recognition, autonomous systems design etc. It is extended in this paper for the case of multi-input–multi-output (MIMO systems). Both approaches have been tested with real data from an engineering process.     

模糊c-均值算法改进及其对卫星遥感数据聚类的对比

提出的改进的模糊c-均值聚类方法采用基于标准协方差矩阵的Mahalanobis距离,即椭球体聚类方法,这种聚类算法更接近遥感数据散点图的实际情况,从而可以显著提高聚类效果。对北京卫星ASTER数据的聚类分析实验表明,改进的模糊c-均值聚类方法的聚类效果要优于K-均值聚类方法和常规的模糊c-均值聚类方法。     

基于模糊等价矩阵的无线传感器聚类分区算法

基于模糊等价矩阵的聚类方法是模糊聚类中一种经典的分析方法。首次将其引入无线传感器节点分区的应用中。该聚类分区算法通过计算节点间的Euclid距离、分析其相关性、形成模糊等价矩阵、进行节点分区,实现了对该分区算法的应用设计。分析了其算法时间复杂度,并利用Matlab软件完成了算法仿真。仿真结果显示,该算法可以根据其疏密程度的不同很好地将无线传感节点分成不同区域。