Common Lyapunov function approach to matrix root clustering

This paper proposes an alternative route to the matrix root clustering problem, which enables to use a result on the common Lyapunov function for solving the problem efficiently. A necessary and sufficient condition is obtained in terms of the existence of a common positive definite solution to a set of Lyapunov inequalities for eigenvalues of a matrix to lie in a prescribed subregion of the complex plane. Applications to root clustering in sector regions are shown for illustration.     

Robust matrix 𝒟U‐stability analysis

In this paper, the problem of robust matrix root‐clustering is addressed. The studied matrices are subject to both polytopic and unstructured uncertainties. An original point is the large choice of clustering regions enabled by the proposed approach since these regions can be unions of possibly disjoint and non‐symmetric subregions of the complex plane. The precise purpose is, considering a specified polytope, to determine the greatest robustness bound on the unstructured uncertainty such that robust matrix root‐clustering is ensured. To reduce conservatism in the derivation of the bound, the reasoning relies on a framework based upon parameter‐dependent Lyapunov functions. The bound value is computed by solving an ?? ?? ? problem. Copyright © 2003 John Wiley & Sons, Ltd.     

具有结构式不确定性线性系统特征根的鲁棒群聚

采用广义Ｌｙａｐｕｎｏｖ方程，讨论具有结构式不确定性线性系统的特征根在复平面上某些区域内的鲁棒群聚性，如果标称矩阵的所有特征根都在复平面上的特定区域内，本文所给出充分条件将保证当存在有结构式不确定性时矩阵的特征根也在同一区域内，所提出的判断比当前文献中的结论具有较少的保守性。     

节能高效的无线传感器网络非均匀分簇路由协议

为了有效均衡无线传感器网络能耗、缓解能量洞问题、延长网络生命周期,提出了一种节能高效的非均匀分簇路由协议,其核心思想是采用结合计时广播和簇头轮换机制的非均匀分簇（BR—EEUC）算法对网络分簇,并根据代价函数选择代价较低的簇头作为中继节点,形成以汇聚节点为根节点的多跳路由,从而大大降低了能量开销。通过在OMNet＋＋平台上的仿真实验结果表明：与LEACH和EEUC等路由协议相比,该协议有效地均衡了网络能量消耗,延长了网络寿命。     

Location‐dependent generalization of road networks based on equivalent destinations

Suppose a user located at a certain vertex in a road network wants to plan a route using a wayfinding map. The user's exact destination may be irrelevant for planning most of the route, because many destinations will be equivalent in the sense that they allow the user to choose almost the same paths. We propose a method to find such groups of destinations automatically and to contract the resulting clusters in a detailed map to achieve a simplified visualization. We model the problem as a clustering problem in rooted, edge‐weighted trees. Two vertices are allowed to be in the same cluster if and only if they share at least a given fraction of their path to the root. We analyze some properties of these clusterings and give a linear‐time algorithm to compute the minimum‐cardinality clustering. This algorithm may have various other applications in network visualization and graph drawing, but in this paper we apply it specifically to focus‐and‐context map generalization. When contracting shortest‐path trees in a geographic network, the computed clustering additionally provides a constant‐factor bound on the detour that results from routing using the generalized network instead of the full network. This is a desirable property for wayfinding maps.     

基于k-d树的k-means聚类方法

在直接k-means算法的基础上提出了一种新的基于k-d树的聚类方法。通过把所有的对象组织在一棵k-d树中，可以高效地发现给定原型的所有最近邻对象。利用的主要思想是：在根结点，所有的聚类中心(或称为候选原型)都是所有对象的最近邻候选集合，对于根结点的子结点，通过简单几何约束来剪枝该候选集，这种方法可以被递归使用。使用基于k-d树的方法可以使直接k-means算法的总体性能提高一到两个数量级。     

An Algorithm for Clustering Using L1‐Norm Based on Hyperbolic Smoothing Technique

Cluster analysis deals with the problem of organization of a collection of objects into clusters based on a similarity measure, which can be defined using various distance functions. The use of different similarity measures allows one to find different cluster structures in a data set. In this article, an algorithm is developed to solve clustering problems where the similarity measure is defined using the L₁‐norm. The algorithm is designed using the nonsmooth optimization approach to the clustering problem. Smoothing techniques are applied to smooth both the clustering function and the L₁‐norm. The algorithm computes clusters sequentially and finds global or near global solutions to the clustering problem. Results of numerical experiments using 12 real‐world data sets are reported, and the proposed algorithm is compared with two other clustering algorithms.     

On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems

This paper measures the solution bounds for the generalized Lyapunov equations (GLE). By making use of linear algebraic techniques, we estimate the upper and lower matrix bounds for the solutions of the above equations. All the proposed bounds are new, and it is also shown that the majority of existing bounds are the special cases of these results. Furthermore, according to these bounds, the problem of robust root clustering in sub-regions of the complex plane for linear time-invariant systems subjected to parameter perturbations is solved. The tolerance perturbation bounds for robust clustering in the given sub-regions are estimated. Compared to previous results, the feature of these tolerance bounds is that they are independent of the solution of the GLE.     

A hierarchical modeling approach for clustering probability density functions

The problem of clustering probability density functions is emerging in different scientific domains. The methods proposed for clustering probability density functions are mainly focused on univariate settings and are based on heuristic clustering solutions. New aspects of the problem associated with the multivariate setting and a model-based perspective are investigated. The novel approach relies on a hierarchical mixture modeling of the data. The method is introduced in the univariate context and then extended to multivariate densities by means of a factorial model performing dimension reduction. Model fitting is carried out using an EM-algorithm. The proposed method is illustrated through simulated experiments and applied to two real data sets in order to compare its performance with alternative clustering strategies.     

Genetic clustering: An adaptive heuristic for the multidepot vehicle routing problem

A generalized clustering method based on a Genetic Algorithm is proposed. The Genetic Clustering (GenClust) method is used for solving the multidepot vehicle routing problem. The solution obtained by the genetic clustering method is improved using an efficient postoptimizer. A set of problems obtained from the literature are used to compare the efficiency of the genetic clustering method for solving the multidepot vehicle routing problem. The genetic clustering method found 11 new best known solutions from the 23 problems in the literature set.     

An intelligent hybrid approach for hepatitis disease diagnosis: Combining enhanced k‐means clustering and improved ensemble learning

In real world, the automatic detection of liver disease is a challenging problem among medical practitioners. The intent of this work is to propose an intelligent hybrid approach for the diagnosis of hepatitis disease. The diagnosis is performed with the combination of k‐means clustering and improved ensemble‐driven learning. To avoid clinical experience and to reduce the evaluation time, ensemble learning is deployed, which constructs a set of hypotheses by using multiple learners to solve a liver disease problem. The performance analysis of the proposed integrated hybrid system is compared in terms of accuracy, true positive rate, precision, f‐measure, kappa statistic, mean absolute error, and root mean squared error. Simulation results showed that the enhanced k‐means clustering and improved ensemble learning with enhanced adaptive boosting, bagged decision tree, and J48 decision tree‐based intelligent hybrid approach achieved better prediction outcomes than other existing individual and integrated methods.     

Hierarchical clustering for OLAP: the CUBE File approach

This paper deals with the problem of physical clustering of multidimensional data that are organized in hierarchies on disk in a hierarchy-preserving manner. This is called hierarchical clustering. A typical case, where hierarchical clustering is necessary for reducing I/Os during query evaluation, is the most detailed data of an OLAP cube. The presence of hierarchies in the multidimensional space results in an enormous search space for this problem. We propose a representation of the data space that results in a chunk-tree representation of the cube. The model is adaptive to the cube’s extensive sparseness and provides efficient access to subsets of data based on hierarchy value combinations. Based on this representation of the search space we formulate the problem as a chunk-to-bucket allocation problem, which is a packing problem as opposed to the linear ordering approach followed in the literature. We propose a metric to evaluate the quality of hierarchical clustering achieved (i.e., evaluate the solutions to the problem) and formulate the problem as an optimization problem. We prove its NP-Hardness and provide an effective solution based on a linear time greedy algorithm. The solution of this problem leads to the construction of the CUBE File data structure. We analyze in depth all steps of the construction and provide solutions for interesting sub-problems arising, such as the formation of bucket-regions, the storage of large data chunks and the caching of the upper nodes (root directory) in main memory. Finally, we provide an extensive experimental evaluation of the CUBE File’s adaptability to the data space sparseness as well as to an increasing number of data points. The main result is that the CUBE File is highly adaptive to even the most sparse data spaces and for realistic cases of data point cardinalities provides hierarchical clustering of high quality and significant space savings.     

基于模糊C均值聚类的环境感知推荐算法

针对现有环境感知推荐算法存在的不足,提出一种基于模糊C均值聚类的环境感知推荐算法.首先采用模糊C均值聚类算法对历史环境信息进行聚类,产生聚类及隶属矩阵;然后匹配活动用户环境信息与历史环境信息聚类,采用聚类隶属度作为映射系数将符合条件的非隶属数据映射为隶属数据,最终选择与活动环境匹配的隶属用户评分数据为用户产生推荐.同现有算法相比,该算法不仅解决了因用户环境改变不能准确推荐项目的问题,而且通过采用模糊聚类算法克服了传统硬聚类问题,并且借助于隶属映射函数解决了聚类产生的数据稀疏性问题.在MovieLens数据集上比较了新算法和其他算法的性能,验证了所提算法的有效性.     

基于流形距离的迭代聚类算法路面裂缝提取

针对现有算法检测精度不高和边缘定位不准确的问题,提出一种基于流形距离的迭代聚类路面裂缝提取算法。通过计算2个数据点之间的流形距离,设计聚类目标准则函数,利用迭代最优方法解决准则函数的优化问题,将所有数据点划分为背景和目标2个聚类,并结合图像分割算法提取路面裂缝信息。实验结果表明,该算法能稳定有效地提取出图像中的连续裂缝边缘,可用于路面裂缝的自动检测。     

Fast accurate fuzzy clustering through data reduction

Clustering is a useful approach in image segmentation, data mining, and other pattern recognition problems for which unlabeled data exist. Fuzzy clustering using fuzzy c-means or variants of it can provide a data partition that is both better and more meaningful than hard clustering approaches. The clustering process can be quite slow when there are many objects or patterns to be clustered. This paper discusses the algorithm brFCM, which is able to reduce the number of distinct patterns which must be clustered without adversely affecting the partition quality. The reduction is done by aggregating similar examples and then using a weighted exemplar in the clustering process. The reduction in the amount of clustering data allows a partition of the data to be produced faster. The algorithm is applied to the problem of segmenting 32 magnetic resonance images into different tissue types and the problem of segmenting 172 infrared images into trees, grass and target. Average speed-ups of as much as 59-290 times a traditional implementation of fuzzy c-means were obtained using brFCM, while producing partitions that are equivalent to those produced by fuzzy c-means.     

Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.     

基于集束搜索的可解释阈值树构造

传统的聚类算法能够将数据集划分成不同的簇,但是这些簇通常都是难以解释的. IMM (iterative mistake minimization)是一种常见的可解释聚类算法,通过单个特征来构造阈值树,每个簇都可以用根节点到叶子节点路径上的特征-阈值对进行解释.然而,阈值树在每一轮划分数据时仅考虑错误最少的特征-阈值对,这种贪心的方法容易导致局部最优解.针对这一问题,本文引入了集束搜索,通过在阈值树的每一轮划分过程当中保留预定数量的状态来减缓局部最优,进而提高阈值树提供的聚类划分与初始聚类划分的一致性.最后,通过实验验证了该算法的有效性.     

Understanding the scalability of Bayesian network inference using clique tree growth curves

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a BN, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.     

A linear assignment clustering algorithm based on the least similarcluster representatives

This paper presents a linear assignment algorithm for solving the clustering problem. By using the most dissimilar data as cluster representatives, a linear assignment algorithm is developed based on the linear assignment model for clustering multivariate data. The computational results evaluated using multiple performance criteria show that the clustering algorithm is very effective and efficient, especially for clustering a large number of data with many attributes     

Parametric calibration of speed-density relationships in mesoscopic traffic simulator with data mining

Speed-density relationships are used by mesoscopic traffic simulators to represent traffic dynamics. While classical speed-density relationships provide useful insights into the traffic dynamics problem, they may be restrictive for such applications. This paper addresses the problem of calibrating speed-density relationship parameters using data mining techniques, and proposes a novel hierarchical clustering algorithm based on K-means clustering. By combining K-means with agglomerative hierarchical clustering, the proposed new algorithm is able to reduce early-stage errors inherent in agglomerative hierarchical clustering resulted in improved clustering performance. Moreover, in order to improve the precision of parametric calibration, densities and flows are utilized as variables. The proposed approach is tested against sensor data captured from the 3rd Ring Road of Beijing. The testing results show that the performance of our algorithm is better than existing solutions.