确定聚类数目的一个准则

Aiming to provide an appropriate number K of clusters, in this paper, we propose a new criterion function - H criterion function, whose three properties have also been proved. We validate the performance of the H criterion function on one artificial dataset and three real-world datasets, and the results are almostly consistent with a previous method. The nonparametric criterion we proposed is intuitive, simple and the computational cost is acceptable.     

Clustering Rules: A Comparison of Partitioning and Hierarchical Clustering Algorithms

Previous research has resulted in a number of different algorithms for rule discovery. Two approaches discussed here, the ‘all-rules’ algorithm and multi-objective metaheuristics, both result in the production of a large number of partial classification rules, or ‘nuggets’, for describing different subsets of the records in the class of interest. This paper describes the application of a number of different clustering algorithms to these rules, in order to identify similar rules and to better understand the data.     

Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

聚类分析的竞争决策算法

聚类分析是数据挖掘的重要技术,是一种无监督的学习方式,可根据数据间的相似程度,将数据进行分类.竞争决策算法是一种基于竞争造就优化和决策左右结果的新型优化算法,针对聚类分析的特点,设计了一种竞争决策算法进行求解,经实验测试和验证,并与其它算法的结果进行比较,获得了较好的结果.     

半马氏环境连续时间马氏决策过程：平均准则

本文讨论半马氏环境连续时间马氏决策过程中的平均准则．首先讨论了半马氏报酬过程中的逼近问题，进而讨论平均目标函数逼近问题。     

The Number of Hierarchical Orderings

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single “hierarchy” these are enumerated by the ordered Bell numbers. In this note we determine the number of “hierarchical orderings” or “societies”, where the n elements are first partitioned into m ≤ n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case. This revised version was published online in September 2006 with corrections to the Cover Date.     

A Criterion for an Optimal Control System to have Finite Switchings

A simple criterion is suggested which determines whether ornot an optimal control system has a finite number of switches.The results are developed using as an example the simple system with performance criterion , but are shown to hold for the more general system where f(0, 0) = 0 (i.e. the uncontrolled system has the originas an equilibrium point) subject to a performance criterion where g(0, 0) 0. The cases where g(0, 0)and are zero for all are also discussed. In particular one obtains a very simpleproof of the result that all two dimensional time optimal controlsystems with a single linear control, whose objective set consistsof the (assumed) unique critical point of the uncontrolled system,have a finite number of switches.     

Incremental Model-Based Clustering for Large Datasets With Small Clusters

Clustering is often useful for analyzing and summarizing information within large datasets. Model-based clustering methods have been found to be effective for determining the number of clusters, dealing with outliers, and selecting the best clustering method in datasets that are small to moderate in size. For large datasets, current model-based clustering methods tend to be limited by memory and time requirements and the increasing difficulty of maximum likelihood estimation. They may fit too many clusters in some portions of the data and/or miss clusters containing relatively few observations. We propose an incremental approach for data that can be processed as a whole in memory, which is relatively efficient computationally and has the ability to find small clusters in large datasets. The method starts by drawing a random sample of the data, selecting and fitting a clustering model to the sample, and extending the model to the full dataset by additional EM iterations. New clusters are then added incrementally, initialized with the observations that are poorly fit by the current model. We demonstrate the effectiveness of this method by applying it to simulated data, and to image data where its performance can be assessed visually.     

Calculating the Symmetry Number of Flexible Sphere Clusters

We present a theoretical and computational framework to compute the symmetry number of a flexible sphere cluster in \({\mathbb {R}}^3\), using a definition of symmetry that arises naturally when calculating the equilibrium probability of a cluster of spheres in the sticky-sphere limit. We define the sticky symmetry group of the cluster as the set of permutations and inversions of the spheres which preserve adjacency and can be realized by continuous deformations of the cluster that do not change the set of contacts or cause particles to overlap. The symmetry number is the size of the sticky symmetry group. We introduce a numerical algorithm to compute the sticky symmetry group and symmetry number, and show it works well on several test cases. Furthermore, we show that once the sticky symmetry group has been calculated for indistinguishable spheres, the symmetry group for partially distinguishable spheres (those with nonidentical interactions) can be efficiently obtained without repeating the laborious parts of the computations. We use our algorithm to calculate the partition functions of every possible connected cluster of six identical sticky spheres, generating data that may be used to design interactions between spheres so they self-assemble into a desired structure.

     

Estimating the Number of Clusters via the GUD Statistic

Estimating the number of clusters is one of the most difficult problems in cluster analysis. Most previous approaches require knowing the data matrix and may not work when only a Euclidean distance matrix is available. Other approaches also suffer from the curse of dimensionality and work poorly in high dimension. In this article, we develop a new statistic, called the GUD statistic, based on the idea of the Gap method, but use the determinant of the pooled within-group scatter matrix instead of the within-cluster sum of squared distances. Some theory is developed to show this statistic can work well when only the Euclidean distance matrix is known. More generally, this statistic can even work for any dissimilarity matrix that satisfies some properties. We also propose a modification for high-dimensional datasets, called the R-GUD statistic, which can give a robust estimation in high-dimensional settings. The simulation shows our method needs less information but is generally found to be more accurate and robust than other methods considered in the study, especially in many difficult settings.     

基于EU-R准则的多属性风险决策方法

风险决策问题中确定方案间的优劣关系必须综合方案前景的期望效用以及前景风险.针对一类多属性风险决策问题,首先规范了其描述方法,其次明确了标准差-信息熵风险度量的概念,然后提出期望效用-风险评价准则,并建立方案的综合评价函数,能够反映决策者风险偏好和效用-风险权衡对决策的影响,最后通过算例验证所提方法的有效性,深入分析决策者主观态度与决策结果间的关系.     

Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees

This article presents an alternative derivation of the generalized approximate crossvalidation (GACV) score of Xiang and Wahba (1996) for smoothing parameter selection in penalized likelihood regression. The new derivation suggests a simple numerical solution that is stable for all sample sizes. Also suggested is a variant of the score that can be computationally more convenient. Simple simulations are presented to illustrate the effectiveness of the scores.     

基于误差传递和联系数的动态区间型多属性决策方法

提出了一种基于误差传递和联系数的动态区间型多属性决策方法。该方法从区间数型属性值的误差视角出发,运用误差传递模型确定了属性权重区间;兼顾多时间段内信息“累积存量”和“增长速率”,确定时间变权;利用UDWA算子集结所有决策时间段的属性权重区间,获得综合属性权重区间;利用IWAA算子集结不同属性下决策信息,得到属性综合决策矩阵;根据集对分析理论,利用联系数和投影隶属度得到备选方案的优劣性排序。以高专利密集型企业研发伙伴选择为例,验证了该方法的可行性和有效性。     

A New Criterion for Controlling the Number of Limit Cycles of Some Generalized Liénard Equations

We consider a class of planar differential equations which include the Liénard differential equations. By applying the Bendixson-Dulac Criterion for ?-connected sets we reduce the study of the number of limit cycles for such equations to the condition that a certain function of just one variable does not change sign. As an application, this method is used to give a sharp upper bound for the number of limit cycles of some Liénard differential equations. In particular, we present a polynomial Liénard system with exactly three limit cycles.     

A Method of Systematic Search for Optimal Multipliers in Congruential Random Number Generators

This paper presents a method of systematic search for optimal multipliers for congruential random number generators. The word-size of computers is a limiting factor for development of random numbers. The generators for computers up to 32 bit word-size are already investigated in detail by several authors. Some partial works are also carried out for moduli of 2⁴⁸ and higher sizes. Rapid advances in computer technology introduced recently 64 bit architecture in computers. There are considerable efforts to provide appropriate parameters for 64 and 128 bit moduli. Although combined generators are equivalent to huge modulus linear congruential generators, for computational efficiency, it is still advisable to choose the maximum moduli for the component generators. Due to enormous computational price of present algorithms, there is a great need for guidelines and rules for systematic search techniques. Here we propose a search method which provides ‘fertile’ areas of multipliers of perfect quality for spectral test in two dimensions. The method may be generalized to higher dimensions. Since figures of merit are extremely variable in dimensions higher than two, it is possible to find similar intervals if the modulus is very large. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal Criterion Weights in Repetitive Multicriteria Decision-Making

In repetitive judgmental discrete decision-making with multiple criteria, the decision maker usually behaves as if there is a set of appropriate criterion weights such that the decisions chosen are based on the weighted sum of all the criteria. Many different procedures for estimating these implied criterion weights have been proposed. Most of these procedures emphasize the preference trade-off among the multiple criteria of the decision maker, and thus the criterion weights obtained are not directly related to the hit ratio of matching decisions. Based on past data, statistical discriminant analysis can be used to determine the implied criterion weights that would reflect the past decisions. The most interesting performance measure is the hit ratio. In this work, we use the integer linear goal-programming technique to determine optimal criterion weights which minimize the number of misclassification of decisions. The linear goal-programming formulation has m constraints and m + k + 1 variables, where m is the number of cases and k is the number of criteria. Empirical study is done by using two different procedures on the actual past admission data of an M.B.A. programme. The hit ratios of the different procedures are compared.     

双层规划的递阶交互决策有效化方法

本文讨论了协调集上双层规划问题解的性质,所得结论表明上层将所得利益全部让给下层,或下层将所得利益全部让给上层.当决策者不满足此种有效化方式时,必须寻找体现递阶结构的有效化方法.本文给出了一种保持递阶结构的递阶交互决策有效化方法.该方法适用于下层有多个平行子问题的双层线性规划.     

基于均值-方差准则的保险公司最优投资策略

研究了保险公司在均值-方差准则下的最优投资问题,其中保险公司的盈余过程由带随机扰动的Cramer-Lundberg模型刻画,而且保险公司可将其盈余投资于无风险资产和一种风险资产.利用随机动态规划方法,通过求解相应的HJB方程,得到了均值方差模型的最优投资策略和有效前沿.最后,给出了数值算例说明扰动项对有效前沿的影响.     

A Counterexample on Sample-Path Optimality in Stable Markov Decision Chains with the Average Reward Criterion

This note deals with Markov decision chains evolving on a denumerable state space. Under standard continuity-compactness requirements, an explicit example is provided to show that, with respect to a strong sample-path average reward criterion, the Lyapunov function condition does not ensure the existence of an optimal stationary policy.     

Optimal Decision Rules for Producing Greeting Cards

A first attempt at applying OR techniques and approaches in a fine art printing firm manufacturing greeting cards is reported in this paper. The problem of economic production of cards is formulated and four related methods are presented, the fourth being a probabilistic model with possibly wider applications in the fashion industry