聚类有效性函数：熵公式

依据香农信息熵理论。本文引入了一个新的划分熵公式。结合Ｊ．Ｃ．Ｂｅｚｄｅｋ给出的划分熵，定义了一个新的聚类有效性函数。通过四组数据对该聚类有效性函数的判决功能和鲁棒性进行了研究。     

模糊聚类与模糊识别理论模型研究

指出文 [1]模糊聚类与模糊识别模型的局限性 ,进一步研究模糊环境下的目标函数 ,修改模糊聚类中心的计算公式 ,提出计算权重的一个公式 ,拓广模糊聚类与模糊识别理论模型的应用范围     

硬聚类和模糊聚类的结合——双层FCM快速算法

模糊c均值(FCM)聚类算法在模式识别领域中得到了广泛的应用,但FCM算法在大数据集的情况下需要大量的CPU时间,令用户感到十分不便,提高算法的速度是一个急待解决的问题。本文提出的双层FCM聚类算法是一种快速算法,它体现了硬聚类和模糊聚类的结合,以硬聚类的结果对模糊聚类的初始值进行指导,从而明显地缩短了迭代过程。双层FCM算法所用的CPU时间仅为FCM算法的十三分之一,因而具有很强的实用价值。     

基于样本最大分类信息的聚类有效性函数

根据每一样本的最大分类信息，对Bezdek定义的划分系数进行修改，提出了一个新的聚类有效性函数，讨论了该函数的若干性质。实验结果表明在某些情形该函数的判决效果优于划分系数。     

一种改进的遗传k-means聚类算法

在经典的k-means聚类算法中,聚类数k必须事先给定,然而在现实中k很难被精确的确定.本文提出了一种改进的遗传k-means聚类算法,并构造了一个用来评价分类程度好坏的适应度函数,该适应度函数考虑的是在提高紧凑度(类内距)和分离度(类间距)的同时使得分类个数尽可能少.最后采用两个人工数据集和三个UCI数据集对k-means聚类算法(KM),遗传聚类算法(GA),遗传k-means聚类算法(GKM)和改进的遗传k-means聚类算法(IGKM)进行比较研究,比较的指标有类间距、类内距和分类正确率.研究证明改进的遗传k-means算法能够自动获取最佳聚类数k并且保持较高的正确率.     

一种基于子集测度的FCM聚类加权指数计算方法

在模糊C均值(Fuzzy C-Means,FCM)聚类应用过程中,针对目前模糊加权指数的确定缺乏理论依据和有效评价方法这一问题,提出了一种基于子集测度的模糊加权指数计算方法.首先根据子集测度理论定义了一个聚类有效性函数,然后依据该函数在聚类过程中通过循环进化迭代来计算聚类结果的有效性,并将其值反馈到模糊加权指数m的变化中,而使m收敛到一个稳定解,即得到最佳模糊加权指数.理论分析和实验表明,该算法是有效的,为模糊加权指数m的探讨研究提供了一种新的思路和途径.     

基于自适应模糊聚类的T-S模糊辨识方法

针对模糊建模在进行结构辨识时需事先设定聚类数的问题,本文在改进模糊分割聚类算法的基础上,对算法中聚类数c给出优选方法,提出了参数自适应模糊聚类算法,并结合递推最小二乘法构建T-S模糊辨识算法。为了验证本文提出的模糊辨识方法的有效性,采用该算法对熟知的Box-Jenkins煤气炉数据和实际的电液位置伺服系统数据进行建模,结果显示该辨识方法具有较高的逼近精度和较好的泛化能力。     

函数型聚类分析:基于距离的一步法框架

基于距离的函数型聚类分析包含曲线拟合和聚类两个独立步骤,最优曲线拟合未必有利于类别信息的提取和保留。根据曲线拟合与聚类分析的计算过程,重新梳理了函数型聚类算法;基于距离度量,提出了同时考虑拟合和聚类效果的函数型聚类一步法;在交替方向乘子法(ADMM)框架下推导并给出了迭代求解算法。模拟试验结果显示,该函数型聚类算法有助于提高聚类精度;针对北京市空气质量监测站点二氧化氮(NO_2)污染物小时浓度数据的实例验证分析表明,该函数型聚类算法对不同类别空气质量监测点具有更好的区分度。     

基于核函数的混合C均值聚类算法

提出了一种基于核函数的混合C均值聚类算法.首先利用模糊C均值聚类算法和另一种类型的可能性C均值聚类算法的优点,设计出一种混合C均值聚类算法.然而鉴于该算法存在的不足,本文将Mercer核函数引入到该算法中,仿真实验结果证实了该方法的可行性和有效性.     

模糊神经网络在多源数据融合中的应用研究

在T-S模糊神经网络数据融合的基础上,改进了标准T-S模糊融合算法中的模糊算子,并利用聚类算法对网络结构中模糊隶属度个数进行选取.通过仿真实验,验证了改进的算法在融合过程中的合理性、稳定性和准确性.以及聚类算法在T-S模糊神经网络数据融合算法中运用的合理性和有效性.     

Epistemic management in mathematics classroom interactions: Student claims of not knowing or not understanding

An important role of classroom interaction is the processes involved in knowing or coming to know. Following a conversation analytical approach, this study investigates how students’ claims of not knowing, not remembering or not understanding are handled by mathematics teachers in whole class interactions. The study draws on video recordings of 42 mathematics lessons from 8 secondary schools in England. It is argued that claims of not knowing and claims of not remembering perform different social actions and are consequently treated differently by teachers. Claims of not knowing can challenge the assumption that knowledge can be taken-as-shared in a way that claims of not remembering do not. This contributes to the research field of mathematics classroom interaction as it nuances the epistemic management within these interactions and how this can contribute to the norms around the negotiation of meaning.     

Contextualism on a pragmatic,not a skeptical,footing

Contextualism is supposed to explain why the following argument for skepticism seems plausible: (1) I don’t know that I am not a bodiless brain-in-a-vat (BIV); (2) If I know I have hands, then I know I am not a bodiless BIV; (3) Therefore, I do not know I have hands. Keith DeRose claims that (1) and (2) are “initially plausible.” I claim that (1) is initially plausible only because of an implicit argument that stands behind it; it is not intuitively plausible. The argument DeRose offers is based on the requirement of sensitivity, that is, on the idea that if you know something then you would not believe it if it were false. I criticize the sensitivity requirement thereby undercutting its support for (1) and the skeptical data that contextualism is meant to explain. While skepticism is not a plausible ground for contextualism, I argue that certain pragmatic considerations are. It’s plausible to think that to know something more evidence is required when more is at stake. The best way to handle skepticism is to criticize the arguments for it. We should not adopt contextualism as a means of accommodating skepticism even if there are other pragmatic reasons for being a contextualist about knowledge.     

On contractible polyhedra that are not simply contractible

In answer to a question of Michael, Dydak, Segal and Spiez have constructed a contractible polyhedron that is not strictly contractible. In the present note we prove a related result; by using alternative methods we show that there exist contractible polyhedra that are not simply (hence not strictly) contractible.

     

Zero-sum games with incompletely defined payoff

It is shown that a saddle-point solution exists in a two-person, zero-sum game whose payoff is given by a matrix which is not completely defined. On the other hand, we show that such games do not always have a value, so that a saddle-point solution is not necessarily an optimal solution.This work was supported by the Centre d'Etudes Atomiques, Saclay, France.     

Stochastic programs with binary distributions: structural properties of scenario trees and algorithms

Binary random variables often refer to such as customers that are present or not, roads that are open or not, machines that are operable or not. At the same time, stochastic programs often apply to situations where penalties are accumulated when demand is not met, travel times are too long, or profits too low. Typical for these situations is that the penalties imply a partial order on the scenarios, leading to a partition of the scenarios into two sets: those that can result in penalties for some decisions, and those that never lead to penalties. We demonstrate how this observation can be used to efficiently calculate out-of-sample values, find good scenario trees and generally simplify calculations. Most of our observations apply to general integer random variables, and not just the 0/1 case.     

Coherentism,Truth, and Witness Agreement

Coherentists on epistemic justification claim that all justification is inferential, and that beliefs, when justified, get their justification together (not in isolation) as members of a coherent belief system. Some recent work in formal epistemology shows that “individual credibility” is needed for “witness agreement” to increase the probability of truth and generate a high probability of truth. It can seem that, from this result in formal epistemology, it follows that coherentist justification is not truth-conducive, that it is not the case that, under the requisite conditions, coherentist justification increases the probability of truth and generates a high probability of truth. I argue that this does not follow.     

关于过程能力指数公式的几点辨析

文献[1-2]认为当过程能力指数为零时,合格率却不为零的情形不符合常理。因而对过程能力指数C_p及C_(pk)公式提出质疑。本文从多个角度辨析这种质疑是不成立的.     

A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

A remark on sets having the Steinhaus property

A point set satisfies the Steinhaus property if no matter how it is placed on a plane, it covers exactly one integer lattice point. Whether or not such a set exists, is an open problem. Beck has proved [1] that any bounded set satisfying the Steinhaus property is not Lebesgue measurable. We show that any such set (bounded or not) must have empty interior. As a corollary, we deduce that closed sets do not have the Steinhaus property, fact noted by Sierpinski [3] under the additional assumption of boundedness.     

On balking from an empty queue

The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above) are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queue is not empty. This research was supported by The Israel Science Foundation Grant No. 237/02.