Size of random Galois lattices and number of closed frequent itemsets

Given a sample of binary random vectors with i.i.d. Bernoulli(p) components, that is equal to 1 (resp. 0) with probability p (resp. 1−p), we first establish a formula for the mean of the size of the random Galois lattice built from this sample, and a more complex one for its variance. Then, noticing that closed α-frequent itemsets are in bijection with closed α-winning coalitions, we establish similar formulas for the mean and the variance of the number of closed α-frequent itemsets. This can be interesting for the study of the complexity of some data mining problems such as association rule mining, sequential pattern mining and classification.     

图模式挖掘中的子图同构算法

图模式挖掘问题在Web挖掘、生物信息学、社会关系等众多领域有广泛的应用,它涉及到子图的搜索以及子图的同构问题.这两个问题都具有相当高的计算复杂度,现有的子图同构问题大多采用最小编码算法,但对无标签图特别是对无标签无向图,该算法效率较底,从而子图的同构成为图模式挖掘问题的一个瓶颈.针对无标签图,以代数理论为基础,分别利用度序列和特征值构造了两种子图同构算法,用于对有向图和无向图的同构判别.最后对2个真实生物网络进行了仿真实验,结果表明,算法的效率优于现有算法.     

基于数据挖掘建立高校系科办学评估体系的合理性评价系统

本文运用关联规则发现方法与人事信息库进行数据挖掘,寻找高校系科办学评估体系中各因素间的关联关系,并根据关联关系强弱分析各因素的权重设置的合理性。本文分析和指出了现有一些看法的优缺点,提出了在Tid-optim算法,并对发现的规则进行分析,通过数据抽样建立合理性评价体系,有效地解决了权重设置的不合理问题,为高校管理决策提供科学依据。     

关联规则增量式更新的改进算法

关联规则是数据挖掘中的重要研究内容之一，对在事务数据库不变，只对最小支持度和最小可信度进行改变的情况下，针对关联规则的维护问题，设计了一个增量式更新的改进算法AIUA。     

返航备降航班高风险频发子集搜索模型

返航备降航班是一种保证航空安全的有效措施,但返航备降航班会带来成本损失,所以对返航备降业务规律进行分析,从而重点监控,在确保安全生产的基础上,有效降低返航备降航班的经济损失。我们可以把确定返航备降航班发生的密集时间段描述为一个多属性空间搜索问题,在许多实践领域存在该类问题,比如商业银行对贷款客户的信用评级、绩效考核等。在多属性组成的多维空间中,存在许多正常点和不正常点,通过建立高风险频发子集搜索模型和算法确定不正常点比较密集的多属性范围,使得在该空间范围内不正常点的比例较高并且总的点的数量达到一定的水平。本文以航空公司安全生产为例,其模型结果在实际生产的运用中取得良好效果,在一年内避免30余班次返航备降。     

基于散列技术的高效剪枝关联规则挖掘算法

该算法结合项集的有序特性有效压缩了频繁项集的数量,提高了算法效率,但是频繁2-项集的产生仍需要占用大量的存储空间,本文利用散列函数对候选频繁2-项集进行剪枝,这样频繁集的数目大大减少,不仅节省了存储空间、减少了计算开销,而且又保持了频繁项集的完整性。     

An Integrated Fuzzy Analytic Hierarchy Process (AHP) Model for Studying Significant Factors Associated with Frequent Lane Changing

Frequent lane changes cause serious traffic safety concerns, which involve fatalities and serious injuries. This phenomenon is affected by several significant factors related to road safety. The detection and classification of significant factors affecting lane changing could help reduce frequent lane changing risk. The principal objective of this research is to estimate and prioritize the nominated crucial criteria and sub-criteria based on participants’ answers on a designated questionnaire survey. In doing so, this paper constructs a hierarchical lane-change model based on the concept of the analytic hierarchy process (AHP) with two levels of the most concerning attributes. Accordingly, the fuzzy analytic hierarchy process (FAHP) procedure was applied utilizing fuzzy scale to evaluate precisely the most influential factors affecting lane changing, which will decrease uncertainty in the evaluation process. Based on the final measured weights for level 1, FAHP model estimation results revealed that the most influential variable affecting lane-changing is ‘traffic characteristics’. In contrast, compared to other specified factors, ‘light conditions’ was found to be the least critical factor related to driver lane-change maneuvers. For level 2, the FAHP model results showed ‘traffic volume’ as the most critical factor influencing the lane changes operations, followed by ‘speed’. The objectivity of the model was supported by sensitivity analyses that examined a range for weights’ values and those corresponding to alternative values. Based on the evaluated results, stakeholders can determine strategic policy by considering and placing more emphasis on the highlighted risk factors associated with lane changing to improve road safety. In conclusion, the finding provides the usefulness of the fuzzy analytic hierarchy process to review lane-changing risks for road safety.     

A random walk proof of the Erdős-Taylor conjecture

Summary For the simple random walk in ]]>\mathbb{Z}^2$ we study those points which are visited an unusually large number of times, and provide a new proof of the Erdős-Taylor Conjecture describing the number of visits to the most visited point.     

产出时间序列的遍历性

主要研究产出时间序列的遍历性质,得出了市场经济条件下产出时间序列是马氏过程的结论,并讨论了它的遍历态;证明了市场经济发展的周期状形态.     

基于关系数据库的频繁项集挖掘算法研究

Apriori算法及其改进是目前应用最为广泛的频繁项集挖掘算法,但其在关系数据库中挖掘频繁项集时,产生大量候选项集,导致重复扫描数据库,从而导致其效率低下.本文在深入研究Apriori算法及其改进算法和关系数据库特征的基础上,提出了基于关系数据库的频繁项集挖掘算法,并详细描述了其实现和优化方法.本算法不产生候选项集,只需一次事务扫描,大幅提高算法执行效率,此外,本算法经过简单修改就能满足大部分的关联分析需求.在零售业中的应用实验证明:该算法在一定的条件下比经典的Apriori算法具有更高的效率.