基于Hash函数取样的线性时间聚类方法LCHS

作为数据挖掘中的经典算法，k-中心点算法存在效率低、对大数据集适应性差等严重不足．该文针对这一不足，提出并实现Hash分层模型LCHS（Linear Clustering Based Hash Sampling），主要贡献包括：（1）将m雏超立方体按等概率空间进行分桶，使得每层（即Hash桶）的数据个数相近，以较小的计算代价获得分层抽样的效果；（2）新算法保证了样本具有对总体数据的充分的统计代表性；（3）从理论上证明了新算法复杂度为O（N）；（4）对比实验表明新算法在数据集的个数接近10000时，效率比传统算法提高2个数量级，数据集的个数接近8000时，聚类质量比CLARA算法提高55％．     

Approximate K-Median of Location Streams with Redundancy and Inconsistency

Data streams produced by positioning systems such as Global Positioning System (GPS) or RFID readers can be considered as location streams[12]. Location streams are usually generated in a distributed fashion by a large scale distributed system covering a wide range of areas. Computing on distributed location streams is both practically useful and theoretically challenging. The results of computation could be used to schedule the traffic in a metropolis to avoid traffic jam, dispatch taxis to serve the passengers more quickly and display the current position of goods in supply chain management, etc. Since location streams are usually generated with very high rate in uncertain ways over hostile environments, the collected updates of location are probably redundant and inconsistent in a wide positioning system. To process distributed location streams with redundancy and inconsistency, this paper proposes a novel method based on min-wise hash. With this method, redundant updates of distributed location streams can be effiectively filtered out, while the true location could be derived from inconsistent ones. Consequently, globally uniform samples can be obtained. Based on the uniform samples, an algorithm for computing the approximate k-median of huge number of moving objects is presented in this paper. Furthermore, it is demonstrated that sketch-based methods are not necessarily effiective in processing location streams with redundancy and inconsistency. In addition to theoretical analysis, some extensive experiments are conducted to validate the efficiency and effiectiveness of the proposed approach.     

求解k中间点问题的新局部搜索算法

为有效求解大规模k中间点问题,利用适应度距离相关性方法分析,发现该问题局部最优解的适应度与其到全局最优解的距离无太大关系,且多个局部最优解求交所得子集以极大概率包含全局最优解中的元素,进而提出一种基于求交操作的k中间点问题局部搜索算法。实验结果表明该算法在求解质量上与目前已知算法相比有较大改进。     

k-Median近似计算复杂度与局部搜索近似算法分析

k-Median问题的近似算法研究一直是计算机科学工作者关注的焦点,现有研究结果大多是关于欧式空间和Metric空间的,一般距离空间k-Median的结果多年来一直未见.考虑一般距离空间k-Median问题,设d_max/d_min表示k-Median实例中与客户点邻接的最长边长比最短边长的最大者.首先证明d_max/d_min≤ω+ε的k-Median问题不存在近似度小于1+ω-1/e的多项式时间近似算法,除非,由此推出Metric k-Median问题不可近似到1+2/e,除非NP(∈)DTME(N^{O(log logn)}).然后给出k-Median问题的一个局部搜索算法,分析表明,若有d_max/d_min≤ω,则算法的近似度为1+ω-1/2.该结果亦适用于Metric k-Median,ω≤5时,局部搜索算法求解Metric k-Median的近似度为3,好于现有结果3+2/P.通过计算机实验,进一步研究了k-Median局部搜索求解算法的实际计算效果和该算法的改进方法.     

贪心算法求解k-median问题

文章讨论了用贪心算法解k-m edian问题以及其试验结果。首先提出了一个解k-m edian问题的简单贪心算法,然后对求解质量和求解的近似性能比进行了探讨。主要讨论了公制空间和非公制空间初始解的产生,用贪心算法解k-m edian问题以及全局最优解的计算。试验结果表明:贪心算法解公制空间的k-m edian问题效果要好于解非公制空间的k-m edian问题;用贪心算法解公制空间和非公制空间k-m edian问题都能得到较好的结果。     

近似k-median分类属性数据聚类

数据挖掘中解决分类属性数据聚类的算法有很多种,但大多数基于划分的方法得到的聚类中心一般不是数据集中的实际数据对象,缺乏实际的物理意义,有时会导致某一聚类为空。该文研究了近似k-median的求解算法,用数据的近似中值来代替模式进行聚类,提出了分类属性数据的近似k-median聚类算法,克服了一般基于划分的可分类属性数据聚类中所遇到的问题,仿真实验证明该算法有效。     

A K-Median Facility Location Agent for Low-Cost Service Selection in Digital Community Network

With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collaborative mechanism for the purpose of service selection. The participation usually brings unnecessary burdens for users, such as giving opinions, storing service information. Extra communication overhead hinders the performance of the network. Thus, the community administrators are facing a problem of how to obtain an overall service selection result for the whole community readily and effectively. To address this problem, we present a k-median facility location agent model. The model analyzes the procedure of service selection through five entities and six types of messages. Two algorithms are elaborated in pursuit of a global optimization concerning connection costs between users and facilities where services are deployed. To evaluate our model, we conduct extensive simulations and present a detailed analysis of the simulation results.