全最小一乘准则下的LGA新算法  

New linear grouping algorithm based on total least absolute deviation criteria

作　　者：曹慧荣[1] 方杰[1] 

机构地区：[1]廊坊师范学院数学与信息科学学院,河北廊坊065000

出　　处：《计算机应用》2010年第3期810-812,共3页journal of Computer Applications

基　　金：河北省教育厅自然科学研究项目(Z2009138)

摘　　要：为克服传统提取数据集中线性结构的LGA对噪声数据比较敏感的缺陷,提出了两种基于稳健的全最小一乘准则下的LGA新算法。首先证明了全最小一乘准则下数据集最优划分的存在性,并据此给出一种有限步终止算法。其次为提高计算速度,根据k-means算法、全最小一乘准则和重抽样方法给出另一种快速收敛算法。通过与传统的LGA和基于Trimmedk-means思想的稳健LGA的比较,仿真结果表明提出的算法具有较好的稳健性,可以在离群数据较多的情形下,同时找出数据集合中的所有强线性结构。To overcome the drawback that the traditional Linear Grouping Algorithm（LGA）,when extracting linear structures,is sensitive to outliers in datasets,a new finite step according to existence of optimal linear grouping in data set and a new algorithm based on k-means clustering,total least absolute deviation and resampling were proposed,which detected several different linear relations at once to minimize the total orthogonal distances from n given points to its nearest hyperplanes.Finally,by comparison with linear grouping algorithm and robust linear grouping algorithm based on impartial trimmed k-means,the proposed algorithms are more robust and can detect all strong linear structures in datasets including a lot of outliers.

关 键 词：LGA 全最小一乘 稳健性 聚类分析 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]