基于流形弯曲度的有序自适应邻域选择算法  

An Orderly Adaptive Neighborhood Selection Algorithm Based on Manifold Curvature

作　　者：李德玉[1,2] 高翠珍[1] 翟岩慧[1] 

机构地区：[1]山西大学计算机与信息技术学院,山西太原030006 [2]山西大学计算智能与中文信息处理教育部重点实验室,山西太原030006

出　　处：《山西大学学报（自然科学版）》2012年第2期219-223,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(60970014;61175067;60875040);教育部高等学校博士点基金(200801080006);山西省自然科学基金(2010011021-1);山西省科技攻关项目(20110321027-02)

摘　　要：针对传统邻域选择方法不能根据流形样本密度和弯曲度合理选择邻域的缺点,提出了一种有序自适应的邻域选择算法.该算法从流形上曲率最小的点开始,以宽度优先的次序不断地处理每个点.对搜索到的数据点,基于流形结构的局部线性特性,利用已有的邻域信息估算其局部切空间,然后通过其邻域边在切空间的投影自适应地选择合适的邻域.实验结果表明:该算法应用于Isomap后,对不同结构的数据集嵌入结果更准确.An orderly adaptive neighborhood selection algorithm is introduced because the traditional neighborhood selection algorithm has a defect that can not select neighbors adaptively based on the sample density and curvature.In this algorithm,data points start with the smallest curvature point in the manifold,and breadth-first searching algorithm was used to expand manifold data.For each point,we estimate the local tangent space based on the local linearity of manifold structure with existing neighborhood and then choose the right neighborhood adaptively through mapping of the neighborhood edge in the tangent space.This method is applied to Isomap,and experimental results validate the accurate of the embedding results for different data sets.

关 键 词：流形学习 邻域选择 切空间 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]