基于LLE方法的本征维数估计

Intrinsinc Dimension Estimation Based on LLE

基于局部线性嵌入(LLE)方法所确定的数据集的拓扑结构和高维数据空间的距离特性,提出了自逼近度和可分离度的概念.然后利用二者构建了一种新的本征维数估计方法.这种估计方法揭示了 LLE 降维过程中涉及的数据维数与邻域大小的选取之间的内在关联.最后,通过与主成分分析(PCA)进行实例对比,说明这种方法更加合理,更能反映数据集的本征特性.

A new algorithm to estimate the intrinsic dimension of data sets is proposed. The method is constructed by approximation and separation, which comes from the topological structure of data set and the distance characteristics of high dimensional space . Thereinto , the topological structure is intruduced by LLE. It discloses the relation between dimension and neighborhood then improves LLE. Experiments show that this method is reasonable and reliable than PCA.