基于特征子空间邻域的局部保持流形学习算法*

局部保持流形学习算法通过保持局部邻域特性来挖掘隐藏在高维数据中的内在流形结构。然而,对于缺乏足够训练样本的高维数据集,或者高维数据集存在非线性结构和高维数据特征中存在冗余、干扰特征,使得在原特征空间中利用欧式距离定义的邻域关系并不能真实反映数据的内在流形结构,从而影响算法的性能。提出利用正约束寻找特征子空间的方法,使得在此子空间中更多的同类样本紧聚,并进一步在该子空间中构建邻域关系来挖掘高维数据的内在流形,形成基于特征子空间邻域特性的局部保持流形学习算法(NFS-LPP和NFS-NPE)。它们在一定程度上克服了高维小样本数据集难以正确挖掘内在流形结构的问题,在Yale和ORL人脸库上的分类和聚类实验验证了其有效性。

Locality preserving manifold learning algorithm based on neighborhood in feature space

Locality preserving manifold learning algorithms always discover intrinsic manifold in high-dimensional data by preserving locality neighborhood structures.However,for high-dimensional data with non-enough training samples,or with nonlinear structure and redundant or interrupted features,it is difficult to directly estimate real neighbor relation defined by Euclidean distance in original feature space.This paper proposed a novel method to find a feature subspace best suited to representing neighborhood relation using positive constraints.In this subspace more inner-class samples come together.Further,constructed neighborhood graph in this subspace to discover intrinsic manifold in high-dimensional data,which caused novel locality preserving manifold learning algorithms called NFS-LPP and NFS-NPE.Experimental results on Yale and ORL face database verify their effectiveness.