一种基于局部稀疏线性嵌入的降维方法及其应用  

A dimension-reduction method based on locally and sparsely linear embedding and its application

作　　者：冷亦琴[1] 张莉[1] 杨季文[1] 

机构地区：[1]苏州大学计算机科学与技术学院,苏州215006

出　　处：《南京大学学报（自然科学版）》2013年第4期403-410,共8页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(61033013);江苏省自然科学基金(BK2011284;BK201222725);江苏省青蓝工程;苏州大学国家自然科学基金预研(SDY2011B09)

摘　　要：局部线性嵌入(LLE)是一种非线性的降维方法.LLE方法采用的近邻邻域大小是全局一致的,而且如果近邻个数过大则可能会把非同一个线性空间的点选作为近邻点.本文对LLE方法进行了改进,提出了一种局部稀疏线性嵌入(LSLE)降维法.在LSLE方法中,用解0范数问题的正交匹配追踪(OMP)方法来解线性表示问题.每个样本点都可以用K个近邻点中最能表示该数据的几个样本点稀疏表示.实验表明,在有监督学习和无监督学习应用上,LSLE方法是可行的.Manifold learning has been widely researched in machine learning,computer vision and pattern recognition.As a classical method of manifold learning,locally linear embedding（LLE）attracts a lot of attention.The LLE method has merits with easy implemention and small computional complexity.The basic idea behind the LLE method is that each data point and its neighbors lie on or be close to a locally linear patch of the manifold if there is sufficient data.Then the local geometry of these patches is described by using linear coefficients which can reconstruct each data point from its neighbors.However,the neighbor number is globally fixed parameter in the LLE method.In addition,a larger neighbor number would result in selecting points from another linear space as neighbors.In recent years,compressed sensing has attracted substantial attention in signal processing,machine learning,computer vision,etc.There is the similar linear representation problem in compressed sensing,or sparse signal reconstruction.So far,a lots of methods for sparse signal reconstruction have been proposed.Generally,three main techniques or their combinations are available to obtain a sparse representation,including zero-trapped loss functions,sparse regularization and matching pursuit.Here,we focus on matching pursuit methods,which are greedy to solve the 0-norm problem.In fact,the 0-norm regularization is the desirable one to obtain sparseness,but the 0-norm regularization is so discontinuous that it is very difficult to optimize the objective function containing it.Therefore,the greedy matching pursuit methods are the best ones for finding the 0-norm problem.This paper proposes a locally and sparsely linear embedding（LSLE）,which improves the LLE method.In the LSLE method,we introduce orthogonal matching pursuit（OMP）method which solves the 0-norm problem of linear representation.Each sample is well sparsely represented with its closed neighbors.Experimental results on some real-world data sets including the Heart_c,Wine,and MNIST dat

关 键 词：局部线性嵌入 正交匹配追踪 稀疏表示 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]