一种基于配对矩阵改进的LE分类算法

An improved LE classification algorithm based on pairing matrix

拉普拉斯特征映射(LE)算法基于流形学习思想将原始数据映射到低维空间,然而其无法解决样本外点学习问题,更没有使用类别信息。针对这些实际应用问题提出了一种新的基于配对矩阵的拉普拉斯特征映射(PM-LE)算法。PM-LE的目标是使得高维空间中的"相似点"投影到本征低维空间后为近邻点,同时该算法引入类别信息帮助构建近邻图,并且利用最大化相似矩阵及其配对矩阵内积的算法来重新计算权值矩阵,从而更适合应用于分类问题。应用于人脸识别的实验结果证明,PM-LE算法能很好地完成实际的降维和分类任务。

Laplacian Eigenmaps algorithm is a low- dimensional space set from the original data based on manifold learning theory. However,this algorithm is poor out- of- sample learning ability,and does not identify the class information. Aiming at the actual application problem,it proposes a new Laplacian Eigenmaps algorithm（PM- LE） based on pairing matrix. It sets LE＇s goal to make close points in high dimension space stay close,and projects these points to the intrinsic low dimensional space,defines PM- LE maps ＂ similar points＂ in the original space to neighbor points in the target space. This algorithm introduces class information to help build a nearest neighbor graph,recalculates the weight matrix to maximize the inner product of a given similarity matrix and corresponding pairing matrix. The experimental results on face recognition indicate that the PM- LE algorithm can effectively reduce the dimensionality and accomplish classification task.