一种反对称变换下的有监督局部保持投影算法

摘要

Classification of nonlinear high-dimensional data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size condition.To address this problem,a novel supervised locality preserving projection(SLPP) learning algorithm based on the anti-symmetric transformation is developed.Firstly,according to the problem that SLPP has the over-learning problem and does not preserve the diversity information of data which is also useful for data recognition,a concise transformation of feature extraction criterion is raised by minimizing the local scatter,which efficiently preserves the local structure and simultaneously maximizes the diversity scatter.Furthurmore,a special equivalent form of direct linear discriminant analysis (D-LDA) is obtained.Secondly,anti-symmetric matrix is a kind of specific matrix in matrix theory,and skew symmetric transformation is the basic linear transformation in Euclidean space.By this special equivalent form of D LDA and anti-symmetric transformation,two solution spaces derived from the local scatter matrix and its corresponding anti-symmetric subspace are respectively utilized to obtain the efficient discriminatory information of the samples.Therefore,the shortcoming of nonlinear small sample sizes problem in the traditional subspace learning algorithms is overcome.Experimental results on the NUST603 and ORL face databases demonstrate the effectiveness of the proposed method.%提出一种基于反对称变换下的有监督局部保持投影方法.首先针对监督局部保持投影(Supervised locality preserving projection,SLPP)存在过学习和不能较好地保持图像空间的差异信息等问题,通过最小化局部离散度和最大化差异离散度准则提取投影方向,寻找到SLPP与直接线性鉴别分析(Direct linear discriminant analysis,D-LDA)的一种特殊等价形式.其次,反对称矩阵是一种特殊矩阵,与其相对应的反对称变换是欧氏空间中一类重要的线性变换,本文进一步对特殊等价形式的D-LDA转换矩阵进行反对称变换,得到其对应的反对称矩阵,通过对线性空间下两种矩阵的分别求解,从而得到样本完备的鉴别信息.本文所提方法有效解决了线性空间下小样本问题的特征抽取问题,在NUST603和ORL人脸库上的实验结果验证了该方法的有效性.