基于大间距准则的不相关保局投影分析

Uncorrelated Locality Preserving Projections Analysis Based on Maximum Margin Criterion

局部保持投影(Locality preserving projections,LPP)算法只保持了目标在投影后的邻域局部信息,为了更好地刻画数据的流形结构,引入了类内和类间局部散度矩阵,给出了一种基于有效且稳定的大间距准则(Maximum margin criterion,MMC)的不相关保局投影分析方法,该方法在最大化散度矩阵迹差时,引入尺度因子α,对类内和类间局部散度矩阵进行加权,以便找到更适合分类的子空间并且可避免小样本问题;更重要的是,大间距准则下提取的判别特征集一般情况下是统计相关的,造成了特征信息的冗余,因此,通过增加一个不相关约束条件,利用推导出的公式提取不相关判别特征集,这样做,对正确识别更为有利.在Yale人脸库、PIE人脸库和MNIST手写数字库上的测试结果表明,本文方法有效且稳定,与LPP、LDA(Linear discriminant analysis)和LPMIP(Locality-preserved maximum information projection)方法等相比,具有更高的正确识别率。

Locality preserving projections(LPP) algorithm can only preserve nearest local quantity,so within-class and between-class local scatter matrices are introduced for characterizing the manifold structure better,and a method called uncorrelated locality preserving projection analysis based on effective and stable maximum margin criterion(MMC) is proposed.When maximizing the trace difference of scatter matrix,weight the within-class and between-class local scatter matrix through a regularized parameter so as to find the better classification subspace and avoid small sample problem.More importantly,the discriminant feature set based on the MMC is generally statistical correlated,which makes the feature information be redundant,so an uncorrelated constraint was added in the paper and the uncorrelated discriminant feature set is extracted by the derived formulas,which are more favorable for the correct recognition.Ultimately experiments on Yale,PIE face database and MNIST handwritten digit database show that the method in this paper is effective and stable and has a higher correct recognition rate compared with the LPP,LDA(Linear discriminant analysis) and LPMIP(Locality-preserved maximum information projection).