为了在保持数据局部几何结构不变的同时使数据分类边界最大化,提出了一种用于分类的线性局部切空间判别分析算法.该算法是改进的流形学习算法的监督版,样本的局部切空间排列矩阵确保样本低维嵌入的局部几何结构不变;基于最大边界准则的数据散度矩阵确保数据分类的类内散度最小和类间散度最大;对上述2个矩阵和进行特征分解,获得平衡的投影向量基,使样本投影后的子空间被优化.对Yale,UMIST与MIT这3个人脸数据库的实验结果表明,与现有多种经典分类方法相比,提出的算法在降维的同时提取了用于人脸识别的更有效特征,识别性能较好,具有较高的判别分析能力.
A novel algorithm, called linear local tangent space discriminant analysis (LLTSDA), is proposed for classification, which is motivated by the desire to preserve the local geometry structure of data and to maximize the classification margin of data. The proposed algorithm is a supervised and modified manifold learning algorithm. The matrix of local tangent space alignment preserves the local geometry structure of data in low-dimensional embedded space; while the scatter matrix can ensure the within-class scatter minimization and the between-class scatter maximization; and a trade-off projected vector base can be taken by solving the generalized eigenvalue problem to the summation of above both matrices. Compared with classical classification methods, the experimental results from Yale, UMIST (University of Manchester Institute of Science and Technology) and MIT face databas- es show that LLTSDA algorithm can extract the more efficient features for face recognition while the dimensionality is reduced, and obtains much higher recognition accuracies and stronger classification power,