直接线性图嵌入算法及其在人脸识别中的应用

图嵌入算法使用无向有权图来描述数据集的流形结构，目前许多流形学习算法都可统一到这个框架下。线性图嵌入算法(LGE)在高维小样本应用中往往会遇到的奇异值问题，因此需把数据集预先投影到PCA子空间，往往会丢失了一些有用的信息。本文提出了一种直接的线性图嵌入算法(DLGE)，可直接从原始数据集中提取特征。此外DLGE算法相对于基于迭代的正交化算法，在最小二乘意义下对截断的征向量进行正交化处理，计算简便有效。在多个人脸数据库库上的仿真结果表明，相对于传统算法，DLGE算法具有更强的人脸表征能力，更好的分类性能，且更加鲁棒。

A Direct LGE Algorithm and Its Application to Face Recognition

The algorithms of Graph Embedding model the manifold of data set by an undirected weighted graph. Some manifold learning algorithms can be unified by this framework according to the respective weighted matrix. For the small sample size problem, Linearization of Graph Embedding (LGE) needs to project the data to the PCA subspace. In this paper, a Direct LGE (DLGE) algorithm is proposed which can directly extract features from the data set. Moreover, DLGE employs the least-squares orthogonalization for the preserving feature vectors. The simulation results on several face databases show that DLGE has better ability for face representation, and also demonstrate the effectiveness and robustness of our proposed algorithm.