Abstract: Neighborhood Preserving Embedding (NPE) is still an unsupervised method in nature, and it does not take advantage of the existing classification information to improve the classification efficiency. Therefore, two supervised manifold learning methods named Orthogonal Marginal Neighborhood Preserving Embedding (OMNPE) and Uncorrelated Marginal Neighborhood Preserving Embedding (UMNPE) were proposed. Both methods firstly constructed within-class graph and between-class graph and defined within-class reconstructive error and between-class reconstructive error. Then, OMNPE and UMNPE sought to find a projection that simultaneously minimized the within-class reconstructive error and maximized the between-class reconstructive error, under the orthogonal and uncorrelated constraint conditions, respectively. The training samples and testing samples were projected onto low-dimensional subspace respectively. Finally, the nearest neighbor classifier was used for classification. Extensive experiments in ORL and Yale face databases illustrate that the proposed algorithms outperform those of subspace face recognition algorithms with average recognition rate by 0.5%~3%, such as Linear Discriminant Analysis (LDA), Marginal Fisher Analysis (MFA), which proves the effectiveness of the proposed algorithms.

Key words: dimensionality reduction, manifold learning, face recognition, Neighborhood Preserving Embedding (NPE), orthogonal, uncorrelated

摘要： 邻域保持嵌入(NPE)算法本质上仍是一种无监督方法，并没有有效利用已有的类别信息提高分类效率。为此提出两种有监督流形学习方法：正交边界邻域保持嵌入(OMNPE)和不相关边界邻域保持嵌入(UMNPE)。首先构造类内和类间邻接图，并定义类内和类间重构误差；然后分别在正交和不相关约束条件下寻找最小化类内重构误差同时最大化类间重构误差的投影向量；将训练样本和测试样本分别投影到低维子空间中，再利用最近邻分类器进行分类识别。在ORL和Yale人脸库上的实验结果表明，与线性判别分析(LDA)、边界Fisher分析(MFA)等子空间人脸识别算法相比，所提算法的平均识别率提高了0.5%~3%，验证了算法的有效性。

关键词: 降维, 流形学习, 人脸识别, 邻域保持嵌入, 正交, 不相关