正交流形保持投影方法

来源期刊：中南大学学报(自然科学版)2011年第3期

论文作者：张伟 夏利民 罗大庸

文章页码：688 - 692

关键词：保局投影；流形保持投影；正交流形保持投影；格拉姆-施密特正交变换

Key words：locality preserving projections; manifold preserving projections; orthogonal manifold preserving projections; Gram-Schmidt orthogonalization

摘    要：为克服保局投影的局限，在保局投影的基础上，提出正交流形保持投影方法。在保局投影目标函数中引入数据的非近邻信息，有效地保持数据的局部流形结构和全局流形结构；采用格拉姆-施密特正交化过程获取正交投影基向量，解决保局投影非正交问题。采用ORL和Yale人脸数据库中图像进行实验，实验结果验证了该方法的有效性。

Abstract: In order to overcome the shortcomings of locality preserving projections (LPP), a new feature extraction methods-orthogonal manifold preserving projections (OMPP) was proposed. The non-locality information of data is incorporates to the objective function, in contrast to LPP, which preserves the local and global structure of the data manifold. Gram-Schmidt orthogonalization was used to determine basic orthogonal vectors，which solves the non-orthogonal problem of LPP. Experiments on ORL and Yale face databases were performed to test and evaluate the proposed algorithm, and the results show that the proposed method is effective.