全局加局部的线性判别投影

Enhanced Linear Discriminant Projections with Global plus Local Information

摘要: 线性判别投影(Linear Discriminant Projection, LDP)是一种有监督的特征提取方法，在图像处理等邻域得到了很好的效果。然而LDP只考虑全局信息，忽略了局部邻近点中包含的信息。忽略局部信息的问题也出现在线性判别分析(Linear Discriminant Analysis, LDA)中。目前在LDA的研究中，针对这个问题已经有学者整理出了一个完整的全局结合局部的算法框架。由于LDP和LDA的目标函数结构相似，本文考虑在LDP的算法基础上，将LDA全局结合局部的算法框架沿用到LDP中，使LDP实现全局信息和局部信息的完整结合，得到新算法：增强组间线性判别投影(Enhanced Within-class Linear Discriminant Projection, EWLDP)、完全线性判别投影(Complete Global-local Linear Discriminant Projection, CGLDP)。最后本文利用鸢尾花数据集(Iris)，证实CGLDP、EWLDP算法的降维效果比LDP更优，并且CGLDP更完整地结合了局部信息，效果也比EWLDP更优。

Abstract: Linear Discriminant Projection (LDP) is a supervised feature extraction method, which makes good results in image processing and other areas. However, the LDP only considers global information, ignoring information contained in local neighboring points. The problem of ignoring local information also exists in Linear Discriminant Analysis (LDA). At present, in the research of LDA, some scholars have sorted out a complete algorithm framework combining global and local aspects to solve this problem. Since the structure of the objective function of LDP and LDA is similar, this paper considers to apply the algorithm framework of LDA’s global and local combination to LDP on the basis of LDP algorithm, so as to realize the complete combination of global and local information of LDP, and obtain the new algorithm: Enhanced Within-class Linear Discriminant Projection (EWLDP) and Complete Global-local Linear Discriminant Projection (CGLDP). Finally, this paper uses Iris data set to prove that the dimensionality reduction effect of CGLDP and EWLDP algorithm is better than LDP, and CGLDP integrates local information more completely, and the performance is also better than EWLDP.