摘要
提出了一种边界近邻零空间鉴别分析算法。算法首先定义了新的目标函数,通过对该目标函数的理论分析与证明指出首先用PCA将高维样本降维至一个低维子空间,而在此低维子空间该目标函数并不损失任何有效的鉴别信息;算法不但能有效地解决本问题,而且仅需通过3次特征值分解就可求出具有正交性的投影矩阵,从而有效地提高了算法的识别性能。最后也给出了该算法基于核映射的非线性拓展。人脸库上的实验结果证实了所提方法的有效性。
A marginal neighborhood nullspace discriminant analysis was proposed. The proposed method firstly defines the obiective function, and then gives the theory analysis and proof of the objective function. Therefore, this paper pointed out that the algorithm must firstly projects high-dimensional samples into low-dimensional subspace by using PCA algo- rithm as the first step. In the low-dimensional subspace, the objective function does not lose any effective discriminant information. This algorithm can effectively not only resolve the small sample size problem but also work out the orthog- onality projection matrix only by the three eigenvalue decomposition. Finally, the nonlinear marginal neighborhood nullspace discriminant analysis based on kernel mapping was given. Experimental results on face database demonstrate the effectiveness of the proposed method.
出处
《计算机科学》
CSCD
北大核心
2013年第3期291-294,共4页
Computer Science
基金
国家自然科学基金(60975009
61170060)
安徽省自然科学基金(1208085QF123
11040606M135)
安徽省高等学校自然科学基金(KJ2012Z084
KJ2011A083)资助
关键词
边界近邻
零空间
目标函数
小样本问题
特征值分解
Marginal neighborhood, Nullspace, Objective function, Small sample size problem, Eigenvalue decomposition
