完备的双子空间边界近邻鉴别分析  

A complete dual subspace marginal neighborhood discriminant analysis algorithm

作　　者：林玉娥[1] 李敬兆[1] 梁兴柱[1] 林玉荣[2] 

机构地区：[1]安徽理工大学计算机科学与工程学院,安徽淮南232001 [2]哈尔滨工业大学航天学院,黑龙江哈尔滨150001

出　　处：《计算机工程与科学》2014年第7期1357-1362,共6页Computer Engineering & Science

基　　金：国家自然科学基金资助项目(61170060);安徽省自然科学基金资助项目(1208085QF123;11040606M135);安徽省高等学校自然科学基金资助项目(KJ2012Z084;KJ2011A083);安徽理工大学中青年学术骨干资助项目

摘　　要：针对边界Fisher鉴别分析算法不能够有效解决小样本问题,提出了一种完备的双子空间边界近邻鉴别分析算法。该算法通过理论分析将MFA的目标函数分解成两部分,对此目标函数的求解,首先要对高维样本进行PCA降维至一个低维子空间,而这一过程并不损失任何有效的鉴别信息,对此通过定理1和定理2进行了证明;然后再分别求出类内边界近邻互补子空间的两投影矩阵。最后人脸库上的实验结果表明了所提方法的有效性。Aiming at the shortcomings that the marginal Fisher discriminant analysis algorithm can not effectively solve the small sample size problem, a complete dual subspace marginal neighborhood discriminant analysis algorithm is proposed. According to the theoretical analysis, the proposed algorithm breaks down the criterion function of the Fisher discriminant analysis into two parts. To solve the crite- rion function, the algorithm firstly uses PCA to project high-dimensional samples into a low-dimensional subspace. In the low-dimensional subspace, the objective function does not lose any effective discriminant information, which is proved by theorem 1 and theorem 2. Secondly, projection matrix from the complementary subspace of within-class marginal neighborhood is calculated. Finally, the experimental results on face database demonstrate the effectiveness of the proposed algorithm.

关 键 词：边界Fisher鉴别分析 小样本问题 双子空间 目标函数 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]