Recently, an effective improvement of linear discriminant analysis (LDA) called L2-norm linear discriminant analysis via the Bhattacharyya error bound estimation (L2BLDA) was proposed in its adaptability and nonsingularity. However, L2BLDA assumes all samples from the same class are independently identically distributed (i.i.d.). In real world, this assumption sometimes fails. To solve this problem, in this paper, reverse nearest neighbor (RNN) technique is imbedded into L2BLDA and a novel linear discriminant analysis named RNNL2BLDA is proposed. Rather than using classes to construct within-class and between-class scatters, RNNL2BLDA divides each class into subclasses by using RNN technique, and then defines the scatter matrices on these classes that may contain several subclasses. This makes RNNL2BLDA get rid of the i.i.d.assumption in L2BLDA and applicable to multimodal data, which have mixture of Gaussian distributions. In addition, by setting a threshold in RNN, RNNL2BLDA achieves robustness. RNNL2BLDA can be solved through a simple standard generalized eigenvalue problem. Experimental results on an artificial data set, some benchmark data sets as well as two human face databases demonstrate the effectiveness of the proposed method.

最近，有人提出了通过Bhattacharyya误差界限估计（L2BLDA）来有效改进称为L2-范数线性判别分析的线性判别分析（LDA）的适应性和非奇异性。但是，L2BLDA假定来自同一类别的所有样本都独立地相同地分布（iid）。在现实世界中，这种假设有时会失败。为了解决这个问题，本文将反向最近邻（RNN）技术嵌入到L2BLDA中，并提出了一种新颖的线性判别分析方法，称为RNNL2BLDA。RNNL2BLDA没有使用类来构造类内和类间散布，而是使用RNN技术将每个类划分为子类，然后在这些类中定义散布矩阵，这些散布矩阵可能包含多个子类。这使得RNNL2BLDA摆脱了iid L2BLDA中的假设，适用于具有高斯分布混合的多峰数据。此外，通过在RNN中设置阈值，RNNL2BLDA可以实现鲁棒性。RNNL2BLDA可以通过一个简单的标准广义特征值问题来解决。在人工数据集，一些基准数据集以及两个人脸数据库上的实验结果证明了该方法的有效性。