Guo Yan-Ru, Bai Yan-Qin, Li Chun-Na, Bai Lan, Shao Yuan-Hai
Department of Mathematics, Shanghai University, Shanghai, 200444 People's Republic of China.
Management School, Hainan University, Haikou, 570228 People's Republic of China.
Appl Intell (Dordr). 2022;52(8):8793-8809. doi: 10.1007/s10489-021-02843-z. Epub 2021 Nov 5.
The recently proposed L2-norm linear discriminant analysis criterion based on Bhattacharyya error bound estimation (L2BLDA) was an effective improvement over linear discriminant analysis (LDA) and was used to handle vector input samples. When faced with two-dimensional (2D) inputs, such as images, converting two-dimensional data to vectors, regardless of the inherent structure of the image, may result in some loss of useful information. In this paper, we propose a novel two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance, which is measured by the weighted pairwise distances of class means and minimizes the matrix-based within-class distance. The criterion of 2DBLDA is equivalent to optimizing the upper bound of the Bhattacharyya error. The weighting constant between the between-class and within-class terms is determined by the involved data that make the proposed 2DBLDA adaptive. The construction of 2DBLDA avoids the small sample size (SSS) problem, is robust, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of 2DBLDA.
最近提出的基于巴氏误差界估计的L2范数线性判别分析准则（L2BLDA）是对线性判别分析（LDA）的有效改进，用于处理向量输入样本。当面对二维（2D）输入（如图像）时，将二维数据转换为向量，而不考虑图像的固有结构，可能会导致一些有用信息的丢失。在本文中，我们提出了一种新颖的二维巴氏界线性判别分析（2DBLDA）。2DBLDA最大化基于矩阵的类间距离，该距离由类均值的加权成对距离测量，并最小化基于矩阵的类内距离。2DBLDA的准则等同于优化巴氏误差的上界。类间项和类内项之间的加权常数由所涉及的数据确定，这使得所提出的2DBLDA具有自适应性。2DBLDA的构建避免了小样本量（SSS）问题，具有鲁棒性，并且可以通过一个简单的标准特征值分解问题来解决。在图像识别和人脸图像重建方面的实验结果证明了2DBLDA的有效性。
