School of Computer Science and Information, AnHui Polytechnic University, WuHu, AnHui 241000, China.
School of Computer Science and Information, AnHui Polytechnic University, WuHu, AnHui 241000, China.
Neural Netw. 2018 Jan;97:127-136. doi: 10.1016/j.neunet.2017.09.014. Epub 2017 Oct 16.
Discriminant locality preserving projections (DLPP), which has shown good performances in pattern recognition, is a feature extraction algorithm based on manifold learning. However, DLPP suffers from the well-known small sample size (SSS) problem, where the number of samples is less than the dimension of samples. In this paper, we propose a novel matrix exponential based discriminant locality preserving projections (MEDLPP). The proposed MEDLPP method can address the SSS problem elegantly since the matrix exponential of a symmetric matrix is always positive definite. Nevertheless, the computational complexity of MEDLPP is high since it needs to solve a large matrix exponential eigenproblem. Then, in this paper, we also present an efficient algorithm for solving MEDLPP. Besides, the main idea for solving MEDLPP efficiently is also generalized to other matrix exponential based methods. The experimental results on some data sets demonstrate the proposed algorithm outperforms many state-of-the-art discriminant analysis methods.
判别局部保持投影（DLPP）在模式识别中表现出色，它是一种基于流形学习的特征提取算法。然而，DLPP 存在着众所周知的小样本量（SSS）问题，即样本数量少于样本的维度。在本文中，我们提出了一种新的基于矩阵指数的判别局部保持投影（MEDLPP）。由于对称矩阵的矩阵指数总是正定的，因此所提出的 MEDLPP 方法可以优雅地解决 SSS 问题。然而，MEDLPP 的计算复杂度很高，因为它需要求解一个大型矩阵指数特征值问题。然后，在本文中，我们还提出了一种有效的求解 MEDLPP 的算法。此外，求解 MEDLPP 效率高的主要思想也被推广到其他基于矩阵指数的方法。在一些数据集上的实验结果表明，所提出的算法优于许多最先进的判别分析方法。
