二元分类问题的最优分类线性降维

Optimal Classification Linear Dimension Reduction in Two-hypothesis Classification Problem

军事领域经常会遇到高维二元分类问题,过高的数据维度大大提高了数据获取的难度和分类计算难度。文中,针对高维高斯模型的二元分类问题,研究如何在降低分类问题维度的情况下保留最多的差异信息,使降维后进行分类的平均误差概率最小。使用切诺夫距离作为衡量两个高维高斯模型差异的度量,文中给出了高斯分类问题的最优分类线性降维方法,并证明其最优性。通过该方法对两个高维高斯模型线性降维,可在保留两个分布之间最多差异信息的基础上,降低其存储和计算资源需求。

There are many high-dimensional two-hypothesis classification problems in military fields. Too large data dimensions make it highly complex to collect and calculate data in classification problem. For two-hypothesis classification of high-dimensional Gaussian distributions, we study how to do dimension reduction with maximal difference information and, at the same time, minimum average error probability. Using Chernoff Information as metric of difference, this paper proposes an optimal classification linear dimension reduction method and proves its optimization. With this method, we can keep maximum difference information of two distributions and reduce its storage and calculation requirements after dimension reduction of two high-dimensional Gaussian distributions.