Huge amount of applications in various fields, such as gene expression analysis or computer vision, undergo data sets with high-dimensional low-sample-size (HDLSS), which has putted forward great challenges for standard statistical and modern machine learning methods. In this paper, we propose a novel classification criterion on HDLSS, tolerance similarity, which emphasizes the maximization of within-class variance on the premise of class separability. According to this criterion, a novel linear binary classifier is designed, denoted by No-separated Data Maximum Dispersion classifier (NPDMD). The objective of NPDMD is to find a projecting direction w in which all of training samples scatter in as large an interval as possible. NPDMD has several characteristics compared to the state-of-the-art classification methods. First, it works well on HDLSS. Second, it combines the sample statistical information and local structural information (supporting vectors) into the objective function to find the solution of projecting direction in the whole feature spaces. Third, it solves the inverse of high dimensional matrix in low dimensional space. Fourth, it is relatively simple to be implemented based on Quadratic Programming. Fifth, it is robust to the model specification for various real applications. The theoretical properties of NPDMD are deduced. We conduct a series of evaluations on one simulated and six real-world benchmark data sets, including face classification and mRNA classification. NPDMD outperforms those widely used approaches in most cases, or at least obtains comparable results.
翻译:基因表达分析或计算机视觉等不同领域的大量应用,如基因表达分析或计算机视觉,经过高维低抽样规模(HDLSS)的数据集,这给标准统计和现代机器学习方法带来了巨大的挑战。在本文件中,我们提出了关于HDLSS的新分类标准,即容忍性相似性,强调在等级分离前提下尽可能扩大类内差异。根据这一标准,设计了一个新型线性双轨分类器,由无分离数据最大分散分类器(NPDMD)表示。NDDMD的目标是找到一个预测方向,使所有培训样品尽可能在大间隔内分布。NDDMD具有与最新分类方法相比的若干特性。首先,HDLSS工作效果良好。第二,将抽样统计信息和地方结构信息(支持矢量)结合到客观功能中,以找到在整个特征空间预测方向的解决方案。第三,NDDMDM的目标是在低维度空间找到一个面面面最小矩阵,在最短的矩阵中,在真实的基数矩阵应用中,在真实的模型中,在最精确的模型中进行。