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.Comment: arXiv admin note: text overlap with arXiv:1901.0137