  Various applications in different fields, such as gene expression analysis or
computer vision, suffer from data sets with high-dimensional low-sample-size
(HDLSS), which has posed significant challenges for standard statistical and
modern machine learning methods. In this paper, we propose a novel linear
binary classifier, denoted by population-guided large margin classifier
(PGLMC), which is applicable to any sorts of data, including HDLSS. PGLMC is
conceived with a projecting direction w given by the comprehensive
consideration of local structural information of the hyperplane and the
statistics of the training samples. Our proposed model has several advantages
compared to those widely used approaches. First, it is not sensitive to the
intercept term b. Second, it operates well with imbalanced data. Third, it is
relatively simple to be implemented based on Quadratic Programming. Fourth, it
is robust to the model specification for various real applications. The
theoretical properties of PGLMC are proven. We conduct a series of evaluations
on two simulated and six real-world benchmark data sets, including DNA
classification, digit recognition, medical image analysis, and face
recognition. PGLMC outperforms the state-of-the-art classification methods in
most cases, or at least obtains comparable results.
