Population-Guided Large Margin Classifier for High-Dimension Low -Sample-Size Problems

TL;DR

This paper introduces PGLMC, a new linear classifier designed for high-dimensional, low-sample-size data, which is robust, simple to implement, and effective across various applications.

Contribution

The paper proposes PGLMC, a population-guided large margin classifier that addresses HDLSS challenges and demonstrates theoretical properties and superior empirical performance.

Findings

PGLMC outperforms existing methods on multiple datasets.

It is robust to model misspecification and class imbalance.

The model is simple to implement using quadratic programming.

Abstract

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.