Nonparametric discriminant analysis with network structures in predictor

Abstract

ABSTRACT Multiclassification, known as classification for multi-label responses, has been an important problem in supervised learning and has attracted our attention. Discriminant analysis (DA) is a popular method to deal with multiclassification. With the increasing availability of complex data, it becomes more challenging to analyse them. One of the important features in complex data is the network structure, which is ubiquitous in high-dimensional data because of strong or weak correlations among variables. In addition, in the framework of DA, an assumption of normal distributions is imposed on the predictors, but it is usually invalid in applications. To relax the normality assumption, we propose a nonparametric discriminant function to address multiclassification. In addition, to incorporate the network structure and improve the accuracy of classification, we develop three different network-based surrogate predictors to replace conventional predictors. The key features of the proposed method include the incorporation of network structures in predictors and allowance of predictors to follow exponential family distributions. Finally, numerical studies, including simulation and real data analysis, are conducted to assess the performance of the proposed method.