Network-Based Discriminant Analysis for Multiclassification

Classification for multi-label responses, known as multiclassification, has been an important problem in supervised learning and has attracted our attention. In the framework of statistical learning, discriminant analysis is a powerful method to do multiclassification. With the increasing availability of complex data, it becomes more challenging to analyze 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. Although discriminant analysis is one of the supervised learning methods to deal with multiclassification and relevant extensions have been explored, little method has been available to handle multiclassification with network structures accommodated. To incorporate network structures in predictors and improve the accuracy of classification, we propose network-based linear discriminant analysis and network-based quadratic discriminant analysis in this paper. The main advantage of the proposed methods is to estimate the inverse of covariance matrices directly and do classification for multi-label responses instead of restricting on binary responses. In addition, the proposed methods are easy to compute and implement. Finally, numerical studies are conducted to assess the performance of the proposed methods, and numerical results verify that the proposed methods outperform their competitors.