Network linear discriminant analysis

Linear discriminant analysis (LDA) is one of the most popularly used classification methods. With the rapid advance of information technology, network data are becoming increasingly available. A novel method called network linear discriminant analysis (NLDA) is proposed to deal with the classification problem for network data. The NLDA model takes both network information and predictive variables into consideration. Theoretically, the misclassification rate is studied and an upper bound is derived under mild conditions. Furthermore, it is observed that real networks are often sparse in structure. As a result, asymptotic performance of NLDA is also obtained under certain sparsity assumptions. In order to evaluate the finite sample performance of the newly proposed methodology, a number of simulation studies are conducted. Lastly, a real data analysis about Sina Weibo is also presented for illustration purpose.