Network Discriminant Analysis Based On Heterogeneous Edge Model And Its Application

Linear discriminant analysis(LDA)is one of the most commonly used classification methods,and the theoretical properties of LDA are clear and easy to extend.Statisticians have proposed a large number of statistical classification methods based on LDA ideas for different data types.Network data,which describe the connections between individuals,are common in many scientific fields,including and not limited to biology,sociology,medicine,and social networks.For network data,we can examine both node characteristics and network relationship information,which contains important information about individual characteristics and group structure.In recent years,the problems of potential structure analysis,node prediction and classification for network data have received a lot of attention.In this thesis,we propose a new method,named heterogeneous network discriminant analysis(HNLDA),to address the classification problem of network data.We first construct a new probabilistic model for the network of edge covariance.Under this model,we propose a fast network fitting algorithm based on projected gradient descent,and establish the statistical convergence rate of the algorithm.Second,using the edge covariance probability model,we derive a Bayes optimal classifier that contains both node features and network connectivity information.This classifier degenerates to a traditional LDA classifier when there is no tendency towards group connectivity in the network.Furthermore,we establish an upper bound on the theoretical misclassification risk of this classifier.Finally,we evaluate the network fitting algorithm and the finite sample performance of the proposed classifier via simulation and the adolescent friendship network(Glasgow dataset).On the one hand,the method considers both network information and node information.On the other hand,this method perform better than other classification models by modeling the heterogeneity of nodes.