High-Dimensional Covariance Matrix Estimation Based on Network

A new method for estimating high-dimensional covariance matrix based on network structure with heteroscedasticity of response variables is proposed in this paper. This method greatly reduces the computational complexity by transforming the high-dimensional covariance matrix estimation problem into a low-dimensional linear regression problem. Even if the size of sample is finite, the estimation method is still effective. The error of estimation will decrease with the increase of matrix dimension. In addition, this paper presents a method of identifying influential nodes in network via covariance matrix. This method is very suitable for academic cooperation networks by taking into account both the contribution of the node itself and the impact of the node on other nodes.