Estimating large covariance matrix with network topology for high-dimensional biomedical data

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Interactions between features of high-dimensional biomedical data often exhibit complex and organized, yet latent, network topological structures. Estimating the non-sparse large covariance matrix of these high-dimensional biomedical data while preserving and recognizing the latent network topology are challenging. A two step procedure is proposed that first detects latent network topological structures from the sample correlation matrix by implementing new penalized optimization and then regularizes the covariance matrix by leveraging the detected network topological information. The network topology guided regularization can reduce false positive and false negative rates simultaneously because it allows edges to borrow strengths from each other precisely. Empirical data examples demonstrate that organized latent network topological structures widely exist in high-dimensional biomedical data across platforms and identifying these network structures can effectively improve estimating covariance matrix and understanding interactive relationships between biomedical features.