  The correlation matrix of massive biomedical data (e.g. gene expression or
neuroimaging data) often exhibits a complex and organized, yet latent graph
topological structure. We propose a two step procedure that first detects the
latent graph topology with parsimony from the sample correlation matrix and
then regularizes the correlation matrix by leveraging the detected graph
topological information. We show that the graph topological information guided
thresholding can reduce false positive and false negative rates simultaneously
because it allows edges to borrow strengths from each other precisely. Several
examples illustrate that the parsimoniously detected latent graph topological
structures may reveal underlying biological networks and guide correlation
matrix estimation.
