Matrix compression along isogenic blocks

Abstract

A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectralpermanence properties. The basic observation that Hadamard entrywise functional calculus preserves isogenic blocks has already proved to be of paramount importance for thresholding large correlation matrices. An array of applications to current investigations in computational matrix analysis arises, touching concepts such as symmetric statistical models, hierarchical matrices and coherent matrix organization induced by partition trees.