Geometric statistics with subspace structure preservation for SPD matrices
This work addresses the challenge of handling SPD-valued data in machine learning and statistics, offering a domain-specific advancement for applications like computer vision or signal processing.
The authors tackled the problem of processing symmetric positive definite (SPD) matrices by developing a geometric framework that preserves subspace structures using Thompson geometry and extreme generalized eigenvalues, resulting in a novel inductive mean for SPD matrices.
We present a geometric framework for the processing of SPD-valued data that preserves subspace structures and is based on the efficient computation of extreme generalized eigenvalues. This is achieved through the use of the Thompson geometry of the semidefinite cone. We explore a particular geodesic space structure in detail and establish several properties associated with it. Finally, we review a novel inductive mean of SPD matrices based on this geometry.