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Geometric statistics with subspace structure preservation for SPD matrices

arXiv 2407.03382 ↗First posted 2 Jul 2024math.NA cs.LG cs.NAcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 3 of its 12 references that are in the map. First posted on arXiv 2 Jul 2024.

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References · 3

  1. 2023Differential geometry with extreme eigenvalues in the positive semidefinite conecited by 5
  2. 2019Geometric Matrix Midrangescited by 3
  3. 2020Inductive Geometric Matrix Midrangescited by 3

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