Manifold curvature learning from hypersurface integral invariants

Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any dimension major results known for surfaces in space, which in tur...

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Veröffentlicht in:	Linear algebra and its applications 2020-10, Vol.602, p.179-205
Hauptverfasser:	Álvarez-Vizoso, Javier, Kirby, Michael, Peterson, Chris
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic series Center of gravity Covariance matrix Curvature Differential geometry Domains Eigenvalues Eigenvectors Hyperspaces Integrals Intersections Invariants Linear algebra Local eigenvalue decomposition Machine learning Manifold learning Manifolds (mathematics) Principal component analysis Principal components analysis Riemann curvature tensor Statistical analysis Tensors
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