The Geometry of Nonparametric Filament Estimation

DOI10.1080/01621459.2012.682527zbMath1261.62030arXiv1003.5536OpenAlexW1969447312MaRDI QIDQ4916513

Christopher R. Genovese, Isabella Verdinelli, Marco Perone-Pacifico, Larry Alan Wasserman

Publication date: 22 April 2013

Published in: Journal of the American Statistical Association (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.5536

zbMATH Keywords

clusteringdensity estimationprincipal curvesmanifold learning

Mathematics Subject Classification ID

Density estimation (62G07) Non-Markovian processes: estimation (62M09) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Cites Work

• Unnamed Item
• A note on two problems in connexion with graphs
• On the path density of a gradient field
• Curve reconstruction from noisy samples
• Curve reconstruction from unorganized points
• Finding the homology of submanifolds with high confidence from random samples
• Adaptive multiscale detection of filamentary structures in a background of uniform random points
• Curve and Surface Reconstruction
• Detection of Abnormal Behavior Via Nonparametric Estimation of the Support
• Global curvature, thickness, and the ideal shapes of knots
• Principal curves with bounded turn
• On boundary estimation