Efficient Weingarten map and curvature estimation on manifolds

• Published in: Machine learning Vol. 110; no. 6; pp. 1319 - 1344
• Main Authors: Cao, Yueqi, Li, Didong, Sun, Huafei, Assadi, Amir H., Zhang, Shiqiang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2021; Springer Nature B.V
• Subjects: Artificial Intelligence; Asymptotic properties; Computer Science; Control; Convergence; Curvature; Euclidean geometry; Euclidean space; Machine Learning; Manifolds; Mechatronics; Natural Language Processing (NLP); Robotics; Simulation and Modeling; Statistical models; Curvature estimation; Weingarten map; Point cloud data; Unsupervised learning

In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size...