A nonlinear dimensionality reduction framework using smooth geodesics
作者：
Highlights：
• Our algorithm reveals underlying smooth manifolds of high-dimensional data.
• The smoothing spline approach ensures the smoothness of a corrupted manifold.
• The algorithm handles noise and sparsity gracefully.
• Performance versus neighborhood size, smoothness, sparsity, and noise are analyzed.
• Compared to Isomap, embeddings of face images and hand written digits are improved.
摘要
•Our algorithm reveals underlying smooth manifolds of high-dimensional data.•The smoothing spline approach ensures the smoothness of a corrupted manifold.•The algorithm handles noise and sparsity gracefully.•Performance versus neighborhood size, smoothness, sparsity, and noise are analyzed.•Compared to Isomap, embeddings of face images and hand written digits are improved.
论文关键词：Manifold,Nonlinear dimensionality reduction,Smoothing spline,Geodesics,Noisy measurements
论文评审过程：Received 7 December 2017, Revised 20 June 2018, Accepted 16 October 2018, Available online 19 October 2018, Version of Record 25 October 2018.
论文官网地址：https://doi.org/10.1016/j.patcog.2018.10.020
