Bounded manifold completion
作者：
Highlights：
• Our algorithm detects a low-dimensional manifold that lies within a set of bounds.
• The bounds are derived using a given high-dimensional dataset of a point cloud.
• A matrix representing the distances on a low-dimensional manifold is low-rank.
• Our method recovers a partially observed distance matrix using fully observed entries.
• Low-rank matrix completion is used to recover partially observed distance matrices.
摘要
•Our algorithm detects a low-dimensional manifold that lies within a set of bounds.•The bounds are derived using a given high-dimensional dataset of a point cloud.•A matrix representing the distances on a low-dimensional manifold is low-rank.•Our method recovers a partially observed distance matrix using fully observed entries.•Low-rank matrix completion is used to recover partially observed distance matrices.
论文关键词：Manifold,Low-rank matrix completion,Positive semi-definite,Truncated nuclear norm,Gramian
论文评审过程：Received 12 November 2019, Revised 24 April 2020, Accepted 18 September 2020, Available online 19 September 2020, Version of Record 28 September 2020.
论文官网地址：https://doi.org/10.1016/j.patcog.2020.107661
