Curvature-aware manifold learning

作者：

Highlights：

• Adding curvature information to manifold learning.

• Using second fundamental form to analyze the geometric structure of sub-manifold.

• The curvature information is obtained by estimating the Hessian matrix of local analytic structure.

• The theoretical analysis of curvature-aware manifold learning is given to illustrate the improvements of CAML.

摘要

•Adding curvature information to manifold learning.•Using second fundamental form to analyze the geometric structure of sub-manifold.•The curvature information is obtained by estimating the Hessian matrix of local analytic structure.•The theoretical analysis of curvature-aware manifold learning is given to illustrate the improvements of CAML.

论文关键词：Manifold learning,Riemannian curvature,Second fundamental form,Hessian operator

论文评审过程：Received 12 June 2017, Revised 9 April 2018, Accepted 6 June 2018, Available online 7 June 2018, Version of Record 18 June 2018.

论文官网地址：https://doi.org/10.1016/j.patcog.2018.06.007