Details

Autor(en) / Beteiligte

• Ma, Zhengming
• Zhan, Zengrong
• Feng, Zijian
• Guo, Jiajing

Titel

Manifold Learning Based on Straight-Like Geodesics and Local Coordinates

Ist Teil von

• IEEE transaction on neural networks and learning systems, 2021-11, Vol.32 (11), p.4956-4970

Ort / Verlag

Piscataway: IEEE

Erscheinungsjahr

2021

Quelle

IEEE/IET Electronic Library (IEL)

Beschreibungen/Notizen

• In this article, a manifold learning algorithm based on straight-like geodesics and local coordinates is proposed, called SGLC-ML for short. The contribution and innovation of SGLC-ML lie in that; first, SGLC-ML divides the manifold data into a number of straight-like geodesics, instead of a number of local areas like many manifold learning algorithms do. Figuratively speaking, SGLC-ML covers manifold data set with a sparse net woven with threads (straight-like geodesics), while other manifold learning algorithms with a tight roof made of titles (local areas). Second, SGLC-ML maps all straight-like geodesics into straight lines of a low-dimensional Euclidean space. All these straight lines start from the same point and extend along the same coordinate axis. These straight lines are exactly the local coordinates of straight-like geodesics as described in the mathematical definition of the manifold. With the help of local coordinates, dimensionality reduction can be divided into two relatively simple processes: calculation and alignment of local coordinates. However, many manifold learning algorithms seem to ignore the advantages of local coordinates. The experimental results between SGLC-ML and other state-of-the-art algorithms are presented to verify the good performance of SGLC-ML.