Manifold learning based on straight-like geodesics and local coordinates

• Main Authors: Ma, Zhengming, Zhan, Zengrong, Feng, Zijian, Guo, Jiajing
• Other Authors: Interdisciplinary Graduate School (IGS)
• Format: Article
• Language: English
• Published: 2022
• Subjects: Engineering::Computer science and engineering; Dimensionality Reduction; Geodesic
• Online Access: https://hdl.handle.net/10356/159584
• Institution: Nanyang Technological University

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.