4.7 Article

Manifold Learning Based on Straight-Like Geodesics and Local Coordinates

Journal

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2020.3026426

Keywords

Dimensionality reduction; geodesic; local coordinates; manifold learning

Funding

  1. National Natural Science Foundation of China [61773022]
  2. Character and Innovation Project of Education of Guangdong Province [2018GKTSCX081]
  3. Project of Education Scientific Planning of Guangzhou [201811675]

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The SGLC-ML algorithm divides data into straight-like geodesics, maps them to straight lines in a low-dimensional Euclidean space, and utilizes local coordinates for dimensionality reduction, achieving good performance compared to other algorithms.
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.

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