Manifold learning based on straight-like geodesics and local coordinates

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...

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Main Authors: Ma, Zhengming, Zhan, Zengrong, Feng, Zijian, Guo, Jiajing
Other Authors: Interdisciplinary Graduate School (IGS)
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/159584
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1595842022-06-28T01:15:35Z Manifold learning based on straight-like geodesics and local coordinates Ma, Zhengming Zhan, Zengrong Feng, Zijian Guo, Jiajing Interdisciplinary Graduate School (IGS) Engineering::Computer science and engineering Dimensionality Reduction Geodesic 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. This work was supported in part by the National Natural Science Foundation of China under Grant 61773022, in part by the Character and Innovation Project of Education of Guangdong Province under Grant 2018GKTSCX081, and in part by the Project of Education Scientific Planning of Guangzhou under Grant 201811675. 2022-06-28T01:15:35Z 2022-06-28T01:15:35Z 2020 Journal Article Ma, Z., Zhan, Z., Feng, Z. & Guo, J. (2020). Manifold learning based on straight-like geodesics and local coordinates. IEEE Transactions On Neural Networks and Learning Systems, 32(11), 4956-4970. https://dx.doi.org/10.1109/TNNLS.2020.3026426 2162-237X https://hdl.handle.net/10356/159584 10.1109/TNNLS.2020.3026426 33027005 2-s2.0-85092933673 11 32 4956 4970 en IEEE Transactions on Neural Networks and Learning Systems © 2020 IEEE. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Computer science and engineering
Dimensionality Reduction
Geodesic
spellingShingle Engineering::Computer science and engineering
Dimensionality Reduction
Geodesic
Ma, Zhengming
Zhan, Zengrong
Feng, Zijian
Guo, Jiajing
Manifold learning based on straight-like geodesics and local coordinates
description 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.
author2 Interdisciplinary Graduate School (IGS)
author_facet Interdisciplinary Graduate School (IGS)
Ma, Zhengming
Zhan, Zengrong
Feng, Zijian
Guo, Jiajing
format Article
author Ma, Zhengming
Zhan, Zengrong
Feng, Zijian
Guo, Jiajing
author_sort Ma, Zhengming
title Manifold learning based on straight-like geodesics and local coordinates
title_short Manifold learning based on straight-like geodesics and local coordinates
title_full Manifold learning based on straight-like geodesics and local coordinates
title_fullStr Manifold learning based on straight-like geodesics and local coordinates
title_full_unstemmed Manifold learning based on straight-like geodesics and local coordinates
title_sort manifold learning based on straight-like geodesics and local coordinates
publishDate 2022
url https://hdl.handle.net/10356/159584
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