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...
Saved in:
Main Authors: | , , , |
---|---|
Other Authors: | |
Format: | Article |
Language: | English |
Published: |
2022
|
Subjects: | |
Online Access: | https://hdl.handle.net/10356/159584 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Nanyang Technological University |
Language: | English |
id |
sg-ntu-dr.10356-159584 |
---|---|
record_format |
dspace |
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 |
_version_ |
1738844880210231296 |