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Lie group machine learning is recognized as the theoretical basis of brain intelligence, brain learning, higher machine learning, and higher artificial intelligence. Sample sets of Lie group matrices are widely available in practical applications. Lie group learning is a vibrant field of increasing importance and extraordinary potential and thus needs to be developed further. This study aims to provide a comprehensive survey on recent advances in Lie group machine learning. We introduce Lie group machine learning techniques in three major categories: supervised Lie group machine learning, semisupervised Lie group machine learning, and unsupervised Lie group machine learning. In addition, we introduce the special application of Lie group machine learning in image processing. This work covers the following techniques: Lie group machine learning model, Lie group subspace orbit generation learning, symplectic group learning, quantum group learning, Lie group fiber bundle learning, Lie group cover learning, Lie group deep structure learning, Lie group semisupervised learning, Lie group kernel learning, tensor learning, frame bundle connection learning, spectral estimation learning, Finsler geometric learning, homology boundary learning, category representation learning, and neuromorphic synergy learning. Overall, this survey aims to provide an insightful overview of state-of-the-art development in the field of Lie group machine learning. It will enable researchers to comprehensively understand the state of the field, identify the most appropriate tools for particular applications, and identify directions for future research.


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Survey on Lie Group Machine Learning

Show Author's information Mei LuFanzhang Li( )
School of Software Engineering, Jinling Institute of Technology, Nanjing 211169, China and is also with the School of Computer Science and Technology, Jiangsu Normal University, Xuzhou 221000, China
School of Computer Science and Technology, Soochow University, Suzhou 215006, China

Abstract

Lie group machine learning is recognized as the theoretical basis of brain intelligence, brain learning, higher machine learning, and higher artificial intelligence. Sample sets of Lie group matrices are widely available in practical applications. Lie group learning is a vibrant field of increasing importance and extraordinary potential and thus needs to be developed further. This study aims to provide a comprehensive survey on recent advances in Lie group machine learning. We introduce Lie group machine learning techniques in three major categories: supervised Lie group machine learning, semisupervised Lie group machine learning, and unsupervised Lie group machine learning. In addition, we introduce the special application of Lie group machine learning in image processing. This work covers the following techniques: Lie group machine learning model, Lie group subspace orbit generation learning, symplectic group learning, quantum group learning, Lie group fiber bundle learning, Lie group cover learning, Lie group deep structure learning, Lie group semisupervised learning, Lie group kernel learning, tensor learning, frame bundle connection learning, spectral estimation learning, Finsler geometric learning, homology boundary learning, category representation learning, and neuromorphic synergy learning. Overall, this survey aims to provide an insightful overview of state-of-the-art development in the field of Lie group machine learning. It will enable researchers to comprehensively understand the state of the field, identify the most appropriate tools for particular applications, and identify directions for future research.

Keywords:

Lie group machine learning, Lie group subspace orbit generation learning, quantum group learning, symplectic group learning, Lie group fiber bundle learning
Received: 14 May 2020 Accepted: 09 June 2020 Published: 16 November 2020 Issue date: December 2020
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Publication history

Received: 14 May 2020
Accepted: 09 June 2020
Published: 16 November 2020
Issue date: December 2020

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© The authors 2020

Acknowledgements

This work was supported by the National Key Research and Development Program (Nos. 2018YFA0701700 and 2018YFA0701701) and Scientific Research Foundation for Advanced Talents (No. jit-b-202045). The authors thank all of the reviewers for their valuable comments.

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