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*16 November 2020*

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Lie group machine learning, Lie group subspace orbit generation learning, quantum group learning, symplectic group learning, Lie group fiber bundle learning
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Lu M, Li F.
Survey on Lie Group Machine Learning.
Big Data Mining and Analytics,
2020, 3(4): 235-258.
https://doi.org/10.26599/BDMA.2020.9020011
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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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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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Received: 14 May 2020

Accepted: 09 June 2020

Published:
16 November 2020

Issue date: December 2020

© The authors 2020

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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