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Theories, algorithms and applications in tensor learning

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Abstract

Due to the accelerated development and popularization of Internet, mobile Internet, and Internet of Things and the breakthrough of storage and communication technologies, the amount of data obtained in the fields of health care, social media, and climate science is increasing, showing complex high-dimensional, multimodal, and heterogeneous characteristics. As the expansion of a vector and matrix, a tensor is the natural and essential mode of representation for this kind of data. The theory of tensor algebra provides a powerful mathematical tool and an extensible framework for learning algorithms for processing data with high-dimensional heterogeneity and complex dependence. In recent years, tensor theory and its applications have become a research hotspot, from new tensor models and scalable algorithms in academia to industry solutions. The article shows its advances in tensor theories, algorithms, and applications. Firstly, tensor operation, classical tensor decomposition theory, and t-product tensor theory are introduced. Secondly, tensor supervised learning, tensor unsupervised learning, and tensor deep learning are discussed from the perspective of tensor decomposition and t-product, and then their application research is summarized. Finally, the opportunities and challenges of tensor learning are briefly discussed.

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Acknowledgements

We acknowledge the financial support by the National Natural Science Foundation of China (62172182), the Hunan Provincial Natural Science Foundation of China (2020JJ4489 and 2020JJ4490), A Project Supported by Scientific Research Fund of Hunan Provincial Education Department (19A394), and Huaihua University Double First-Class initiative Applied Characteristic Discipline of Control Science and Engineering.

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  1. School of Computer Science and Engineering, Huaihua University, Huaihua, People’s Republic of China

    Xiaowu Deng, Yuanquan Shi & Dunhong Yao

  2. Key Laboratory of Wuling-Mountain Health Big Data Intelligent Processing and Application in Hunan Province Universities, Huaihua, People’s Republic of China

    Xiaowu Deng, Yuanquan Shi & Dunhong Yao

  3. Key Laboratory of Intelligent Control Technology for Wuling-Mountain Ecological Agriculture in Hunan Province, Huaihua, People’s Republic of China

    Xiaowu Deng, Yuanquan Shi & Dunhong Yao

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  1. Xiaowu Deng
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  2. Yuanquan Shi
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Correspondence to Xiaowu Deng.

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Deng, X., Shi, Y. & Yao, D. Theories, algorithms and applications in tensor learning. Appl Intell 53, 20514–20534 (2023). https://doi.org/10.1007/s10489-023-04538-z

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