Abstract
In this chapter, we will first introduce the preliminaries on tensors, including terminologies and the associated notations, related multi-linear algebra, and more importantly, widely used tensor decomposition formats. Then, we link the tensor decompositions to the recent representation learning for multi-dimensional data, showing the paramount role of tensors in modern signal processing and machine learning. Finally, we review the recent algorithms for tensor decompositions, and further analyze their common challenge in rank determination.
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Cheng, L., Chen, Z., Wu, YC. (2023). Tensor Decomposition: Basics, Algorithms, and Recent Advances. In: Bayesian Tensor Decomposition for Signal Processing and Machine Learning. Springer, Cham. https://doi.org/10.1007/978-3-031-22438-6_1
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DOI: https://doi.org/10.1007/978-3-031-22438-6_1
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