A New Tensor Network: Tubal Tensor Train Network and its Applications

Salman Ahmadi-Asl, Valentin Leplat, ANH-HUY PHAN, Andrzej Cichocki

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: Higher-order tensor decomposition models, Tensor Train decomposition, tubal product, T-SVD, Tubal Tensor Train, tensor completion, tensor compression

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Abstract: This paper introduces the Tubal Tensor Train (TTT) decomposition, a novel tensor decomposition model that effectively mitigates the curse of dimensionality inherent in the Tensor Singular Value Decomposition (T-SVD). The TTT decomposition represents an $N$-order tensor as the Tubal product (T-product) of a series of two third-order and $(N-3)$ fourth-order core tensors, contracted. Similar to the Tensor-Train (TT) decomposition, our approach addresses the curse of dimensionality problem. In order to decompose a given tensor into the TTT format, we propose two high-performing algorithms. Numerical simulations are conducted on diverse tasks to demonstrate the efficiency and accuracy of these algorithms compared to the State-of-the-Art methods.

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Submission Number: 2531