
Accelerating Alternating Least Squares for Tensor Decomposition by Pairwise Perturbation
The alternating least squares algorithm for CP and Tucker decomposition ...
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More Efficient Sampling for Tensor Decomposition
Recent papers have developed alternating least squares (ALS) methods for...
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Coupled Tensor Completion via Lowrank Tensor Ring
The coupled tensor decomposition aims to reveal the latent data structur...
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Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squares
We consider the asymmetric orthogonal tensor decomposition problem, and ...
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The trouble with tensor ring decompositions
The tensor train decomposition decomposes a tensor into a "train" of 3w...
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Tensor Grid Decomposition with Application to Tensor Completion
The recently prevalent tensor train (TT) and tensor ring (TR) decomposit...
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Adaptive force biasing algorithms: new convergence results and tensor approximations of the bias
A modification of the Adaptive Biasing Force method is introduced, in wh...
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Tensor Ring Decomposition: Energy Landscape and Oneloop Convergence of Alternating Least Squares
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the existence of spurious local minima for the optimization energy landscape even when the tensor ring format is much overparameterized, i.e., with bond dimension much larger than that of the true target tensor. On the other hand, when the bond dimension is further increased, we establish oneloop convergence for alternating least square algorithm for tensor ring decomposition. The theoretical results are complemented by numerical experiments for both local minimum and oneloop convergence for the alternating least square algorithm.
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