Due to the explosive growth of large-scale data sets, tensors have been a useful tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be further used to define the best low-rank approximation of a tensor to significantly reduce the dimensionality. Equipped with tensor analysis basics, we can consider the tensor recovery problem. In this talk, we introduce various tensor iterative hard thresholding algorithms based on the low-rank tensor approximations. Convergence guarantees and one accelerated variant with mini-batch are provided along with the special case with linear measurements. Numerical results are conducted to demonstrate convergence and computational efficiency.
Tensor Decomposition Based Iterative Hard Thresholding Algorithms
Jing Qin, University of KentuckyAuthors: Rachel Grotheer, Shuang Li, Anna Ma, Deanna Needell and Jing Qin
2022 AWM Research Symposium