A Randomized Tensor Train Singular Value Decomposition
For researchers in tensor computations, this work provides a faster alternative to the expensive hierarchical SVD, enabling scalable low-rank approximations for high-dimensional data.
The paper presents a randomized algorithm for computing the hierarchical SVD in the tensor train format, achieving near-optimal low-rank approximations with reduced computational cost compared to deterministic methods.
The hierarchical SVD provides a quasi-best low rank approximation of high dimensional data in the hierarchical Tucker framework. Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the present work we examine generalizations of randomized matrix decomposition methods to higher order tensors in the framework of the hierarchical tensors representation. In particular we present and analyze a randomized algorithm for the calculation of the hierarchical SVD (HSVD) for the tensor train (TT) format.