Hierarchical Tucker Tensor Optimization - Applications to Tensor Completion

摘要

In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. Using the differential geometric tools presented here, we construct standard optimization algorithms such as Steepest Descent and Conjugate Gradient for interpolating tensors in HT format. We also empirically examine the importance of one's choice of data organization in the success of tensor recovery by drawing upon insights from the matrix completion literature. Using these algorithms, we recover various seismic data sets with randomly missing sources.