Hierarchical Tucker tensor optimization - applications to tensor completion
| Title | Hierarchical Tucker tensor optimization - applications to tensor completion |
| Publication Type | Conference |
| Year of Publication | 2013 |
| Authors | Curt Da Silva, Felix J. Herrmann |
| Month | 07 |
| Keywords | differential geometry, hierarchical tucker, riemannian optimization, SAMPTA, structured tensor, tensor interpolation |
| Abstract | In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker 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 source pairs. |
| URL | https://slim.gatech.edu/Publications/Public/Conferences/SAMPTA/2013/dasilva2013SAMPTAhtuck/dasilva2013SAMPTAhtuck.pdf |
| Presentation | |
| Citation Key | dasilva2013SAMPTAhtuck |