A randomized tensor singular value decomposition based on the t‐product
Abstract
The tensor SVD (t‐SVD) for third‐order tensors, previously proposed in the literature, has been applied successfully in many fields, such as computed tomography, facial recognition, and video completion. In this paper, we propose a method that extends a well‐known randomized matrix method to the t‐SVD. This method can produce a factorization with similar properties to the t‐SVD, but it is more computationally efficient on very large data sets. We present details of the algorithms and theoretical results and provide numerical results that show the promise of our approach for compressing and analyzing image‐based data sets. We also present an improved analysis of the randomized and simultaneous iteration for matrices, which may be of independent interest to the scientific community. We also use these new results to address the convergence properties of the new and randomized tensor method as well.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 09, 2018
- Source ID
- 10.1002/nla.2179
Entities
People
- Arvind K Saibaba
- Jiani Zhang
- Misha E. Kilmer
- Shuchin Aeron
Organizations
- Intelligence Advanced Research Projects Activity
- National Science Foundation
- North Carolina State University
- Office of the Director of National Intelligence
- Tufts University