Spectral methods from tensor networks
Name
1811.00944.pdf
Description
Submitted version
Size
385.85 KB
Format
Adobe PDF
Checksum (MD5)
2bbf996075e3871c6cf2876d45d40075
Author(s)
Moitra, Ankur
Wein, Alexander S.
Date Issued
June 23, 2019
Publisher
ACM
Citation
Moitra, Ankur and Wein, Alexander S. 2019. "Spectral methods from tensor networks."
Version
Original manuscript
Abstract
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. A tensor network is a diagram that specifies a way to “multiply” a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices built from simple tensor networks. In this work we leverage the full power of this abstraction to design new algorithms for certain continuous tensor decomposition problems. An important and challenging family of tensor problems comes from orbit recovery, a class of inference problems involving group actions (inspired by applications such as cryo-electron microscopy). Orbit recovery problems over finite groups can often be solved via standard tensor methods. However, for infinite groups, no general algorithms are known. We give a new spectral algorithm based on tensor networks for one such problem: continuous multi-reference alignment over the infinite group SO(2). Our algorithm extends to the more general heterogeneous case.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3313276.3316357
