
Low Rank Triple Decomposition and Tensor Recovery
A simple approach for matrix completion and recovery is via low rank mat...
read it

Learning Paths from Signature Tensors
Matrix congruence extends naturally to the setting of tensors. We apply ...
read it

How to Decompose a Tensor with Group Structure
In this work we study the orbit recovery problem, which is a natural abs...
read it

Isomorphism problems for tensors, groups, and cubic forms: completeness and reductions
In this paper we consider the problems of testing isomorphism of tensors...
read it

A Comparative Analysis of Tensor Decomposition Models Using Hyper Spectral Image
Hyper spectral imaging is a remote sensing technology, providing variety...
read it

A unifying PerronFrobenius theorem for nonnegative tensors via multihomogeneous maps
Inspired by the definition of symmetric decomposition, we introduce the ...
read it

Fast and robust tensor decomposition with applications to dictionary learning
We develop fast spectral algorithms for tensor decomposition that match ...
read it
Spectral Methods from Tensor Networks
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 cryoelectron 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 multireference alignment over the infinite group SO(2). Our algorithm extends to the more general heterogeneous case.
READ FULL TEXT
Comments
There are no comments yet.