
On the tensor rank of 3× 3 permanent and determinant
The tensor rank and border rank of the 3 × 3 determinant tensor is known...
01/01/2018 ∙ by Siddharth Krishna, et al. ∙ 0 ∙ shareread it

Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squares
We consider the asymmetric orthogonal tensor decomposition problem, and ...
05/25/2018 ∙ by Jialin Li, et al. ∙ 0 ∙ shareread it

Multiresolution Lowrank Tensor Formats
We describe a simple, blackbox compression format for tensors with a mu...
08/29/2019 ∙ by Oscar Mickelin, et al. ∙ 0 ∙ shareread it

Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neurons
We analyze linear independence of rank one tensors produced by tensor po...
10/28/2018 ∙ by Nima Anari, et al. ∙ 0 ∙ shareread it

Orthogonalized ALS: A Theoretically Principled Tensor Decomposition Algorithm for Practical Use
The popular Alternating Least Squares (ALS) algorithm for tensor decompo...
03/06/2017 ∙ by Vatsal Sharan, et al. ∙ 0 ∙ shareread it

UserDevice Authentication in Mobile Banking using APHEN for Paratuck2 Tensor Decomposition
The new financial European regulations such as PSD2 are changing the ret...
05/23/2019 ∙ by Jeremy Charlier, et al. ∙ 0 ∙ shareread it

Error Preserving Correction for CPD and BoundedNorm CPD
In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in so...
09/25/2017 ∙ by AnhHuy Phan, et al. ∙ 0 ∙ shareread it
Guaranteed NonOrthogonal Tensor Decomposition via Alternating Rank1 Updates
In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence guarantees are established for third order tensors of rank k in d dimensions, when k=o ( d^1.5) and the tensor components are incoherent. Thus, we can recover overcomplete tensor decomposition. We also strengthen the results to global convergence guarantees under stricter rank condition k <β d (for arbitrary constant β > 1) through a simple initialization procedure where the algorithm is initialized by top singular vectors of random tensor slices. Furthermore, the approximate local convergence guarantees for pth order tensors are also provided under rank condition k=o ( d^p/2). The guarantees also include tight perturbation analysis given noisy tensor.
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