Matches in SemOpenAlex for { <https://semopenalex.org/work/W1955967056> ?p ?o ?g. }
- W1955967056 abstract "Author(s): Anandkumar, Animashree; Ge, Rong; Janzamin, Majid | Abstract: 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 rank-$1$ 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 $k=o bigl( d^{1.5} bigr)$ 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 $k le beta d$ (for arbitrary constant $beta g 1$) 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 $p$-th order tensors are also provided under rank condition $k=o bigl( d^{p/2} bigr)$. The guarantees also include tight perturbation analysis given noisy tensor." @default.
- W1955967056 created "2016-06-24" @default.
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- W1955967056 date "2014-02-20" @default.
- W1955967056 modified "2023-09-27" @default.
- W1955967056 title "Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-$1$ Updates" @default.
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