Some convergence results on the Regularized Alternating Least-Squares method for tensor decomposition

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some Convergence Results on the Regularized Alternating Least-Squares Method for Tensor Decomposition

We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergen...

متن کامل

Orthogonal Low Rank Tensor Approximation: Alternating Least Squares Method and Its Global Convergence

With the notable exceptions of two cases — that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption that only one set...

متن کامل

Regularized Alternating Least Squares Algorithms for Non-negative Matrix/Tensor Factorization

Nonnegative Matrix and Tensor Factorization (NMF/NTF) and Sparse Component Analysis (SCA) have already found many potential applications, especially in multi-way Blind Source Separation (BSS), multi-dimensional data analysis, model reduction and sparse signal/image representations. In this paper we propose a family of the modified Regularized Alternating Least Squares (RALS) algorithms for NMF/...

متن کامل

Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation

A local convergence theorem for calculating canonical low-rank tensor approximations (PARAFAC, CANDECOMP) by the alternating least squares algorithm is established. The main assumption is that the Hessian matrix of the problem is positive definite modulo the scaling indeterminacy. A discussion, whether this is realistic, and numerical illustrations are included. Also regularization is addressed.

متن کامل

Convergence of Common Proximal Methods for L1-Regularized Least Squares

We compare the convergence behavior of ADMM (alternating direction method of multipliers), [F]ISTA ([fast] iterative shrinkage and thresholding algorithm) and CD (coordinate descent) methods on the model `1-regularized least squares problem (aka LASSO). We use an eigenanalysis of the operators to compare their local convergence rates when close to the solution. We find that, when applicable, CD...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2013

ISSN: 0024-3795

DOI: 10.1016/j.laa.2011.12.002