Tensor Decompositions, Alternating Least Squares and other Tales
نویسندگان
چکیده
This work was originally motivated by a classification of tensors proposed by Richard Harshman. In particular, we focus on simple and multiple “bottlenecks”, and on “swamps”. Existing theoretical results are surveyed, some numerical algorithms are described in details, and their numerical complexity is calculated. In particular, the interest in using the ELS enhancement in these algorithms is discussed. Computer simulations feed this discussion. Journal of Chemometrics, vol.23, pp.393–405, Aug. 2009
منابع مشابه
Decompositions of a Higher-Order Tensor in Block Terms - Part III: Alternating Least Squares Algorithms
In this paper we derive alternating least squares algorithms for the computation of the block term decompositions introduced in Part II. We show that degeneracy can also occur for block term decompositions.
متن کاملSome 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 کاملSPALS: Fast Alternating Least Squares via Implicit Leverage Scores Sampling
Tensor CANDECOMP/PARAFAC (CP) decomposition is a powerful but computationally challenging tool in modern data analytics. In this paper, we show ways of sampling intermediate steps of alternating minimization algorithms for computing low rank tensor CP decompositions, leading to the sparse alternating least squares (SPALS) method. Specifically, we sample the Khatri-Rao product, which arises as a...
متن کاملTensor Decompositions with Banded Matrix Factors
The computation of themodel parameters of a Canonical Polyadic Decomposition (CPD), also known as the parallel factor (PARAFAC) or canonical decomposition (CANDECOMP) or CP decomposition, is typically done by resorting to iterative algorithms, e.g. either iterative alternating least squares type or descent methods. In many practical problems involving tensor decompositions such as signal proces...
متن کاملA Scalable Optimization Approach for Fitting Canonical Tensor Decompositions
Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as CANDECOMP/PARAFAC (CP), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, ne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009