一种多分辨率低秩张量分解
A Multi-resolution Low-rank Tensor Decomposition
AI总结：
针对高阶张量分解的基础问题，受PARAFAC启发提出一种多分辨率低秩张量分解方法，通过将张量重塑为多个低维张量以分层利用不同分辨率结构，并讨论了交替最小二乘算法，初步仿真验证了其潜在实用性。
摘要：
高阶张量的（高效且简约的）分解是一个在多个领域具有众多应用的基础问题。文献中已提出多种方法，其中Tucker和PARAFAC分解最为突出。受后者启发，本文提出一种多分辨率低秩张量分解，以分层方式描述（近似）张量。该分解的核心思想是将张量重塑为多个低维张量，以利用不同分辨率层次的结构。文中首先解释了该方法，讨论了交替最小二乘算法，并提供了初步仿真以说明其潜在的实际相关性。
英文摘要：
The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC decompositions being the most prominent ones. Inspired by the latter, in this work we propose a multi-resolution low-rank tensor decomposition to describe (approximate) a tensor in a hierarchical fashion. The central idea of the decomposition is to recast the tensor into \emph{multiple} lower-dimensional tensors to exploit the structure at different levels of resolution. The method is first explained, an alternating least squares algorithm is discussed, and preliminary simulations illustrating the potential practical relevance are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
