张量回归模型及其应用研究综述

A Brief Survey on Tensor Regression Model and Its Application

21世纪以来,张量引起了数据科学和统计学领域的极大兴趣,张量技术被广泛应用于数据挖掘、机器学习和统计学等领域,其中,张量回归模型是一类很重要的工具。本文研究了近十年张量回归模型理论及应用的发展和现状,对张量回归模型进行了简单梳理,主要介绍了张量线性回归模型的理论和应用。为了方便读者理解,本文还介绍了张量、张量分解等基本概念。

Since the 21st century, tensor has aroused great interest in the field of data science and statistics. Tensor technology has been widely used in data mining, machine learning and statistics, among which tensor regression model is a very important tool. This paper studies the development and current situation of the theory and application of tensor regression model in the past ten years. It simply sorts out the tensor regression model, and mainly introduces the theory and application of tensor linear regression model. In order to facilitate readers to understand, this paper also introduces the basic concepts of tensor and tensor decomposition.