张量分解及其在统计模型中的应用

Tensor decomposition and its applications in statistics

首先介绍张量基本概念、张量乘积及张量CP分解和Tucker分解.其次,将张量运用于统计模型当中,得到张量回归模型.再结合张量矩阵化和张量分解,给出该模型参数张量的最小二乘估计公式.最后,举例说明张量模型的重要性.

In this paper,we introduce some basic concepts related to tensors and tensor decompositions such as CP decomposition and Tucker decomposition,fol-lowing the introduction of tensor multiplications.We apply tensor to express the multilinear regression model.We employ the matricization and tensor decompo-sition to the model to obtain the least square estimation.Finally,an example is given to illustrate the influence of this kind of the tensor model.