一种新的有噪张量秩的估计方法  

A new method to estimate the rank of tensor in a noisy environment

作　　者：饶伟[1] 田秀梅[1] RAO Wei;TIAN Xiumei(School of Information Engineering,Nanchang Institute of Technology,Nanchang 330099,China)

机构地区：[1]南昌工程学院信息工程学院,江西南昌330099

出　　处：《南昌工程学院学报》2020年第3期76-82,共7页Journal of Nanchang Institute of Technology

基　　金：江西省教育厅科学技术研究重点资助项目(GJJ170975);国家自然科学基金资助项目(61961025)。

摘　　要：有噪张量秩的估计,一直以来都是张量处理领域的重点和难点问题之一。现有大多数估计方法都是针对无噪情况下的张量提出的,而一旦张量含有噪声这些方法则失效。有噪张量的秩尤其是高阶有噪张量的秩较难准确获取,往往需要通过反复实验来判定。借助典范多元张量分解的联合对角化矩阵实现,并结合阵列信号处理领域中的信源信号数的估计方法,提出了一种新的有噪张量秩的估计方法。仿真结果验证了新方法的有效性。The estimation of the rank of a tensor in a noisy environment is one of the key and difficult issues in the field of tensor processing.Most of the existing estimation methods are proposed for the tensor without noise,and these methods fail once the tensor contains noise.The rank of a tensor with noise,especially the rank of a high-order tensor with noise,is difficult to obtain accurately until lots of experiments are carried out.Therefore,in this paper,with the help of the source number estimation method,a new method to estimate the rank of a tensor in a noisy environment is proposed,which is inspired by the fact that the canonical polyadic decomposition of a tensor can equivalently be seen as the simultaneous diagonalization of its matrix slices.Simulation results verify the effectiveness of the proposed method.

关 键 词：张量秩 典范多元张量分解 联合矩阵对角化 信源数估计 

分 类 号：TN911.7[电子电信—通信与信息系统]