Tensor decomposition of Toeplitz Jacket matrices for big data processing

Author

Jun Li ; Yier Yan ; Wei Duan ; Sangseob Song ; Moon Ho Lee

Author_Institution

Dept. of Electron. & Inf. Eng., Chonbuk Nat. Univ., Jeonju, South Korea

fYear

2015

fDate

9-11 Feb. 2015

Firstpage

11

Lastpage

14

Abstract

In this paper, we consider the tensor decomposition (TD) of Toeplitz Jacket (TJ) matrices for big data processing by using the conventional higher order singular value decomposition (HOSVD) algorithm and Tensor train (TT) decomposition. In order to use HOSVD algorithm and TT decomposition, we reshape the given matrix and make it as a tensor. Due to the property of Toeplitz matrices, we use a truncated TJ matrix in stead of given matrix to reduce the complexity of TD. The results verified that the TD of the truncated TJ matrices gains a lower complexity due to smaller size of factor matrices and core tensors.

Keywords

Big Data; Toeplitz matrices; computational complexity; singular value decomposition; tensors; HOSVD algorithm; TT decomposition; Toeplitz jacket matrices; big data processing; complexity reduction; core tensors; factor matrices; higher order singular value decomposition; tensor decomposition; tensor train; truncated TJ matrix; Approximation methods; Big data; Complexity theory; Matrix decomposition; Singular value decomposition; Standards; Tensile stress; Tensor Decomposition (TD); Tensor train (TT); Toeplitz Jacket Matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Big Data and Smart Computing (BigComp), 2015 International Conference on

Conference_Location

Jeju

Type

conf

DOI

10.1109/35021BIGCOMP.2015.7072840

Filename

7072840