Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation

CHENG Guanghui; MIAO Jifei; LI Wenrui

doi:10.23919/cje.2019.00.102

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CHENG Guanghui, MIAO Jifei, LI Wenrui, “Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation,” Chinese Journal of Electronics, in press, doi: 10.23919/cje.2019.00.102, 2022.

Citation:

CHENG Guanghui, MIAO Jifei, LI Wenrui, “Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation,” Chinese Journal of Electronics, in press, doi: 10.23919/cje.2019.00.102, 2022.

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Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation

doi: 10.23919/cje.2019.00.102

CHENG Guanghui^1
,,
MIAO Jifei^{1, 2
,},
LI Wenrui^3
,

1.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2.
Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau 999078, China
3.
School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Funds: This work is supported by the National Natural Science Foundation of China (No.11671023).

More Information

Author Bio:
was born in Jilin, China, in 1979. He received the Ph.D. degree in applied mathematics from University of Electronic Science and Technology of China, Sichuan, China, in 2008. He is currently a professor with University of Electronic Science and Technology of China, Sichuan, China. His current research interests include matrix computation, matrix and tensor decomposition, signal processing and image processing. (Email: ghcheng@uestc.edu.cn)

was born in Sichuan, China, in 1992. Jifei Miao received the M.S. degree in the School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, China. He is pursuing the Ph.D. degree in the University of Macau, Macau, China. His current research interests include quaternion algebra, matrix and tensor calculations, image and signal processing (Email: jifmiao@163.com)

was born in Sichuan, China, in 1999. He received the B.S. degree in the School of Information and Software Engineering, University of Electronic Science and Technology of China, Sichuan, China. His current research interests include matrix decomposition and machine learning. (Email: 944683243@qq.com)
Received Date: 2019-04-01
Available Online: 2021-11-05

Abstract

Abstract

We consider the general problem of the approximate joint diagonalization of a set of non-Hermitian matrices. This problem mainly arises in the data model of the joint blind source separation for two datasets. Based on a special parameterization of the two diagonalizing matrices and on adapted approximations of the classical cost function, we establish two Jacobi-like algorithms. They may serve for the canonical polyadic decomposition (CPD) of a third-order tensor, and in some scenarios they can outperform traditional CPD methods. Simulation results demonstrate the competitive performance of the proposed algorithms.
- Joint diagonalization,
- Joint blind source separation,
- Canonical polyadic decomposition,
- Non-Hermitian matrix

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References(31)

References

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