Fast PARAFAC decomposition with application to polarization sensitive array parameter estimations

doi:10.21629/JSEE.2018.04.06

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (4): 714-722.doi: 10.21629/JSEE.2018.04.06

• Electronics Technology • Previous Articles Next Articles

Fast PARAFAC decomposition with application to polarization sensitive array parameter estimations

Yang LI*()

The 10th Research Institute, China Electronics Technology Group Corporation, Chengdu 610036, China

Received:2017-04-11 Online:2018-08-01 Published:2018-08-30
Contact: Yang LI E-mail:yangleecool@qq.com
About author:LI Yang was born in 1987. He received his B.S. degree and Ph.D. degree in electronic engineering from Fudan University, Shanghai, China, in 2009 and 2014 respectively. He is an algorithm engineer at the 10th Research Institute of China Electronics Technology Group Corporation, Chengdu. His research interests are in the areas of array signal processing, high-resolution parameter estimation, as well as numerical linear and multilinear algebra. E-mail: yangleecool@qq.com
Supported by:
the National Natural Science Foundation of China(61571131);the Technology Innovation Fund of the 10th Research Institute of China Electronics Technology Group Corporation(H17038.1);This work was supported by the National Natural Science Foundation of China (61571131), and the Technology Innovation Fund of the 10th Research Institute of China Electronics Technology Group Corporation (H17038.1)

Abstract

Abstract:

In tensor theory, the parallel factorization (PARAFAC) decomposition expresses a tensor as the sum of a set of rank-1 tensors. By carrying out this numerical decomposition, mixed sources can be separated or unknown system parameters can be identified, which is the so-called blind source separation or blind identification. In this paper we propose a numerical PARAFAC decomposition algorithm. Compared to traditional algorithms, we speed up the decomposition in several aspects, i.e., search direction by extrapolation, suboptimal step size by Gauss-Newton approximation, and linear search by n steps. The algorithm is applied to polarization sensitive array parameter estimation to show its usefulness. Simulations verify the correctness and performance of the proposed numerical techniques.

Key words: tensor decomposition, parallel factorization (PARAFAC), alternating least squares (ALS), polarization sensitive array (PSA)

Yang LI. Fast PARAFAC decomposition with application to polarization sensitive array parameter estimations[J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 714-722.

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References 19

1	SIDIROPOULOS N D, GIANNAKIS G, BRO B R. Blind PARAFAC receivers for DS-CDMA systems. IEEE Trans. on Signal Processing, 2010, 48(3): 810-823.
2	SIDIROPOULOS N D, BRO R, GIANNAKIS G B. Parallel factor analysis in sensor array processing. IEEE Trans. on Signal Processing, 2000, 48(8): 2377-2388.
3	LI X C, XU Y G, LIU Z W. Tucker tensor based regularized polarimetric ESPRIT. Systems Engineering and Electronics, 2017, 39 (4): 700- 706. doi: 10.3969/j.issn.1001-506X.2017.04.02
4	SI W J, YU F, QU Z Y, et al. Real-value tensor ESPRIT algorithm based on characteristics of non-circular signals. Systems Engineering and Electronics, 2016, 38 (9): 1975- 1980. doi: 10.3969/j.issn.1001-506X.2016.09.02
5	AI X F, LUO Y J, ZHAO G Q. Underdetermined blind separation of radar signals based on tensor decomposition. Systems Engineering and Electronics, 2016, 38 (11): 2505- 2509.
6	SIDIROPOULOS N D, BRO R. On the uniqueness of multilinear decomposition of N-way arrays. Journal of Chemometrics, 2000, 14 (3): 229- 239. doi: 10.1002/1099-128X(200005/06)14:3<229::AID-CEM587>3.0.CO;2-N
7	ZHANG X F, XU D Z. Blind PARAFAC signal detection for polarization sensitive array. Eurasip Journal on Advances in Signal Processing, 2007, 2007 (1): 1- 7. doi: 10.1155/2007/12025
8	HARSHMAN R A. Foundations of the PARAFAC procedure: models and conditions for an "explanatory" multi-modal factor analysis. UCLA Working Papers in Phonetics, 1970, 16, 1- 84.
9	CARROLL J D, CHANG J J. Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition. Psychometrika, 1970, 35 (3): 283- 319. doi: 10.1007/BF02310791
10	TOMASI G, BRO R. A comparison of algorithms for fitting the PARAFAC model. Computational Statistics & Data Analysis, 2006, 50 (7): 1700- 1734.
11	BRO R. Multi-way analysis in the food industry-models, algorithms, and applications. Amsterdam, Netherlands: University of Amsterdam, 1998.
12	RAJIH M, COMON P, HARSHMAN R A. Enhanced line search: a novel method to accelerate PARAFAC. SIAM Journal on Matrix Analysis and Applications, 2008, 30 (3): 1128- 1147. doi: 10.1137/06065577
13	NION D, DE LATHAUWER L. An enhanced line search scheme for complex-valued tensor decompositions. Application in DS-CDMA. Signal Processing, 2008, 88 (3): 749- 755.
14	CHEN Y N, HAN D R, QI L Q. New ALS methods with extrapolating search directions and optimal step size for complex-valued tensor decompositions. IEEE Trans. on Signal Processing, 2011, 59(12): 5888-5898.
15	BRO R, SIDIROPOULOS N D, GIANNAKIS G B. A fast least squares algorithm for separating trilinear mixtures. Proc. of the International Workshop on Independent Component Analysis and Blind Separation, 1999: 11-15.
16	PAATERO P. A weighted non-negative least squares algorithm for three-way PARAFAC factor analysis. Chemometrics and Intelligent Laboratory Systems, 1997, 38 (2): 223- 242. doi: 10.1016/S0169-7439(97)00031-2
17	ANDERSSON C A, BRO R. The N-way toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems, 2000, 52 (1): 1- 4.
18	NEHORAI A, PALDI E. Vector-sensor array-processing for electromagnetic source localization. IEEE Trans. on Signal Processing, 1994, 42(2): 376-398.
19	KAY S M. Fundamentals of statistical signal processing. Englewood Cliffs: Prentice-Hall PTR, 1993.

Fast PARAFAC decomposition with application to polarization sensitive array parameter estimations

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