Joint Blind Source Separation Algorithm Based on Decomposition of Higher‐Order Cumulant Tensors

doi:10.12068/j.issn.1005-3026.2024.01.004

Abstract

CLC Number:

TN 911.7

Ce JI, Ming‐xin LIU. Joint Blind Source Separation Algorithm Based on Decomposition of Higher‐Order Cumulant Tensors[J]. Journal of Northeastern University(Natural Science), 2024, 45(1): 26-32.

Figures/Tables 11

Fig. 1 CPD and TTD of tensor

Fig. 2 Links between TTD and CPD

Fig. 3 CPD of core tensors

Fig. 4 Tensor graph of permutation and scaling ambiguities

Fig. 5 Adjacent core tensors

Table 1 Running time of algorithms under different numbers of datasets

（I，R，M）	TT-CPD	CP-ALS	CP-FastALS
（5，5，6）	0.452 5	0.580 8	0.090 8
（5，5，7）	0.505 9	1.754 1	0.148 0
（5，5，8）	0.628 5	3.074 8	0.346 7
（5，5，9）	1.410 2	11.071 6	1.837 2

Table 2 Running time of algorithms under different sizes of tensors

（I，R，M）	TT-CPD	CP-ALS	CP-FastALS
（5，4，7）	0.366 7	0.808 8	0.143 7
（7，4，7）	0.438 9	6.014 0	0.509 6
（9，4，7）	1.380 8	15.958 6	2.374 0
（11，4，7）	5.889 4	41.351 8	9.488 2

Fig. 6 Comparison of algorithms under different SNR

Fig. 7 Performance of TT‐CPD algorithm under different numbers of datasets

Fig. 8 Waveforms of signals of group 1

Table 3 Correlation coefficients of source signals and separated signals of 4 groups

信号组	$s (1)$	$s (2)$	$s (3)$	$s (4)$
1	0.998 4	0.998 9	0.997 2	0.986 3
2	0.999 5	0.998 1	0.997 2	0.987 8
3	0.999 6	0.996 5	0.999 2	0.992 2
4	0.998 6	0.996 6	0.996 1	0.995 3

Table 3 Correlation coefficients of source signals and separated signals of 4 groups

信号组	$s (1)$	$s (2)$	$s (3)$	$s (4)$
1	0.998 4	0.998 9	0.997 2	0.986 3
2	0.999 5	0.998 1	0.997 2	0.987 8
3	0.999 6	0.996 5	0.999 2	0.992 2
4	0.998 6	0.996 6	0.996 1	0.995 3

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