Signal Processing - May 2016 - 97
where S [1] = [s 1; s 3; s 2; s 4], S [2] = [s 1; s 3; s *2; s 5], and S [3] =
*
**
[s 1; s 3; s**
2 ; s 6] with the size 4 × 1,000. s 2 and s 2 denote the
five-point and 10-point delayed versions of s 2 , respectively.
This is slightly different from the source configuration of the
simulation in [48]. The underlying sources in each data set are
shown in Figure 4(a). The sources s 1, s 2 , and s 3 exist in all
data sets, representing common information across them. The
where n denotes the sample index vector, valued from 1 to
1,000, and s i (i = 1, 2, ..., 6) represents six simulated sources. Note that here s i is a row vector. Three mixed data sets
X [1], X [2] , and X [3] were generated as follows, with each column denoting one observation in their respective data set:
X [m] = A [m] · S [m], m = 1, 2, 3,
5
s [1]
5
500
-5
1,000 0
5
500
1,000
500
-5
1,000 0
5
500
1,000
0
-5
0
5
500
500
1,000
500
-5
1,000 0
5
500
1,000
500
1,000
500
-5
0
1,000
5
500
1,000
500
-5
1,000 0
5
500
1,000
500
-5
1,000 0
5
500
1,000
0
-5
0
5
0
0
∼
S [1]
5
0
-5
0
5
500
500
1,000
-5
0
5
500
1,000
-5
0
5
500
-5
1,000 0
0
-5
0
5
5
∼
S [1]
∼
S [3]
500
500
1,000
-5
0
5
500
1,000
-5
0
5
500
-5
1,000 0
0
5
0
-5
0
5
500
500
1,000
-5
0
5
500
1,000
-5
0
5
500
-5
1,000
0
500
-5
1,000 0
5
500
1,000
500
-5
1,000 0
5
500
-5
1,000 0
0
0
1,000
500
-5
1,000 0
5
0
-5
0
5
-5
0
5
1,000
-5
0
5
500
1,000
-5
0
0
-5
0
∼
S [2]
5
500
-5
0
1,000
5
500
1,000
500
500
1,000
500
-5
1,000 0
5
500
1,000
0
-5
0
5
-5
0
∼
S [3]
1,000
500
-5
1,000 0
5
∼
S [1]
∼
S [3]
5
500
500
1,000
500
-5
1,000 0
5
500
-5
1,000 0
5
5
0
-5
1,000 0
5
500
-5
1,000
0
5
-5
0
5
500
1,000
-5
0
0
1,000
500
-5
1,000 0
5
0
500
-5
0
1,000
5
500
1,000
500
-5
0
1,000
5
500
-5
0
1,000
500
-5
1,000 0
5
500
1,000
-5
0
5
500
1,000
-5
0
5
500
-5
1,000 0
0
0
-5
0
5
1,000
-5
0
5
500
1,000
-5
0
500
1,000
-5
0
5
500
1,000
-5
0
0
∼
S [2]
∼
S [3]
5
5
0
sICA
jICA
MCCA
1,000
500
1,000
500
1,000
0
∼
S [2]
-5
0
5
∼
S [3]
0
500
-5
1,000 0
5
500
1,000
-5
0
5
500
1,000
-5
0
5
500
-5
1,000 0
500
1,000
500
1,000
500
1,000
500
1,000
0
0
0
1,000
500
-5
1,000 0
5
-5
0
5
500
1,000
500
-5
1,000
0
5
0
1,000
-5
0
5
500
1,000
-5
0
5
0
1,000
500
-5
1,000 0
5
1,000
-5
0
5
500
1,000
-5
0
0
5
1,000
500
-5
1,000 0
5
1,000
-5
0
5
500
1,000
-5
0
0
500
1,000
500
1,000
500
1,000
500
1,000
0
0
500
∼
S [3]
0
-5
0
5
500
0
0
500
∼
S [2]
0
-5
0
5
500
0
0
500
∼
S [1]
0
-5
0
5
500
(h)
Methods
Data
Sets
1,000
500
(f)
0
(g)
500
-5
0
5
0
0
0
0
0
500
500
-5
1,000 0
5
1,000
0
0
0
0
0
0
0
-5
0
5
500
1,000
0
0
-5
0
5
0
1,000
0
1,000
5
0
-5
0
5
500
0
500
∼
S [1]
500
500
(c)
0
5
500
0
-5
0
∼
S [3]
0
-5
1,000 0
5
0
0
0
5
0
-5
0
5
0
-5
0
0
0
0
-5
0
5
500
0
500
1,000
∼
S [2]
0
-5
1,000 0
5
(e)
0
0
1,000
0
-5
0
5
0
0
0
-5
0
5
500
500
500
0
0
-5
1,000
0
5
0
0
∼
S [1]
500
-5
1,000 0
5
500
-5
1,000
0
5
0
-5
0
5
5
(d)
5
1,000
5
0
∼
S [2]
5
0
-5
1,000 0
5
0
0
-5
0
∼
S [2]
0
0
-5
0
5
500
∼
S [1]
(b)
0
-5
1,000 0
5
500
0
-5
0
5
0
-5
1,000 0
5
0
-5
0
X [3]
5
0
-5
0
5
(a)
5
X [2]
0
500
0
-5
0
5
0
-5
1,000
0
5
0
0
-5
0
-5
0
5
X [1]
5
0
0
0
-5
0
s [3]
0
-5
1,000 0
5
0
-5
0
5
0
-5
0
5
5
0
0
-5
0
5
s [2]
(3)
0
500
1,000
-5
0
5
500
1,000
-5
0
0
0
(i)
JDIAG-SOS
MCCA+jICA
IVA-G IVA-GL
X[1]
0.4942
0.7724
0.7745
0.8462
0.9868
0.9962 0.9856
X[2]
0.2880
0.5850
0.7846
0.8412
0.9841
0.9951 0.9804
X[3]
0.0118
0.9830
0.8095
0.8422
0.9886
0.9889 0.9817
(j)
FIGure 4. The original sources in the three mixed data sets and the recovered sources by employing seven different methods: (a) true sources, (b) mixed
data sets, (c) sICA, (d) jICA, (e) MCCA, (f) JDIAG-SOS, (g) MCCA+jICA, (h) IVA-G, and (i) IVA-GL. (j) A reference for performance comparisons among
the different methods.
IEEE Signal Processing Magazine
|
May 2016
|
97
Table of Contents for the Digital Edition of Signal Processing - May 2016
Signal Processing - May 2016 - Cover1
Signal Processing - May 2016 - Cover2
Signal Processing - May 2016 - 1
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Signal Processing - May 2016 - Cover3
Signal Processing - May 2016 - Cover4
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