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
Signal Processing - May 2016 - 2
Signal Processing - May 2016 - 3
Signal Processing - May 2016 - 4
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Signal Processing - May 2016 - Cover3
Signal Processing - May 2016 - Cover4
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