Database Reference
In-Depth Information
2
3
2
3
010001010
010001
1
1
2
1
2
2
0
1
0
4
5
4
5
C
ðÞ
¼ U
þ
p
ðÞ
¼
^
2
100001001
001
2
3
010001
1
4
1
4
100001001
1
2
4
5
C
ðÞ
¼
In matricified form, our Tucker tensor
P
then turns out to be
2
4
3
5
2
4
3
5
010001
1
4
1
4
100001001
1
2
10
10
01
P
ðÞ
¼ U
1
C
ðÞ
ð
Þ
¼
2
4
3
5
010001
1
4
1
2
1
4
P
ðÞ
¼
010001
1
4
1
4
100001001
1
2
Hence, the resulting transition probabilities are
2
4
3
5
010
001
1
4
2
4
3
5
100
001
001
P
ðÞ
¼ P
ðÞ
¼
P
ðÞ
¼
,
1
2
1
4
As compared to
P
, we see that the latter is approximated very well. Indeed,
P
ðÞ
and
P
ðÞ
for
i ¼
1,2 deviate from each other only in the last row, and for
i ¼
3 they
are even identical. The Frobenius error of our approximation turns out to be
r
3
4
F
¼
P P
0
:
:
87
Similarly, we may also choose a different partition. For example, we obtain for
G
1
¼
{1,3},
G
2
¼
{2}
2
4
3
5
1
2
1
2
2
4
3
5
0
010
001
1
2
P
ðÞ
¼ P
ðÞ
¼
P
ðÞ
¼
001
0
,
1
2
0
1
2
1
2
and the approximation error is higher,
