Information Technology Reference
In-Depth Information
8
<
0
1
0
1
9
=
0:405 0:845
0 0:14 0:04
0:14 0 0:02
0:04 0:02 0
@
A
;
@
A
C
0:405
0:155
:
;
0:845 0:155
8
<
9
=
0
1
0
1
0:405 0:845
0 0:14 0:04
0:14 0 0:04
0:04 0:04 0
@
A
;
@
A
C
0:405
0:845
:
;
0:845 0:845
8
<
9
=
0
1
0
1
0:595 0:155
0 0:16 0:02
0:16 0 0:02
0:02 0:02 0
@
A
;
@
A
C
0:595
0:155
:
;
0:155 0:155
8
<
9
=
0
1
0
1
0:595 0:155
0 0:16 0:02
0:16 0 0:04
0:02 0:04 0
@
A
;
@
A
C
0:595
0:845
:
;
0:155 0:845
<
=
0
1
0
1
0:595 0:845
0 0:16 0:04
0:16 0 0:02
0:04 0:02 0
@
A
;
@
A
C
0:595
0:155
:
;
0:845 0:155
8
<
9
=
0
1
0
1
0:595 0:845
0 0:16 0:04
0:16 0 0:04
0:04 0:04 0
@
A
;
@
A
C
0:595
0:845
:
;
0:845 0:845
W
i
is taken to be the norm
Using Lemma
3
, the membership
i
of each matrix
jjL
1
jj
of the matrix with elements the membership values of the weights
w
ij
,
N.N1/2
N
1
.
P
iD1
P
jD1
j.
w
ij
/j/. According to Sect.
10.2.1
this gives W D
1
W
1
C
2
W
2
C C
8
W
8
, where the membership
i
are:
1
D 0:0596,
2
D 0:1171,
3
D 0:1171,
4
D 0:1746,
5
D 0:0754,
6
D 0:1329,
7
D 0:1329, and
8
D 0:1904. By calculating the eigenvectors of matrices W
i
,
the associated memory patterns can be found. These are non-observable attractors
different from the attractors
u
1
,
u
2
, and
u
3
of the initial weight matrix W . Thus, the
number of memory patterns is increased by a factor 2
N
1
i.e.
D 8.
The eigenstructure analysis of matrix W
1
gives:
1
D0:14,
2
D 0:1455,
3
D0:0055, with associated eigenvectors
v
W
1
1
D Œ0:7071; 0:7071; 0
T
,
v
W
1
2
D
Œ0:6941; 0:6941; 0:1908
T
, and
v
W
3
D Œ0:1349; 0:1349; 0:9816
T
.
The eigenstructure analysis of matrix W
2
gives:
1
D0:1415,
2
D0:0104,
3
D 0:1519, with associated eigenvectors
v
W
2
1
D Œ0:6921; 0:7143; 0:1041
T
,
v
W
2
D Œ0:2648; 0:1176; 0:9572
T
, and
v
W
3
D Œ0:6715; 0:6900; 0:2701
T
.
The eigenstructure analysis of matrix W
3
gives:
1
D0:1415,
2
D0:0104,
3
D 0:1519, with associated eigenvectors are
v
W
3
1
D Œ0:7143; 0:6921; 0:1041
T
,
v
W
3
2
D Œ0:1170; 0:2648; 0:9572
T
, and
v
W
3
3
D Œ0:6715; 0:6900; 0:2701
T
.
