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Table 2.
Performance of the Support Vector Machine classifier in free groups
F
3
,
F
5
,
F
10
,
F
15
and
F
20
.
All elements
Elements with
|
w
|
>
100
Kernel
F
3
F
5
F
10
F
15
F
20
F
3
F
5
F
10
F
15
F
20
K
1
.844 .805 .729 .676 .644 .859 .810 .738 .680 .648
K
2
.995 .978 .881 .782 .710 .999 .977 .880 .792 .711
K
3
.996 .988 .962 .888 .772 1.00 .996 .968 .894 .773
K
4
.996 .989 .984 .951 .832 1.00 .997 .991 .956 .834
K
e
.995 .986 .982 .988 .990 1.00 .999 .999 .998 .995
a) accuracy evaluated on the set
S
e
;
All elements
Elements with
|
w
|
>
100
Kernel
F
3
F
5
F
10
F
15
F
20
F
3
F
5
F
10
F
15
F
20
K
1
.806 .783 .760 .670 .676 .818 .798 .768 .717 .687
K
2
.993 .988 .885 .811 .750 .997 .971 .893 .814 .751
K
3
.994 .993 .969 .893 .809 1.00 .998 .976 .897 .810
K
4
.995 .993 .993 .954 .866 1.00 .998 .997 .957 .870
K
e
.995 .993 .985 .986 .989 1.00 1.00 .999 .999 .994
b) accuracy evaluated on the set
S
10
;
All elements
Elements with
|
w
|
>
100
Kernel
F
3
F
5
F
10
F
15
F
20
F
3
F
5
F
10
F
15
F
20
K
1
.880 .833 .743 .710 .691 .915 .887 .768 .729 .727
K
2
.990 .986 .890 .812 .754 .999 .969 .903 .830 .790
K
3
.991 .991 .961 .893 .824 1.00 .996 .985 .911 .842
K
4
.992 .991 .973 .940 .867 1.00 .997 .999 .970 .883
K
e
.990 .986 .980 .973 .970 1.00 1.00 .999 .989 .973
c) accuracy evaluated on the set
S
R
;
All elements
Elements with
|
w
|
>
100
Kernel
F
3
F
5
F
10
F
15
F
20
F
3
F
5
F
10
F
15
F
20
K
1
.732 .798 .770 .694 .610 .674 .682 .769 .690 .612
K
2
.999 .997 .824 .722 .610 .993 .993 .785 .723 .626
K
3
1.00 1.00 .915 .777 .632 1.00 1.00 .877 .756 .648
K
4
1.00 1.00 .982 .821 .659 1.00 1.00 .985 .816 .665
K
e
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
d) accuracy evaluated on the set
S
P
.
grows, quadratic mapping does not guarantee the high classification accuracy.
As one might expect, the accuracy increases when the degree of the polynomial
mapping increases. Nevertheless, even with the polynomial kernel
K
4
of the de-
gree
d
= 4, Support Vector Machine is not able to perform accurate classification
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