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1.1
5
Number of clusters
ATTA-C
K-means
average link
1D-som
1
F-Measure
(b) Number of clusters
0.9
0.8
0.7
0.6
0.5
10
9
8
7
6
5
4
3
2
1
0
4
ATTA-C
Gap statistic
10
9
8
7
6
5
4
Distance between cluster centres
Distance between cluster centres
k36%& iªÝ4,B$! (>57?Z!*f,B&757?/ 36$%5u$!,m/4.-83*j/157?iAaD/jN+5>/4f?6&7*X/4+?5F/4+ *
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0.25
0.25
0.2
0.2
0.25
0.2
0.15
0.15
0.15
0.1
0.1
0.1
0.05
0.05
0.05
0
-10
-5
0
5
10
15
0
-10
-5
0
5
10
15
0
-10
-5
0
5
10
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7{04Hj0]Q/ `caD
7{4HnO5C-/4^`ba
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(a) F−Measure
1.15
5
1.05
1
Number of clusters
ATTA-C
K-means
average link
1D-som
1.1
F-Measure
(b) Number of clusters
0.95
0.9
0.85
0.8
0.75
ATTA-C
Gap statistic
4
3
2
1
0.7
0.65
2
3
4
5
6
7
8
Ratio between cluster sizes
9
0
10
2
3
4
5
6
7
8
Ratio between cluster sizes
9
10
k36%& OÝ4,B$! (>57?%*fw,B&57?D/43'$!5;$,/47> /43'$wAaD/jN+5;?D'&7*j/ O*43'+*s$!5e/4
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3'-58_
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Dermatology : F−Measure
Dermatology : Dunn Index
6.5
6.0
5.5
5.0
4.5
4.0
3.5
0.95
0.90
0.85
0.80
0.75
ATTA
AV
KM
SM
ATTA
Digits : F−Measure
0.75
0.70
0.65
0.60
0.55
0.50
0.45
KM
SM
3.0
2.5
2.0
KM
SM
ATTA
AV
KM
1.5
1.0
0.5
ATTA
AV
KM
SM
ATTA
Wine : F−Measure
AV
KM
SM
2.5
0.970
0.970
0.968
0.968
0.966
0.966
ATTA
AV
KM
SM
5.5
5.4
5.3
5.2
5.1
5.0
4.9
Yeast : F−Measure
0.45
0.40
0.35
ATTA
AV
KM
AV
KM
SM
ATTA
AV
KM
SM
AV
KM
8.365
8.365
ATTA
AV
KM
SM
Yeast : 10.0−Variance
ATTA
Zoo : Dunn Index
AV
KM
SM
Zoo : 10.0−Variance
7.8
7.6
7.4
7.2
7.0
6.8
3
SM
SM
Wisconsin : 10.0−Variance
SM
4
KM
KM
8.4
8.3
8.2
8.1
8.0
7.9
7.8
5
AV
AV
8.375
8.375
8.370
8.370
6
ATTA
ATTA
8.385
8.385
8.380
8.380
ATTA
Zoo : F−Measure
SM
7.1
ATTA
Yeast : Dunn Index
SM
KM
7.2
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.50
AV
Wine : 10.0−Variance
Wisconsin : Dunn Index
Wisconsin : F−Measure
0.972
0.972
SM
7.3
3.0
KM
KM
7.4
3.5
AV
ATTA
Wine : Dunn Index
4.0
ATTA
AV
Iris : 10.0−Variance
SM
4.5
0.95
0.90
0.85
0.80
0.75
0.70
SM
9.0
8.8
8.6
8.4
8.2
2.0
0.6
ATTA
Iris : Dunn Index
2.5
0.7
KM
Digits : 10.0−Variance
SM
3.0
0.8
AV
7.8
7.6
7.4
7.2
7.0
3.5
AV
ATTA
Digits : Dunn Index
Iris : F−Measure
0.90
0.85
0.80
0.75
0.70
0.65
0.60
AV
4.0
ATTA
Dermatology : 10.0−Variance
6.2
6.1
6.0
5.9
5.8
5.7
ATTA
AV
ð
KM
SM
ATTA
AV
KM
SM
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(b) 2D−SOM
0.6
Standard deviation
Overall correlation
Intra−cluster correlation
Inter−cluster correlation
0.8
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
Mean correlation
Mean correlation
Standard deviation
(a) Multidimensional scaling
10
Overall correlation
Intra−cluster correlation
Inter−cluster correlation
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
10
9
8
7
6
5
4
Distance between cluster centres
(d) Random lower bound
Standard deviation
Overall correlation
Intra−cluster correlation
Inter−cluster correlation
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
Mean correlation
Mean correlation
Standard deviation
(c) ATTA−TM
10
9
8
7
6
5
4
Distance between cluster centres
9
8
7
6
5
4
Distance between cluster centres
Overall correlation
Intra−cluster correlation
Inter−cluster correlation
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
10
9
8
7
6
5
4
Distance between cluster centres
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(a) Multidimensional scaling
(b) 2D−SOM
(c) ATTA−TM
(d) Random lower bound
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