APPLICATION OF NEURAL NETWORKS IN THE
IDENTIFICATION OF MORPHOLOGICAL TYPES
Franjo Prot and Ksenija Bosnar
University of Zagreb
Ankica Ho{ek and Konstantin Momirovi}
Institute of criminological and sociological research
A sample of 737 healthy males, 19 to 27 years
old, fairly representative for the Yugoslav
population
of
this
age
and
gender,
was
described over a set of 23 morphological
characteristic selected so to assess factors of
longitudinal and transversal dimensions of
skeleton, muscular mass and fat tissue. An
algorithm for a neural network for cluster
analysis with coded name Triatlon was applied
in order to detect the morphological types. The
essence of the applied clustering algorithm is
a taxonomic neural network based on adaptive
multilayer perceptron as a core engine working
on
the
basis
of
starting
classification
obtained
by
a
rational
method
of
fuzzy
clustering of variables, and then of fuzzy
clustering
of
objects
described
on
fuzzy
clusters of variables. Triatlon conclude that
five clusters are necessary and sufficient for
the taxonomic description of this data set, and
that by only three hidden neurons can produce
an acceptable classification of objects. After
15 iteration Triatlon produce an excellent
fuzzy classification of variable, but initial
fuzzy clustering of objects is obtained after
71 iteration. However, multilayer perceptron
consider this classification as good, but not
satisfactory, and start learning process in
order to obtain a better classification. The
final classification is obtained after 24
learning attempts. However, coefficient of
efficacy of Triatlon in this case was only
0.920, markedly lower then in applications of
this program in other taxonomic problems. In
spite of complex position of types in the space
of manifest morphological characteristics and
not always clear pattern and structure of
discriminant factors obtained types can be
identified as follows:
(1)
Typus
asthenicus,
defined
by
low
development of skeleton, low muscular mass and
low fat tissue;
(2)
Typus
sthenicus,
defined
by
strong
development
of
skeleton,
high
amount
of
muscular mass and above average fat tissue due
to the high amount of fat cells;
(3) Typus gracilis, defined primarily by small
measures of transversal dimensions of skeleton;
(4)
Typus
disharmonicus,
defined
by
inconvergent
development
of
morphological
characteristics and low fat tissue;
(5) Typus leptomorphicus, defined by above
average development of longitudinal dimensions
of skeleton.
KEY WORDS
morphological types / neural networks / cluster analysis
1. INTRODUCTION
In a previous paper (Momirovi}, Ho{ek, Prot and
Bosnar, 2002) a sample of 737 healthy males, 19 to 27
years old, was described, by a procedure which minimize
error of measurement, by 23 anthropometric variables
Morphological types were determined by neural network
SIMTAX. The algorithm implemented in this network
classify objects in the standardized image space by
iterative application of Lebart's multilayer perceptron.
Initial classification was obtained on the basis of
position of objects on the envelope of hyperelipsoid
defined
by
Orthoblique
transformation
of
principal
components
of
data
matrix,
also
transformed
to
standardized image space. Dimensionality of latent, and
in the same time taxonomic space was determined by number
of spectral values greater then inflection point of their
distribution.
Three
taxon
were
obtained,
with
classification efficacy of 0.991 in image and 0.986 in
real space. First taxon, of 35% of examines, was
identified as sthenomorphia, second taxon, of 29% of
examines, as asthenomorphia, and third taxon, of 36% of
examines, as picnomorphia. Obtained taxons were similar,
but not identical, with taxons K, M and R obtained by a
method of fuzzy clustering applied by A. Ho{ek (1978) on
a set of 200 examines described by the same set of
anthropometric measurements, but not to the taxons
obtained by Zlobec (1975) by concurrent application of a
simple fuzzy clustering method and to taxons obtained by
Ward's method of hierarchical clustering and Friedman and
Rubin method of local optimization.
The aim of this paper is to present results of an
alternative attempt to solve the old and at yet unsolved
problem of morphological types by an other taxonomic
neural network who analyze objects in real space on the
basis
of
results
obtained
by
an
initial
fuzzy
classification similar to classification methods applied
in works of Zlobec (1975) and Ho{ek (1978).
2. METHODS
A sample of 737 healthy males, 19 to 27 years old,
fairly representative for the Yugoslav population of this
age and gender, was described over a set of 23
morphological characteristic, defined by the following
variables:
CODED NAME
WEIGHT
HEIGHT
LLENGTH
BIACRO
BICRIS
TRISKIN
SCAPSKIN
AXSKIN
CRUPARM
CRLWARM
CRUPLG
CRLWLG
HANDLG
HANDDM
ABDSKIN
LWLSKIN
CHCIRC
DIWRIST
DIAEL
DIAKNE
FOOTL
FOOTDM
ARMLG
VARIABLE
Body mass
Body height
Leg length
Biacromial span
Bicristal span
Triceps skinfold
Subcapular
skinfold
Axilar skinfold
Upper arm
circumference
Lower arm
circumference
Upper leg
circumference
Lower leg
circumference
Hand length
Hand diameter
Abdominal
skinfold
Lower leg
skinfold
Chest
circumference
Diameter of
wrist
Diameter of
elbow
Diameter of knee
Foot length
Diameter of foot
Arm length
An algorithm for a neural network for cluster
analysis with coded name Triatlon was applied in order to
detect the morphological types. The essence of the
applied clustering algorithm is a taxonomic neural
network based on adaptive multilayer perceptron as a core
engine working on the basis of starting classification
obtained by a rational method of fuzzy clustering of
variables, and then of fuzzy clustering
described on fuzzy clusters of variables.1
of
objects
3. RESULTS
Triatlon conclude that five clusters are necessary
and sufficient for the taxonomic description of this data
set, and that by only three hidden neurons can produce an
acceptable classification of objects. After 15 iteration
Triatlon produce an excellent fuzzy classification of
variable, but initial fuzzy clustering of objects is
obtained
after
71
iteration.
However,
multilayer
perceptron consider this classification as good, but not
satisfactory, and start learning process in order to
obtain a better classification. The final classification
is obtained after 24 learning attempts. The whole process
is presented, in an abbreviated form, in the following
tables.
Table 1. Starting input to hidden layer axons
WEIGHT
f1
.313
HEIGHT
.471
LLENGTH
.021
.250
BIACRO
f2
.91
9
.11
6
.62
0
.14
7
f3
.23
0
.44
5
.57
9
.03
1
Some other taxonomic neural networks were also applied. Hopfield
neural network Hoptax produces unsatisfactory clustering with
coefficient of efficacy of only .882. A perfect coefficient of
efficacy was obtained by neural network Dualtax, but with very
difficult identification of taxons defined in principal component
space. Similar results to these obtained by Triatlon were obtained by
Intruder, a very simple neural network, but identification structures
obtained by Triatlon are more informative then the structures
obtained by Intruder due to the intermediary fuzzy clustering of both
variables and subjects. Of course, both hierarchical methods and
classic methods of local optimization produce quite unsatisfactory
results; Ward method produces five clusters with coefficient of
efficacy of only .822, and McQueen's method produces five clusters
with a relatively good coefficient of efficacy (.917), but not
clearly defined in morphological space.
1
BICRIS
.327
TRISKIN
.038
SCAPSKIN
.042
AXSKIN
.092
CRUPARM
.040
CRLWARM
.201
CRUPLG
.600
CRLWLG
.058
HANDLG
.306
.322
HANDDM
ABDSKIN
LWLSKIN
.070
.195
CHCIRC
.074
DIWRIST
FOOTL
1.05
4
.025
1.05
3
.137
FOOTDM
.286
ARMLG
.113
DIAEL
DIAKNE
.12
6
.10
3
.01
5
.19
7
.34
1
.03
6
.14
5
.18
1
.28
4
.38
7
.26
5
.03
4
.23
6
.04
9
.00
4
.24
2
.31
9
.01
9
.19
9
.03
0
.02
4
.21
9
.00
1
.08
4
.12
8
.06
5
.00
1
.25
3
.31
8
.15
2
.01
2
.18
3
.12
5
.13
5
.02
5
.24
8
.15
6
.30
6
Table 2. Starting hidden layer to output axons
g1
f1 .44
9
g2
.23
6
g3
.17
2
f2 .33
1
.54
4
.52
1
.09
3
f3 .20
1
g4
.81
7
.15
2
.00
6
.73
6
g5
.21
4
.75
0
.38
2
Table 3. Initial and classification in first iteration
g1
g2
g3
g4
g5
g1 g2
g3 g4 g5
10
0
25
54 15
18 150
1
14
9
12
2
159 26 15
1
1
0
116 15
6
0
0
12 76
Table 4. Number of objects and accordance of starting
classifications
g1
g2
g3
g4
g5
numbe
r
104
192
214
133
94
progno
sis
54
150
159
116
76
accorda
nce
.519
.781
.743
.872
.809
Table 5. Final input to hidden layer axons
WEIGHT
g1
.767
g2
1.91
6
HEIGHT
.007
.785
LLENGTH
.118
.958
BIACRO
.015
.062
BICRIS
.011
.898
TRISKIN
.019
.631
g3
.83
4
.24
2
.09
7
.54
3
.15
5
.05
7
SCAPSKIN
.316
.936
AXSKIN
.469
.029
CRUPARM
.024
.098
CRLWARM
.352
.257
.258
CRLWLG
.112
.188
HANDLG
.070
.061
HANDDM
.250
ABDSKIN
LWLSKIN
.261
.168
1.11
0
.086
.178
CHCIRC
.074
DIWRIST
.946
DIAEL
.192
.346
DIAKNE
1.68
4
.023
.020
.064
.263
CRUPLG
FOOTL
FOOTDM
ARMLG
.993
.474
.578
.070
.078
1.49
3
.63
5
.18
0
.34
7
.26
7
.60
3
.02
5
.44
2
.43
9
.92
4
.03
8
.28
0
.21
9
.09
2
.28
8
.20
7
.24
5
.34
1
Table 6. Final hidden layer to output axons
g1
g1
.35
g2
.12
g3
.25
g4
.87
6
g5
.15
g2
g3
3
.05
8
.60
0
5
.00
1
.76
1
8
.69
8
.05
3
.12
8
.18
7
9
.71
2
.09
1
Fisherian
discriminant
analysis
in
the
whole
variable space2, incorporated in program, gives the
following identification structures:
Table 7. Centroids of final taxons
WEIGHT
HEIGHT
LLENGTH
BIACRO
BICRIS
TRISKIN
SCAPSKIN
AXSKIN
CRUPARM
CRLWARM
g1
.69
2
.26
6
.16
9
.64
1
.12
0
.34
4
.45
4
.24
5
.70
4
.48
0
g2
.860
.390
.356
.677
.332
.889
1.00
9
.841
.913
.733
g3
.43
2
.38
6
.54
6
.34
7
.15
9
g4
.075
g5
.07
0
.147
.29
4
.185
.45
7
.037
.11
5
.248
.07
5
.26
1
.19
7
.21
5
.20
7
.566
.20
8
.12
4
.06
9
.04
6
.480
.639
.193
.315
.09
0
.04
9
Identification structures in taxonomic algorithms must be, at least
initially, defined in the whole space of variables because necessary
inversion operations in intrataxon space can produce, in the case of
perfect or almost perfect classification, very unstable results due
to the possible weak conditionality of matrix of intrataxon
dispersion.
2
CRUPLG
CRLWLG
HANDLG
HANDDM
ABDSKIN
LWLSKIN
CHCIRC
DIWRIST
DIAEL
DIAKNE
FOOTL
FOOTDM
ARMLG
.78
1
.57
5
.38
9
.05
2
.13
9
.25
2
.57
1
.60
7
.43
6
.17
2
.869
.19
7
.00
9
.301
.04
6
.250
.701
.180
.099
.247
.537
.736
.172
.455
.753
.105
.31
0
.19
6
.54
7
.63
2
.22
5
.01
0
.109
.03
6
.137
.02
2
.59
5
.38
5
.86
8
.28
3
.11
9
.053
.49
6
.34
6
.63
9
.056
.174
.73
3
.039
.09
2
.246
.19
0
.04
7
.945
.25
4
.081
.03
1
1.55
7
.122
.37
7
.040
.18
8
.179
.57
0
.43
0
Table 8. Discriminant coefficients
WEIGHT
HEIGHT
LLENGTH
g1
.45
0
.05
0
.04
3
g2
.79
6
g3
.711
g4
.671
.21
4
.04
0
.612
.087
.589
.183
g5
1.90
8
.499
.759
BIACRO
BICRIS
TRISKIN
SCAPSKIN
AXSKIN
CRUPARM
CRLWARM
CRUPLG
CRLWLG
HANDLG
HANDDM
.38
6
.01
0
.09
9
.29
5
.14
2
.20
3
.18
8
.77
3
.02
7
.61
1
.41
3
ABDSKIN
.61
8
LWLSKIN
.04
8
.18
5
CHCIRC
DIWRIST
DIAEL
DIAKNE
.38
2
.13
2
.39
9
FOOTL
.12
8
FOOTDM
.32
.38
1
.007
.091
.055
.14
9
.02
7
.679
.080
.589
.444
.037
.440
.53
0
.922
.126
.443
.24
6
.26
2
.016
.436
.092
.012
.20
9
.20
2
.366
.255
.038
.555
.013
.914
.00
8
.188
.098
.086
.13
8
.203
.058
.160
.30
4
.69
1
.03
5
.652
.196
.873
.151
.064
.214
.043
.155
.193
.21
3
.07
8
.326
.094
.339
.712
.763
.202
.05
3
.172
.171
.294
.40
8
.242
.458
.16
0
-
.010
1.54
9
.014
.044
-
.101
-
.049
.080
0
ARMLG
.53
0
.08
7
.12
1
.138
1.14
3
.048
.045
.931
Table 9. Structure of discriminant functions
WEIGHT
HEIGHT
LLENGTH
BIACRO
BICRIS
TRISKIN
SCAPSKIN
AXSKIN
CRUPARM
CRLWARM
CRUPLG
CRLWLG
HANDLG
HANDDM
ABDSKIN
g1
.53
0
.20
3
.12
9
.49
0
.09
2
.26
3
.34
8
.18
8
.53
8
.36
7
.59
8
.44
0
.29
8
.03
9
.10
g2
.64
1
.29
1
.26
5
.50
5
.24
7
.66
3
.75
2
.62
7
.68
1
.54
6
.64
8
.52
3
.13
4
.07
4
.18
4
g3
.31
0
.27
7
.39
2
.24
9
.11
4
.05
4
.18
7
.14
1
.15
4
.14
9
.22
2
.14
1
.39
2
.45
3
.16
g4
.04
1
.07
9
.10
0
.02
0
.13
5
.30
7
.26
0
.34
6
.10
4
.17
1
.05
9
.07
4
.03
0
g5
.05
2
.09
4
.02
.54
4
.21
8
.33
9
.08
5
.15
4
.09
2
.05
1
.03
4
.06
7
.03
7
.02
7
.01
6
.44
2
.06
8
LWLSKIN
CHCIRC
DIWRIST
DIAEL
DIAKNE
FOOTL
FOOTDM
ARMLG
6
.19
3
.43
7
.46
4
.33
3
.13
1
.40
1
.54
9
.12
8
.33
9
.56
2
.15
0
.00
7
.22
4
.03
5
.18
7
.07
8
2
.00
7
.27
6
.62
3
.20
3
.08
5
.35
6
.24
9
.45
8
1
.13
3
.02
9
.51
2
.14
1
.03
5
.18
9
.04
4
.02
3
.84
4
.06
6
.02
2
.28
0
.09
7
.42
3
.31
9
.14
0
Table 10. Pattern of discriminant functions
g1
.17
2
.11
2
.02
5
g2
.48
4
.39
2
.09
7
.24
9
TRISKIN
.27
9
.70
0
SCAPSKIN
.33
9
.81
9
AXSKIN
.34
6
.69
6
WEIGHT
HEIGHT
LLENGTH
BIACRO
BICRIS
.19
2
.23
6
.25
5
g3
.27
9
.16
3
.30
7
.05
1
.04
8
.36
6
.53
0
.43
g4
.04
4
.07
2
.06
7
.06
7
.07
6
.16
4
.11
9
.18
g5
.06
5
.13
2
.12
4
.15
3
.20
8
.39
5
.45
9
.34
.22
4
.15
5
.45
4
.26
2
.71
3
.23
0
.09
8
.48
4
LWLSKIN
.17
9
.43
7
CHCIRC
.06
7
.15
7
.13
4
.11
5
.45
7
.09
5
.30
0
.14
2
.14
1
.22
6
CRUPARM
CRLWARM
CRUPLG
CRLWLG
HANDLG
HANDDM
ABDSKIN
DIWRIST
DIAEL
DIAKNE
FOOTL
FOOTDM
ARMLG
.38
8
.34
0
.32
5
.24
8
.07
1
.21
4
.10
9
.24
3
.44
1
.22
9
6
.14
9
.12
4
.03
3
.06
7
.20
4
.10
0
.22
0
.22
2
.30
2
.45
6
.16
1
.03
1
.20
0
.38
2
.39
6
4
.09
7
.13
8
.10
2
.08
5
.09
3
.10
9
.00
4
.05
8
.02
0
.35
0
.01
8
.58
9
.06
2
.06
4
.04
8
0
.09
5
.01
1
.12
2
.01
0
.71
3
.49
6
.08
7
.31
4
.12
0
.01
8
.02
7
.15
3
.20
1
.16
1
.12
1
Table 11. Correlations of discriminant functions
g1
g2
g3
g4
g5
.221
.251
g1 1.00
0
.615
.411
1.00
g2
.615
g3 .221
0
.106
g4
.411 .354
g5 .251
.094
.106
1.00
0
.308
.693
.354
.308
1.00
0
.273
.094
.693
.273
1.00
0
Table 12. Standardized discriminant coefficients
WEIGHT
HEIGHT
LLENGTH
BIACRO
BICRIS
TRISKIN
SCAPSKIN
AXSKIN
CRUPARM
CRLWARM
CRUPLG
CRLWLG
HANDLG
HANDDM
g1
.34
4
.03
8
.03
3
.29
5
.00
8
.07
6
.22
6
.10
9
.15
5
.14
4
.59
2
.02
1
.46
8
.31
6
g2
.59
3
g3
.51
0
g4
.36
4
g5
1.41
7
.371
.16
0
.03
0
.43
9
.04
7
.42
3
.00
5
.563
.11
1
.02
0
.48
7
.09
9
.04
9
.04
3
.31
9
.02
0
.326
.39
5
.66
2
.01
2
.06
9
.329
.23
6
.05
0
.13
8
.00
7
.009
.05
3
.03
1
.10
.064
.28
4
.18
3
.19
6
.15
5
.15
0
.07
2
.26
3
.00
6
.39
9
.13
5
.10
3
.14
6
.22
.46
.041
.437
.036
.028
.678
.118
.648
ABDSKIN
.47
3
LWLSKIN
.03
7
.14
2
CHCIRC
DIWRIST
DIAEL
DIAKNE
.29
2
.10
1
.30
5
FOOTL
.09
8
FOOTDM
.24
5
ARMLG
.40
6
Table 13.
6
.51
5
.02
6
8
.10
8
.15
9
.05
8
.05
1
.252
.41
3
.150
.03
9
.23
4
.51
1
.12
3
.09
2
.218
.30
4
.17
4
.340
.11
9
.06
5
.09
0
.00
7
.09
9
.82
0
.83
9
.00
7
.02
4
.036
.02
4
.691
.03
1
6
.03
5
.08
4
.159
.143
.059
Contingency matrix of Neural network and
Fisherian classification
g1
g2
g3
g4
g5
g1 g2
g3 g4 g5
0
3
0
3
110
0
4
0
5
162
14
4
0
136 0
1
4
0
137 2
17
2
0
0
133
Therefore,
classification
of
entities
in
morphological space is really a hard task for any
clustering algorithm, as can be seen from the measure of
efficacy of final classification obtained by Triatlon, a
taxonomic neural network with almost perfect behavior in
the classification of objects in other fields of
anthropological space (Momirovi}, 2002).
Table 14. Number of objects and efficacy of final
classification
g1
g2
g3
g4
g5
numbe
r
116
171
154
144
152
progno
sis
110
162
136
137
133
erro
r
6
9
18
7
19
Coefficient of efficacy of Triatlon in this case was
only 0.920, markedly lower then in other applications of
this program in biochemistry, physiology, psychology,
sociology and criminology.
However, in spite of complex position of types in
the space of manifest morphological characteristics and
not always clear pattern and structure of discriminant
factors obtained types can be identified as follows:
(1) Typus asthenicus, defined by low development of
skeleton, low muscular mass and low fat tissue;
(2) Typus sthenicus, defined by strong development of
skeleton, high amount of muscular mass and above average
fat tissue due to the high amount of fat cells;
(3) Typus gracilis, defined primarily by small measures
of transversal dimensions of skeleton;
(4)
Typus
disharmonicus,
defined
by
inconvergent
development of morphological characteristics and low fat
tissue;
(5) Typus leptomorphicus, defined by above average
development of longitudinal dimensions of skeleton.
Therefore, morphological types in real space are
differnt of those obtained in image space by Momirovi},
Ho{ek, Prot and Bosnar (2002) but are similar, altough
not identical, with taxons obtained by method of fuzzy
clustering applied by A. Ho{ek (1978).
4. DISCUSSION
It seems, in any case, that manifes morphological
space is not an ideal envinronment for the determination
of morphological types. Some reasons for this apparently
paradoxical statment is the true nature of anthropometric
variables. Namely, most of them are partially included
one to other to an udetermined manner, and most of them,
altough manifestly different, have the same genetical
origin. This results in very uncertain position of
objects
in
the
space
of
manifest
morphological
characteristics, partly because of latent degeneration of
this space due to the near singularity of some of
segments spanned by specific morphological vectors.
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osnov
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