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, 1
9 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 cluste
rs 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, bu
t 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 manife
st 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 s
thenicus, 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 dis
harmonicus, 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 / c
luster 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
Morphol
ogical 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 o
f
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 t
axon, 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 e
xamines 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 po
pulation of this
age and gender, was described over a set of 23
morphological characteristic, defined by the following
variables:
CODED NAME
VARIABLE
WEIGHT
Body mass
HEIGHT
Body height
LLENGTH
Leg length
BIACRO
Biacromial span
BICRIS
Bicristal span
TRISKIN
Triceps skinfold
SCAPSKIN
Subcapular
skinfold
AXSKIN
Axilar skinfold
CRUPARM
Upper arm
circumference
CRLWARM
Lower arm
circumference
CRUPLG
Upper leg
circumference
CRLWLG
Lower leg
circumference
HANDLG
Hand length
HANDDM
Hand diameter
AB
DSKIN
Abdominal
skinfold
LWLSKIN
Lower leg
skinfold
CHCIRC
Chest
circumference
DIWRIST
Diameter of
wrist
DIAEL
Diameter of
elbow
DIAKNE
Diameter of knee
FOOTL
Foot length
FOOTDM
Diameter of foot
ARMLG
Arm length
An algorithm for a neural networ
k 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 ba
sis 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.
1
3. RESULTS
Triatlon conclude that five clusters are necessary
and s
ufficient 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 cluste
ring 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
f1
f2
f3
WEIGHT
.313
-
.91
9
.23
0
HEIGHT
-
.471
-
.11
6
-
.44
5
LLENGTH
-
.021
.62
0
.57
9
BIACR
O
-
.250
-
.14
7
-
.03
1
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 obtai
ned 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
obtai
ned 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 unsatisfacto
ry
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.
BICRIS
.327
-
.12
6
-
.03
0
TRISKIN
.038
-
.10
3
-
.02
4
SCAPSKIN
.042
-
.01
5
.21
9
AXSKIN
.092
-
.19
7
-
.00
1
CRUPARM
.040
-
.34
1
-
.08
4
CRLWARM
.201
-
.03
6
.12
8
CRUPLG
-
.600
-
.14
5
.06
5
CRLWLG
-
.058
-
.18
1
.00
1
HANDLG
-
.306
.28
4
.25
3
HANDDM
.
322
.38
7
.31
8
ABDSKIN
-
.070
.26
5
.15
2
LWLSKIN
.195
-
.03
4
-
.01
2
CHCIRC
-
.074
-
.23
6
-
.18
3
DIWRIST
-
1.05
4
-
.04
9
.12
5
DIAEL
-
.025
.00
4
.13
5
DIAKNE
1.05
3
.24
2
.02
5
FOOTL
.137
.31
9
.24
8
FOOTDM
.286
-
.01
9
.15
6
ARMLG
.113
.19
9
.30
6
Table 2. Starting hid
den layer to output axons
g1
g2
g3
g4
g5
f1
.44
9
.23
6
.17
2
-
.81
7
-
.21
4
f2
.33
1
-
.54
4
.09
3
-
.15
2
.75
0
f3
.20
1
.52
1
-
.73
6
.00
6
.38
2
Table 3. Initial and classification in first iteration
g1
g2
g3
g4
g5
g1
54
15
10
0
25
g2
18
150
1
14
9
g3
12
2
15
9
26
15
g4
1
1
0
116
15
g5
6
0
0
12
76
Table 4. Number of objects and accordance of starting
classifications
numbe
r
progno
sis
accorda
nce
g1
104
54
.519
g2
192
150
.781
g3
214
159
.743
g4
133
116
.872
g5
94
76
.809
Table 5. Final input to hi
dden layer axons
g1
g2
g3
WEIGHT
.767
1.91
6
-
.83
4
HEIGHT
.007
.785
.24
2
LLENGTH
-
.118
-
.958
-
.09
7
BIACRO
.015
.062
-
.54
3
BICRIS
.011
.898
.15
5
TRISKIN
.019
.631
-
.05
7
SCAPSKIN
.316
-
.936
-
.63
5
AXSKIN
-
.469
-
.029
-
.18
0
CRUPARM
-
.024
-
.098
-
.34
7
CRLWARM
-
.352
.258
.26
7
CRUPLG
.257
-
.993
-
.60
3
CRLWLG
-
.112
.188
-
.02
5
HANDLG
.070
.061
-
.44
2
HANDDM
-
.250
-
1.11
0
.43
9
ABDSKIN
-
.261
-
.086
.92
4
LWLSKIN
.168
.178
-
.03
8
CHCIRC
.074
-
.474
.28
0
DIWRIST
.946
-
.578
-
.21
9
DIAEL
.192
.346
-
.09
2
DIAKNE
-
1.68
4
-
.263
-
.28
8
FOOTL
-
.023
-
.070
.20
7
FOOTDM
-
.020
-
.078
.24
5
ARMLG
-
.064
-
1.49
3
.34
1
Table 6. Final hidden layer to output axons
g1
g2
g3
g4
g5
g1
-
.35
-
.12
-
.25
.87
6
-
.15
3
5
8
9
g2
-
.05
8
-
.00
1
.69
8
.05
3
-
.71
2
g3
.60
0
-
.76
1
.12
8
.18
7
.09
1
Fisherian discriminant analysis in the whole
variable space
2
, incorporated in program, gives the
following identification structures:
Table 7. Centroids of final taxons
g1
g2
g3
g4
g5
WEIGHT
-
.69
2
.860
-
.43
2
-
.075
.07
0
HEIGHT
-
.26
6
.390
-
.38
6
-
.14
7
.29
4
LLENGTH
-
.16
9
.356
-
.54
6
-
.185
.45
7
BIACRO
-
.64
1
.677
-
.34
7
-
.037
.11
5
BICRIS
-
.12
0
.332
.15
9
-
.248
-
.20
8
TRISKIN
-
.34
4
.889
-
.07
5
-
.566
-
.12
4
SCAPSKIN
-
.45
4
1.00
9
-
.26
1
-
.480
-
.06
9
AXSKIN
-
.24
5
.841
-
.19
7
-
.639
.04
6
CRUPARM
-
.70
4
.913
-
.21
5
-
.193
-
.09
0
CRLWARM
-
.48
0
.733
-
.20
7
-
.315
.04
9
2
Identification st
ructures 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.
CRUPLG
-
.78
1
.869
-
.31
0
-
.109
.03
6
CRLWLG
-
.57
5
.701
-
.19
6
-
.137
-
.02
2
HANDLG
-
.38
9
.180
-
.54
7
.056
.59
5
HANDDM
-
.05
2
.099
-
.63
2
-
.174
.73
3
ABDSKIN
-
.13
9
.247
-
.22
5
-
.039
.09
2
LWLSKIN
-
.25
2
.537
.01
0
-
.246
-
.19
0
CHCIRC
-
.57
1
.736
-
.38
5
-
.053
.04
7
DIWRIST
-
.60
7
.172
-
.86
8
.945
.25
4
DIAEL
-
.43
6
.455
-
.28
3
.081
.03
1
DIAKNE
.17
2
.753
.11
9
-
1.55
7
.37
7
FOOTL
-
.19
7
.301
-
.49
6
-
.122
.43
0
FOOTDM
.00
9
.105
-
.34
6
.040
.18
8
ARMLG
-
.04
6
.250
-
.63
9
-
.179
.57
0
Table 8. Discriminant coefficients
g1
g2
g3
g4
g5
WEIGHT
-
.45
0
.79
6
.711
.671
-
1.90
8
HEIGHT
.05
0
-
.21
4
.612
.087
-
.499
LLENGTH
-
.04
3
.04
0
-
.589
-
.183
.759
BIACRO
-
.38
6
.38
1
.007
-
.091
-
.055
BICRIS
-
.01
0
-
.14
9
.679
.080
-
.589
TRISKIN
-
.09
9
.02
7
.444
.037
-
.440
SCAPSKIN
-
.29
5
.53
0
-
.922
.126
.443
AXSKIN
.14
2
.24
6
.016
-
.436
.012
CRUPARM
-
.20
3
.26
2
-
.101
-
.092
.049
CRLWARM
.18
8
-
.20
9
.366
-
.255
-
.038
CRUPLG
-
.77
3
.20
2
-
.555
.013
.914
CRLWLG
-
.02
7
.00
8
.188
-
.098
-
.086
HANDLG
-
.61
1
.13
8
.203
-
.058
.160
HANDDM
.41
3
-
.30
4
-
.652
-
.196
.873
ABDSKIN
.61
8
-
.69
1
.151
-
.064
.214
LWLSKIN
-
.04
8
.03
5
.043
.155
-
.193
CHCIRC
.18
5
-
.21
3
-
.326
.094
.339
DIWRIST
-
.38
2
.07
8
-
.712
.763
.202
DIAEL
-
.13
2
.05
3
.172
.171
-
.294
DIAKNE
.39
9
.40
8
.242
-
1.54
9
.4
58
FOOTL
.12
8
-
.16
0
-
.010
.014
.080
FOOTDM
.32
-
-
.044
-
0
.08
7
.138
.048
ARMLG
.53
0
-
.12
1
-
1.14
3
-
.045
.931
Table 9. Structure of discriminant functions
g1
g2
g3
g4
g5
WEIGHT
-
.53
0
.64
1
-
.31
0
-
.04
1
.05
2
HEIGHT
-
.20
3
.29
1
-
.27
7
-
.07
9
.21
8
LLENGTH
-
.12
9
.26
5
-
.39
2
-
.10
0
.33
9
BIACRO
-
.49
0
.50
5
-
.24
9
-
.02
0
.08
5
BICRIS
-
.09
2
.24
7
.11
4
-
.13
5
-
.15
4
TRISKIN
-
.26
3
.66
3
-
.05
4
-
.30
7
-
.09
2
SCAPSKIN
-
.34
8
.75
2
-
.18
7
-
.26
0
-
.05
1
AXSKIN
-
.18
8
.62
7
-
.14
1
-
.34
6
.03
4
CRUPARM
-
.53
8
.68
1
-
.15
4
-
.10
4
-
.06
7
CRLWA
RM
-
.36
7
.54
6
-
.14
9
-
.17
1
.03
7
CRUPLG
-
.59
8
.64
8
-
.22
2
-
.05
9
.02
7
CRLWLG
-
.44
0
.52
3
-
.14
1
-
.07
4
-
.01
6
HANDLG
-
.29
8
.13
4
-
.39
2
.03
0
.44
2
HANDDM
-
.03
9
.07
4
-
.45
3
-
.09
4
.54
4
ABDSKIN
-
.10
.18
4
-
.16
-
.02
.06
8
6
2
1
LWLSKIN
-
.19
3
.40
1
.00
7
-
.13
3
-
.14
1
CHCIRC
-
.43
7
.54
9
-
.27
6
-
.02
9
.03
5
DIWRIST
-
.46
4
.12
8
-
.62
3
.51
2
.18
9
DIAEL
-
.33
3
.33
9
-
.20
3
.04
4
.02
3
DIAKNE
.13
1
.56
2
.08
5
-
.84
4
.28
0
FOOTL
-
.15
0
.22
4
-
.35
6
-
.06
6
.31
9
FOOTDM
.00
7
.07
8
-
.24
9
.02
2
.14
0
ARMLG
-
.03
5
.18
7
-
.45
8
-
.09
7
.42
3
Table 10. Patter
n of discriminant functions
g1
g2
g3
g4
g5
WEIGHT
-
.17
2
.48
4
-
.27
9
-
.04
4
-
.06
5
HEIGHT
-
.11
2
.19
2
-
.16
3
-
.07
2
.13
2
LLENGTH
.02
5
.23
6
-
.30
7
-
.06
7
.12
4
BIACRO
-
.39
2
.24
9
-
.05
1
-
.06
7
.15
3
BICRIS
.09
7
.25
5
-
.04
8
-
.07
6
-
.20
8
TRISKIN
.27
9
.70
0
-
.36
6
-
.16
4
-
.39
5
SCAPSKIN
.33
9
.81
9
-
.53
0
-
.11
9
-
.45
9
AXSKIN
.34
6
.69
6
-
.43
-
.18
-
.34
6
4
0
CRUPARM
-
.22
4
.48
4
-
.14
9
-
.09
7
-
.09
5
CRLWARM
-
.15
5
.38
8
-
.12
4
-
.13
8
-
.01
1
CRUPLG
-
.45
4
.34
0
-
.03
3
-
.10
2
.12
2
CRLWLG
-
.26
2
.32
5
-
.06
7
-
.08
5
.01
0
HANDLG
-
.71
3
-
.24
8
.20
4
-
.09
3
.71
3
HANDDM
-
.23
0
-
.07
1
-
.10
0
-
.10
9
.49
6
ABDSKIN
.09
8
.21
4
-
.22
0
.00
4
-
.08
7
LWLSKIN
.17
9
.43
7
-
.22
2
-
.05
8
-
.31
4
CHCIRC
-
.06
7
.45
7
-
.30
2
-
.02
0
-
.12
0
DIWRIST
-
.15
7
.10
9
-
.45
6
.35
0
.01
8
DIAEL
-
.13
4
.24
3
-
.16
1
.01
8
-
.02
7
DIAKNE
.11
5
.44
1
.03
1
-
.58
9
.15
3
FOOTL
-
.09
5
.14
2
-
.20
0
-
.06
2
.20
1
FOOTDM
.30
0
.22
9
-
.38
2
.06
4
-
.16
1
ARMLG
.14
1
.22
6
-
.39
6
-
.04
8
.12
1
Table 11. Correlations of discriminant functions
g1
g2
g3
g4
g5
g1
1.00
0
-
.615
.221
-
.411
.251
g2
-
1.00
-
-
-
.615
0
.106
.354
.094
g3
.221
-
.1
06
1.00
0
-
.308
-
.693
g4
-
.411
-
.354
-
.308
1.00
0
-
.273
g5
.251
-
.094
-
.693
-
.273
1.00
0
Table 12. Standardized discriminant coefficients
g1
g2
g3
g4
g5
WEIGHT
-
.34
4
.59
3
.51
0
.36
4
-
1.41
7
HEIGHT
.03
8
-
.16
0
.43
9
.04
7
-
.371
LLENGTH
-
.03
3
.03
0
-
.42
3
-
.09
9
.563
BIACRO
-
.29
5
.28
4
.00
5
-
.04
9
-
.041
BICRIS
-
.00
8
-
.11
1
.48
7
.04
3
-
.437
TRISKIN
-
.07
6
.02
0
.31
9
.02
0
-
.326
SCAPSKIN
-
.22
6
.39
5
-
.66
2
.06
9
.329
AXSKIN
.10
9
.18
3
.01
2
-
.23
6
.009
CRUPARM
-
.15
5
.19
6
-
.07
2
-
.05
0
.036
CRLWARM
.14
4
-
.15
5
.26
3
-
.13
8
-
.028
CRUPLG
-
.59
2
.15
0
-
.39
9
.00
7
.678
CRLWLG
-
.02
1
.00
6
.13
5
-
.05
3
-
.064
HANDLG
-
.46
8
.10
3
.14
6
-
.03
1
.118
HANDDM
.31
6
-
.22
-
.46
-
.10
.648
6
8
6
ABDSKIN
.47
3
-
.51
5
.10
8
-
.03
5
.159
LWLSKIN
-
.03
7
.02
6
.03
1
.08
4
-
.143
CHCIRC
.14
2
-
.15
9
-
.23
4
.05
1
.252
DIWRIST
-
.29
2
.05
8
-
.51
1
.41
3
.150
DIAEL
-
.10
1
.03
9
.12
3
.09
2
-
.218
DIAKNE
.30
5
.30
4
.17
4
-
.83
9
.340
FOOTL
.09
8
-
.11
9
-
.00
7
.00
7
.059
FOOTDM
.24
5
-
.06
5
-
.09
9
.02
4
-
.036
ARMLG
.40
6
-
.09
0
-
.82
0
-
.02
4
.691
Table 13. Contingency matrix of Neural netw
ork and
Fisherian classification
g1
g2
g3
g4
g5
g1
110
0
3
0
3
g2
0
162
4
0
5
g3
14
4
136
0
0
g4
1
4
0
137
2
g5
17
2
0
0
133
Therefore, classification of entities in
morphological space is really a hard task for any
clustering algorithm, as can b
e 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 ob
jects and efficacy of final
classification
numbe
r
progno
sis
erro
r
g1
116
110
6
g2
171
162
9
g3
154
136
18
g4
144
137
7
g5
152
133
19
Coefficient of efficacy of Triatlon in this case was
only 0.920, markedly lower then in other applications of
thi
s 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 tis
sue 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) Ty
pus 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, altou
gh
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 reaso
ns 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. T
his 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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ENCES
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Povezanost morfolo{kih taksona sa manifestnim i latentnim
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[talec,
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