DETERMINATION OF THE PROVENANCE OF VINICA

1
DETERMINATION OF THE PROVENANCE OF VINICA TERRA
COTTA ICONS USING SUPPORT VECTOR MACHINES
Vinka Tanevska, Igor Kuzmanovski, Orhideja
Grupce and Biljana Minceva-ukarova
Institut za hemija, PMF, Univerzitet Sv. Kiril i
Metodij, Arhimedova 5, 1001 Skopje, Republic of
Macedonia e-mail shigor_at_iunona.pmf.ukim.edu.mk
Introduction
Support Vector Machines
Vinica terra cotta icons/reliefs (Figure 1.) were
found during the systematic archaeological
excavations in 1985, in the Vinica Fortress,
Southwest of the town of Vinica, in the Eastern
part of Republic of Macedonia (Figure 2.a.).
Fifty undamaged terra cotta icons and over
hundred fragments with more than fifteen
different scenes, have been discovered so far.
According to the art historians, they are dated
from the 6th to 7th century AD and represent
exceptional examples of our Christian cultural
heritage 1, 2.
Support vector machines (SVM) are an algorithm
suitable for binary classification of linearly
separable classes. SVM are a very fast, simple
and promising algorithm with good generalization
performances. Using an appropriate kernel
function (Figure 3.), SVM could successfully be
trans-formed into a non-linear classifier. The
multi-category classification is performed by
consecutive construction of several binary
classifiers (Figure 4.). The parameters of the
SVM models (the penalty parameter and the width
of the Gaussian kernel function) as well as the
most suitable elements for the classification of
the clay samples were chosen using genetic
algorithms. The encoding of the chromosomes in
the population was performed as presented in
Figure 5.
Figure 3. Nonlinear mapping in higher
dimensional feature space
Figure 1. Vinica terra cotta icons
Ten samples of partially preserved fragments of
terra cotta icons and thirty three clay samples
from eight different sites in a radius of 12 km
from Vinica (Figure 2. b.) have been analyzed.
Nineteen elements were determined using the
following instrumental techniques X-ray
fluores-cence, atomic absorption
spectrophotometry and flame photometry. The
simple comparison of the obtained data did not
reveal the exact location of the clay used for
the terra cotta icons 3. Based on previous
chemometric experience 4, a method using
support vector machines (SVM) was developed to
determine the provenance.
Figure 4. Use of the SVM algorithm for
classification of a data set consisting of three
classes
a.
b.
Genetic Algorithms
During the preliminary in-vestigation, the width
of the kernel function and the penalty parameter
were searched in the inter-vals presented in
Figure 6. Using genetic algorithms, in the final
phase of the analysis, the penalty pa-rameter of
the models as well as the width of the kernel
function, were searched in the intervals that
produce models with no classification errors (for
the samples in the training set) and at the same
time, models with smaller number of support
vectors. In this phase, the best combination of
ele-ments suitable for clas-sification was also
deter-mined.
Figure 2. a Map of the Republic of Macedonia
b Vinica region (clay pits 1 8)
Figure 5. The encoding of the chromosomes used
for optimization of SVM models with GA
Results and discussion
The entire procedure using genetic algorithms was
repeated several times. In order to force the
genetic algorithm to search for simpler models, a
large penalty was introduced to the models
defined by more than six elements. This approach
helps to exclude from the models, the elements
that does not have discriminative power. More
than 68 models (combination of elements, penalty
parameters and width of the Gaussian function)
were able to classify the samples from the
training set correctly using cross validation
leave-one-out. The frequency of appearance of the
analysed elements for the models composed of less
than seven elements are presented in Figure 7.
One can notice that the most frequently two
analysed elements are K2O and Sr. The elements
Cr2O3, V2O5, Pb, Ni, Co, Zn, Cu and Ag are not as
important for classification as the rest of the
elements.
a.
b.
Figure 6. The performances of the SVM models
during the preliminary investigation (a
number of misclassified samples b number of
support vectors for the same models)
References
1. K. Balabanov, Terakotnite ikoni od Makedonija,
Tabernakul, Skopje, 1995. 2. E. Dimitrova,
Keramickite reljefi od Vinickoto Kale, Gjurgja,
Skopje, 1993. 3. S. Pavlovska Josifovska,
Hemiski ispituvanja na vinickite terakoti, M.Sc.
thesis, Univerzitet Sv. Kirili i Metodij,
Prirodnomatematicki fakultet, Institut za
hemija, Skopje, 1996. 4. V. Tanevska, I.
Kuzmanovski, O. Grupce, Ann. Chim-Rome, 97 (2007)
541552. 5. V.N. Vapnik, The Nature of
Statistical Learning Theory, Wiley, New York,
1995. 6. L. Davis, The Handbook of Genetic
Algorithms, Van Nostrand Reingold, New York, 1991.
Figure 7. The frequency of appearance of
different elements in the SVM models
Conclusion
All 68 models with less than 7 elements show that
the material used for production of the analysed
samples of Vinica terra cotta icons is taken from
Grncarka, 2.5 km from Vinica.
9th European Meeting on Ancient Ceramics,
Hungarian National Museum, Budapest, Hungary,
October 2007