DETERMINATION OF THE PROVENANCE OF VINICA TERRA COTTA ICONS USING SUPPORT VECTOR MACHINES

1. DETERMINATION OF THE PROVENANCE OF VINICA TERRA COTTA ICONS USING SUPPORT VECTOR MACHINES Vinka Tanevska, Igor Kuzmanovski*, Orhideja Grupče and Biljana Minčeva-Šukarova Institut za hemija, PMF, Univerzitet “Sv. Kiril i Metodij”, Arhimedova 5, 1001 Skopje, Republic of Macedonia * e-mail: shigor@iunona.pmf.ukim.edu.mk Introduction Support Vector Machines 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. 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]. 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, Keramičkite reljefi od Viničkoto Kale, Gjurgja, Skopje, 1993. 3. S. Pavlovska – Josifovska, Hemiski ispituvanja na viničkite terakoti, M.Sc. thesis, Univerzitet “Sv. Kirili i Metodij”, Prirodno–matematički fakultet, Institut za hemija, Skopje, 1996. 4. V. Tanevska, I. Kuzmanovski, O. Grupče, Ann. Chim-Rome, 97 (2007) 541–552. 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 Grnčarka, 2.5 km from Vinica. 9th European Meeting on Ancient Ceramics, Hungarian National Museum, Budapest, Hungary, October 2007