- Research article
- Open Access
Non-destructive characterisation and classification of ceramic artefacts using pEDXRF and statistical pattern recognition
- Maja D Gajić-Kvaščev†1Email author,
- Milica D Marić-Stojanović†2,
- Radmila M Jančić-Heinemann3,
- Goran S Kvaščev4 and
- Velibor Dj Andrić1
© Gajic-Kvascev et al.; licensee Chemistry Central Ltd. 2012
- Received: 24 June 2012
- Accepted: 12 September 2012
- Published: 14 September 2012
Portable energy dispersive X-ray fluorescence (pEDXRF) spectrometry analysis was applied for the characterisation of archaeological ceramic findings from three Neolithic sites in Serbia. Two dimension reduction techniques, principal component analysis (PCA) and scattering matrices-based dimension reduction were used to examine the possible classification of those findings, and to extract the most discriminant features.
A decision-making procedure is proposed, whose goal is to classify unknown ceramic findings based on their elemental compositions derived by pEDXRF spectrometry. As a major part of decision-making procedure, the possibilities of two dimension reduction methods were tested. Scattering matrices-based dimension reduction was found to be the more efficient method for the purpose. Linear classifiers designed based on the desired output allowed for 7 of 8 unknown samples from the test set to be correctly classified.
Based on the results, the conclusion is that despite the constraints typical of the applied analytical technique, the elemental composition can be considered as viable information in provenience studies. With a fully-developed procedure, ceramic artefacts can be classified based on their elemental composition and well-known provenance.
- pEDXRF spectrometry
- Pattern recognition
- Dimension reduction
- Feature extraction
- Cultural Heritage
- Neolithic ceramics
Archaeological ceramics can be studied in the context of origin of production or production technologies, as well as the distribution of specific ware types or whole assemblages [1–9]. Such studies have at their disposal an arsenal of different techniques, both analytical [10–16] and statistical [17–20], to arrive at answers to archaeological issues. Special place in a long list of analytical techniques belongs to non-destructive analyses performed using IR or Raman spectroscopy, PIXE or XRD, [21–26]. One of the non-destructive techniques that have been most commonly used is energy dispersive X-ray fluorescence (EDXRF) spectrometry proven to be efficient and suitable for archaeological ceramics provenience studies [4, 5, 15]. During the past ten years the use of portable XRF (PXRF, pXRF), field-portable (FPXRF) or handheld XRF spectrometers has increased significantly . Such instruments (and consequently technique) become affordable for many applications that generate fast results which imply almost immediate interpretation and decision.
Different supervised as well as unsupervised multivariate statistical methods are widely and successfully used in archaeometric data analysis. Commonly applied methods include principal component analysis (PCA), various forms of cluster analysis (CA), and discriminant analysis (DA, both linear and quadratic), followed by more recent (neural network and fuzzy) methods , although the application of combined techniques has been reported in the literature . Multivariate statistical methods can be used in provenience studies of artefacts [2, 6], as well as for the recognition of local ceramic production and its characterisation, distinguishing from objects of possible trading activities , production dating , etc. Even so, discussion on applied dimension reduction technique regarding its validity from the aspect of information loss can be rarely found in the literature.
Systematic analytical examinations of archaeological ceramics from the Vinča culture are very obscure. As the ceramics belonging to the Vinča culture play an important role in global archaeology, it is of great importance to study as many aspects of their provenience as possible.
Analytical examinations were followed by application of pattern recognition methods to the obtained results as part of the decision-making procedure developed and improved to classification (and consequently sourcing) purpose which has been described below.
The elemental compositions resulting from pEDXRF measurements of 67 investigated samples were used to form a training data set (TRS) as 67 × 10 matrix. The TRS comprised the intensity results reported as the average net peak area values for X-rays detected over 100 s of live counts for ten elements: Si, K, Ca, Ti, Mn, Fe, Zn, Rb, Sr and Zr, chosen so that net peak area uncertainty remained below 10% (as suggested in ). The uncertainty of the net peak area was usually much less than 10% for most of the selected elements, except for Mn and Zn where the uncertainty was 15% in some measurements. For Cr, Cu, Pb or Y, uncertainty did exceed the desirable 10% level in most of the measurements, or a large number of measured values were affected by poor counting statistics implying that those elements needed to be excluded from the TRS. According to published data [4, 33, 34], the selected elements can be considered as representative for classification purposes.
The test data set (TDS) was formed in the same manner. The same ten elements were measured under the same conditions as for the TRS, for eight additional ceramic sherds (2 from the site of Bubanj, 2 from the site of Pločnik and 4 from the site of Vinča) forming 8 × 10 matrix.
Multivariate analysis and classification
Elemental composition of the three ceramic samples groups and the whole assemblage
BUBANJ (n = 13)
PLOCNIK (n = 25)
VINCA (n = 29)
ALL (n = 67)
Mean ± SD
Mean ± SD
Mean ± SD
Mean ± SD
14.46 ± 4.32
8.87 ± 3.85
13.38 ± 4.16
11.91 ± 4.68
55.01 ± 9.72
24.31 ± 9.48
37.89 ± 8.98
36.14 ± 14.44
40.61 ± 12.30
44.00 ± 28.05
56.38 ± 21.44
48.70 ± 23.57
44.86 ± 11.10
29.19 ± 11.69
37.26 ± 8.82
35.72 ± 11.78
13.61 ± 6.57
13.47 ± 12.37
10.45 ± 7.23
12.19 ± 9.38
1223.56 ± 249.18
789.64 ± 280.00
976.99 ± 197.44
954.92 ± 284.80
14.30 ± 15.79
8.31 ± 5.81
28.21 ± 42.96
18.09 ± 30.41
12.41 ± 3.46
7.86 ± 2.88
10.18 ± 2.95
9.75 ± 3.42
14.98 ± 5.72
11.03 ± 3.15
14.17 ± 4.19
13.16 ± 4.45
19.47 ± 6.16
15.15 ± 6.28
23.62 ± 5.43
19.65 ± 6.95
First two PCs of the training dataset: eigenvalues, explained and cumulative variance, and loadings of the variables
% of Variance
Dependence of extracted features y1 and y2 on original features
Classification results for the three site groups and leave-one-out cross validation results
Predicted Group Membership
The success of the classification model was tested by the leave-one-out cross validation method . Only analysed cases were cross validated, and each case was classified using the functions derived from all cases other than that case. The achieved prediction ability was 76.1% of cross-validated grouped cases correctly classified. Another test of the classification model was performed. Two (h 1 and h 2 ) linear classifiers designed in the training step were used for the classification of the eight vectors belonging to the TDS. The results (Figure 3) show that only one sherd from the TDS was not correctly classified using the model developed during the training process.
According to the results presented, several conclusions can be drawn. Algorithm of the proposed decision-making procedure enables effective classification of ceramic artefacts based on their elemental compositions determined by pEDXRF spectrometry. As shown, the data from the first algorithm step, denoted as in-situ data acquisition, can be used as a viable tool for sourcing ceramics although their accuracy may not be the same as in the case of other methods used for the purpose (e.g. ICP, NAA, PIXE, or laboratory XRF).
The step in algorithm, denoted as dimension reduction gave significant results rarely discussed in the literature. The results derived by PCA dimension reduction show that the elements which contribute the most to the formation of the PCs are not quite informative for classification as well (also confirmed by biplot examination). In other words, reliable classification of ceramics in a space determined by the greatest variance in their elemental compositions is not feasible with the data obtained by pEDXRF characterisation. This outcome underline that the selection of the greatest variance in addressing a new space can lead to a loss of information carried by the data.
On the other hand, it is possible to achieve the initial goal (expressed through the classification of ceramics based on the elemental composition) by a method founded upon dimension reduction, which has scattering matrices as its basis and which takes into account minimal information loss. According to the results obtained it is safe to say that the success of classification, expressed through prediction and recognition ability, allows the application of this method for the identification of objects based on their well-known provenance and that the proposed decision-making procedure yields satisfactory classification results. It should be emphasized that the selection of dimension reduction technique also has to be careful and in accordance with the aim of data analysis.
There are no previous studies dealing with the investigation of elemental patterns of ancient pottery from the Neolithic sites in Serbia therefore no comparison can be made. The results of the present study can support provenience study issues, in developing a compositional databank and establishing reference groups of pottery from Neolithic sites. An ongoing analysis of sherds from the other sites is expected to provide additional insight into pottery making techniques, trade and cultural exchange in the region.
The conclusion that should be emphasized, based on the results obtained, is that pEDXRF spectrometry when used in investigation of the origin of ceramic artefacts can provide viable results by carefully selecting the experimental conditions and well-thought-out procedure of data processing. This conclusion is particularly important in cases when it is not possible to apply the methods with high precision and sensitivity for determination of elemental compositions, although they have been proven to be very successful in meeting the requirements related to the determination of the artefact origin, either because of their destructiveness or non-portability.
pEDXRF analysis for non-destructive and non-invasive characterisation of the ceramic artefacts was performed using a milli-beam spot XRF spectrometer. The spectrometer (in-house developed at the Vinča Institute of Nuclear Sciences, Belgrade) is based on an air cooled X-ray tube (Oxford Instruments, Rh-anode, max 50 kV, 1 mA) with a pin-hole collimator and a SiPIN X-ray detector (6 mm2/500 μm, Be window 12.5 μm thickness), associated with a DSP (X123, Amptek, Inc.) for spectra acquisition. Two laser pointers were used for proper positioning of the analysed sample in the cross-point of the exciting X-ray beam and the detector axis, respectively. ADMCA software was used for spectra analysis. A 35 kV high voltage, 800 μA, no filter and a 100 s measuring time were selected as experimental parameters and kept constant during all measurements. The geometry parameters were chosen as follows: detector-sample distance = 21 mm, X-ray tube-sample distance = 16 mm, detector-X-ray tube angle = 45° and sample-X-ray tube angle = 90°. Instead of quantification, it was presumed (similarly to ) that the high correlation coefficient (R 2 ) values obtained (ranging from 0.863 for K to 0.994 for Fe) between average net peak area values and selected element concentrations for powdered CRM (NIST SRM-2711 Montana soil, NCS CRM DC 73301 rock) and RM (IAEA XRF-PT China ceramic and lake sediment) can also be achieved in ceramic fragments analysis.
The measuring areas of all the samples were polished and cleaned before analysis. Each sample was analysed in three points, as it was suggested in , and the average net peak area values were considered. Whenever possible, different sample fractured sides were selected for measurement. In other cases, the measurements were performed at the most distant spots, providing in this way the representativeness of measurements.
Pattern recognition methods and decision-making procedure
As already stated, the use of in-situ EDXRF spectrometry for non-destructive characterisation of ceramic artefacts generates data whose quick interpretation is an increasingly frequent requirement . To meet this requirement, it is useful to design an efficient and reliable decision-making procedure . This paper presents one such procedure consisting of the following steps: a) in-situ data acquisition; b) generation of vector X; c) dimension reduction; d) classifier design and e) classification followed by classification success testing.
During the analytical examination and characterisation of ceramic sherds, the elemental composition was determined as described above. The result was that 67 different ten-dimensional vectors were generated. This provided a considerable amount of data which did not need to be equally informative for the characterisation of ceramics or the determination of their provenance, and it was therefore necessary to separate those parameters which carry the most information about the characteristics or provenance. The first step towards this goal was to make the performed measurements “more visible”. The pattern recognition theory has developed techniques to address this issue referred to as dimension reduction. The main goal of dimension reduction is to project the original vector X of dimension n onto a vector Y of dimension m (considerably smaller than the initial dimension n) in such a way as to minimise the loss of information. Two approaches were chosen to reduce the initial 10-dimensional space to 2-dimensional space: PCA and scattering matrices-based dimension reduction, described below in more detail. Dimension reduction is a step in the decision-making procedure, followed by classifier design and then classification. The design of a proper classifier is a procedure dependent on the previous step, but it is desirable to choose a procedure as simple and as fast as possible, which will achieve the best classification results at same time.
PCA, also known as Karhunen–Loeve transform, is a widely used method for dimension reduction. The purpose of PCA is to project n-dimensional data onto a lower d-dimensional subspace in a way that maximises the variance [39–42]. The derived new uncorrelated variables that are linear combinations of the original one result in finding of a smaller group of underlying variables that describe the data. The first few components will account for most of the variation in the original data, but they may not be able to accurately represent group membership [35, 40].
As the dimension reduction of the original space is only one step in the procedure whose goal is classification, the scattering matrices-based dimension reduction method was tested as the most appropriate choice. The main advantage of dimension reduction performed in such way as to preserve class membership is two-fold. First, in low-dimensional space it is possible to visualise the classification results and choose the appropriate classifier design approach. Second, it is possible to identify the important measurements with regard to classification. Dimension reduction consists of finding a transformation matrix A (Y = A T X) which will reduce the original data space (X) dimensionality in the new (Y) one, considerably lower dimensionality. The optimal transformation matrix A is the explicate solution of the optimisation criterion , obtained as the solution for the generalised singular value decomposition of the matrix (where S w and S b represent the within-class scatter matrix and between-class scatter matrix, respectively). The m eigenvectors correspond to the m largest eigenvalues form the matrix A. Two-dimensional projection is the most desirable, allowing examination of the classification results in terms of recognition ability (percentage of members of the training set correctly classified) and prediction ability (percentage of members of the test set correctly classified using the rules developed during the training).
The authors express their gratitude to the archaeologists Dušan Šljivar, Prof. Dr. Nenad Tasić and Dr. Aleksandar Bulatović for making ceramic samples available. Maja Gajić-Kvaščev especially wishes to thank Prof. Dr. Željko Đurović from the University of Belgrade/Faculty of Electrical Engineering for his patient scrutiny of all stages of this research and for his comments which helped finalise the paper. The IAEA Regional Technical Cooperation Program RER/0/034 is acknowledged for supporting a part of the present work. The paper was produced with the support of Education and Science (Projects TR37021, TR32038, TR34011, OI 177012, III 42007 and III 45012) and the Serbian Ministry of Culture (451-04-00792/2011-03).
- Tite MS: Ceramic production, provenance and use—a review. Archaeometry. 2008, 50: 216-231. 10.1111/j.1475-4754.2008.00391.x.View ArticleGoogle Scholar
- Montana G, Ontiveros MAC, Polito AM, Azzaro E: Characterisation of clayey raw materials for ceramic manufacture in ancient Sicily. Appl. Clay Sci. 2011, 53: 476-488. 10.1016/j.clay.2010.09.005.View ArticleGoogle Scholar
- Papachristodoulou C, Gravani K, Oikonomou A, Ioannides K: On the provenance and manufacture of red-slipped fine ware from ancient Cassope (NW Greece): evidence by X-ray analytical methods. J Archaeol Sci. 2010, 37: 2146-2154. 10.1016/j.jas.2010.02.013.View ArticleGoogle Scholar
- Freitas PR, Calza C, Lima AT, Rabello A, Lopes TR: EDXRF and multivariate statistical analysis of fragments from Marajoara ceramics. X-Ray Spectrom. 2010, 39: 307-310. 10.1002/xrs.1200.View ArticleGoogle Scholar
- Frankel D, Webb JM: Pottery production and distribution in prehistoric Bronze Age Cyprus. An application of pXRF analysis. J Archaeol Sci. 2012, 39: 1380-1387. 10.1016/j.jas.2011.12.032.View ArticleGoogle Scholar
- Xu A, Wang C, Chi J, Li M, Zhang M, Holmes L, Harbottle G, Koshimizu S, Manabu K, Koichi K: Preliminary Provenance Research on Chinese Neolithic Pottery: Huating (Xinyi County) and Three Yellow River Valley Sites. Archaeometry. 2001, 43: 35-47. 10.1111/1475-4754.00003.View ArticleGoogle Scholar
- Taylor RJ, Robinson VJ, Gibbins DJL: An investigation of the provenance of the Roman Amphora cargo from the Plemmirio B shipwreck. Archaeometry. 1997, 39: 9-21. 10.1111/j.1475-4754.1997.tb00787.x.View ArticleGoogle Scholar
- Vaughn KJ, Dussubieux L, Williams PR: A pilot compositional analysis of Nasca ceramics from the Kroeber collection. J Archaeol Sci. 2011, 38: 3560-3567. 10.1016/j.jas.2011.08.025.View ArticleGoogle Scholar
- Hall M, Minyae S: Chemical Analysis of Xiong-nu Pottery: A Preliminary Study of Exchange and Trade on the Inner Asian Steppes. J Archaeol Sci. 2002, 2: 135-144.View ArticleGoogle Scholar
- Kuleff I, Iliev I, Pernicka E, Gergova D: Chemical and lead isotope compositions of lead artefacts from ancient Thracia (Bulgaria). J Cult Herit. 2006, 7: 244-256. 10.1016/j.culher.2006.04.003.View ArticleGoogle Scholar
- Sánchez S, Bosch F, Gimeno JV, Yusá DJ, Doménech A: Study and dating of medieval ceramic tiles by analysis of enamels with atomic absorption spectroscopy, X-ray fluorescence and electron probe microanalysis. Spectrochim. Acta, Part B. 2002, 57: 689-700. 10.1016/S0584-8547(01)00395-0.View ArticleGoogle Scholar
- Pizarro C, Perez-del-Notario N, Saenz-Gonzalez C, Rodriguez-Tecedor S, Gonzalez Saiz JM: Matching past and present ceramic production in the Banda area (Ghana): improving the analytical performance of neutron activation analysis in archaeology using multivariate analysis techniques. Archaeometry. 2012, 54: 101-113. 10.1111/j.1475-4754.2011.00601.x.View ArticleGoogle Scholar
- Tsolakidou A, Kilikoglou V: Comparative analysis of ancient ceramics by neutron activation analysis, inductively coupled plasma-optical-emission spectrometry, inductively coupled plasma-mass spectrometry, and X-ray fluorescence. Anal Bioanal Chem. 2002, 374: 566-572. 10.1007/s00216-002-1444-2.View ArticleGoogle Scholar
- Padilla R, Van Espen P, Godo Torres PP: The suitability of XRF analysis for compositional classification of archaeological ceramic fabric: A comparison with a previous NAA study. Anal Chim Acta. 2006, 558: 283-289. 10.1016/j.aca.2005.10.077.View ArticleGoogle Scholar
- Cariati F, Fermo P, Gilardoni S, Galli A, Milazzo M: A new approach for archaeological ceramics analysis using total reflection X-ray fluorescence spectrometry. Spectrochim Acta, Part B. 2003, 58: 177-184. 10.1016/S0584-8547(02)00253-7.View ArticleGoogle Scholar
- Glascock MD, Neff H: Neutron activation analysis and provenance research in archaeology. Meas Sci Technol. 2003, 14: 1516-1526. 10.1088/0957-0233/14/9/304.View ArticleGoogle Scholar
- Baxter MJ: A Review of Supervised and Unsupervised Pattern Recognition in Archaeometry. Archaeometry. 2006, 48: 671-694. 10.1111/j.1475-4754.2006.00280.x.View ArticleGoogle Scholar
- Remolá JA, Larrechi MS, Rius FX: Chemometric characterization of 5th century A.D. amphora producing centres in the Mediterranean. Talanta. 1993, 40: 1749-1751. 10.1016/0039-9140(93)80093-7.View ArticleGoogle Scholar
- Fermo P, Delnevo E, Lasagni M, Polla S, de Vos M: Application of chemical and chemometric analytical techniques to the study of ancient ceramics from Dougga (Tunisia). Microchem J. 2008, 88: 150-159. 10.1016/j.microc.2007.11.012.View ArticleGoogle Scholar
- Carrero JA, Goienaga N, Fdez-Ortiz De Vallejuelo S, Arana G, Madariaga JM: Classification of archaeological pieces into their respective stratum by a chemometric model based on the soil concentration of 25 selected elements. Spectrochim. Acta, Part B. 2010, 65: 279-286. 10.1016/j.sab.2010.01.009.View ArticleGoogle Scholar
- Raman spectroscopy in archaeology and art history. Edited by: Edwards HGM, Chalmers JM. 2005, Cambridge: The Royal Society of ChemistryGoogle Scholar
- Akyuz S, Akyuz T, Basaran S, Bolcal C, Gulec A: Analysis of ancient potteries using FT-IR, micro-Raman and EDXRF spectrometry. Vib Spectrosc. 2008, 48: 276-280. 10.1016/j.vibspec.2008.02.011.View ArticleGoogle Scholar
- Centeno SA, Williams VI, Little NC, Speakman RJ: Characterization of surface decorations in Prehispanic archaeological ceramics by Raman spectroscopy, FTIR, XRD and XRF. Vib Spectrosc. 2012, 58: 119-124.View ArticleGoogle Scholar
- Smith GD, Clark RJH: Raman microscopy in archaeological science. J Archaeol Sci. 2004, 31: 1137-1160. 10.1016/j.jas.2004.02.008.View ArticleGoogle Scholar
- Kos M, Šmit Ž: PIXE-PIGE analysis of 18th and early 19th century creamware from Slovenia and Northern Italy. J Cult Herit. 2011, 12: 236-242. 10.1016/j.culher.2010.12.010.View ArticleGoogle Scholar
- Clark RJH: Raman microscopy as a structural and analytical tool in the fields of art and archaeology. J Mol Struct. 2007, 834–836: 74-80.View ArticleGoogle Scholar
- Speakman RJ, Little NC, Creel D, Miller MR, Iñañez JG: Sourcing ceramics with portable XRF spectrometers? A comparison with INAA using Mimbres pottery from the American Southwest. J Archaeol Sci. 2011, 38: 3483-3496. 10.1016/j.jas.2011.08.011.View ArticleGoogle Scholar
- Guoxi X, Songlin F, Xiangqian F, Yongqiang L, Hongye H, Yanqing W, Jihao Z, Lingtong Y, Li L: The Dating of Ancient Chinese Celadon by INAA and Pattern Recognition Methods. Archaeometry. 2009, 51: 682-699. 10.1111/j.1475-4754.2008.00436.x.View ArticleGoogle Scholar
- Gajić-Kvaščev M, Marić-Stojanović M, Šmit Ž, Kantarelou V, Karydas AG, Šljivar D, Milovanović D, Andrić V: New evidence for the use of cinnabar as a colouring pigment in the Vinča culture. J Archaeol Sci. 2011, 39: 1025-1033.Google Scholar
- Vuković J: Neolithic Pottery: Technological and Social Aspects. PhD Thesis, Belgra. 2010, University of Belgrade: Faculty of Philosophy, in SerbianGoogle Scholar
- Stojić M, Jocić M, Vasić M, Pešić D, Vasić A: Niš-Kulturna stratigrafija praistorijskih lokaliteta u Niškoj regiji. (Niš-Cultural Stratigraphy of Prehistoric Sites in the Niš Region). 2006, Belgrade, Niš, Institute of Archaeology: National Museum, 77-87. in SerbianGoogle Scholar
- Hein A, Kilikoglou V: ceraDAT—Prototype of a Web-based Relational Database for Archaeological Ceramics*. Archaeometry. 2012, 54: 230-243. 10.1111/j.1475-4754.2011.00618.x.View ArticleGoogle Scholar
- Forster N, Grave P, Vickery N, Kealhofer L: Non-destructive analysis using PXRF: methodology and application to archaeological ceramics. X-Ray Spectrom. 2011, 40: 389-398. 10.1002/xrs.1360.View ArticleGoogle Scholar
- Bakraji EH, Itlas M, Abdulrahman A, Issa H, Abboud R: X-ray fluorescence analysis for the study of fragments pottery excavated at Tell Jendares site, Syria, employing multivariate statistical analysis. J Radioanal Nucl Chem. 2010, 285: 455-460. 10.1007/s10967-010-0595-4.View ArticleGoogle Scholar
- Fukunaga K: Introduction to Statistical Pattern Recognition. 1990, Orlando: Academic, 2Google Scholar
- Stepanic P, Latinovic I, Djurovic Z: A new approach to detection of defects in rolling element bearings based on statistical pattern recognition. Int J Adv Manuf Techno. 2009, 45: 91-100. 10.1007/s00170-009-1953-7.View ArticleGoogle Scholar
- Alfeld M, Janssens K, Dik J, de Nolf W, van der Snickt G: Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings. J Anal At Spectrom. 2011, 26: 899-909. 10.1039/c0ja00257g.View ArticleGoogle Scholar
- Stricevic R, Djurovic N, Djurovic Z: Drought classification in Northern Serbia based on SPI and statistical pattern recognition. Meteorol Appl. 2011, 18: 60-69. 10.1002/met.207.View ArticleGoogle Scholar
- Brereton RG: Chemometrics Data Analysis for the Laboratory and Chemical Plant. 2003, Chichester West Sussex: John Wiley & Sons LtdGoogle Scholar
- Duda RO, Hart PE, Stork DG: Pattern Classification. 2000, Wiley: New York, 2Google Scholar
- Varmuza K, Filzmoser P: Introduction to Multivariate Statistical Analysis in Chemometrics. 2000, Boca Raton FL: CRC PressGoogle Scholar
- Theodoridis S, Koutroumbas K: Pattern recognition. 2003, Academic Press: San Diego, 2Google Scholar
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