Non-destructive characterisation and classification of ceramic artefacts using pEDXRF and statistical pattern recognition

Abstract

Background
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.

Results
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.

Conclusions
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.

Full text

R E S E A R C H A R T I C L E Open Access
Non-destructive characterisation and classification
of ceramic artefacts using pEDXRF and statistical
pattern recognition
Maja D Gajić-Kvaščev
1*†
, Milica D Marić-Stojanović
2†
, Radmila M Jančić-Heinemann
3
, Goran S Kvaščev
4
and Velibor Dj Andrić
1
Abstract
Background: 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.
Results: 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.
Conclusions: 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.
Keywords: pEDXRF spectrometry, Pattern recognition, Dimension reduction, Feature extraction, Classification,
Cultural Heritage, Neolithic ceramics
Background
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 archaeo-
logical 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 fluores-
cence (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 [27]. Such
instruments (and consequently technique) become afford-
able for many applications that generate fast results which
imply almost immediate interpretation and decision.
Different supervised as well as unsupervised multivari-
ate statistical methods are widely and successfully used
in archaeometric data analysis. Commonly applied meth-
ods 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 [17], although the
application of combined techniques has been reported in
the literature [28]. Multivariate statistical methods can
be used in provenience studies of artefacts [2,6], as well
* Correspondence: gajicm@vinca.rs
†
Equal contributors
1
Vinča Institute of Nuclear Sciences, University of Belgrade, Mike Petrovića
Alasa 12-14, Belgrade, Serbia
Full list of author information is available at the end of the article
© 2012 Gajic-Kvascev et al.; licensee Chemistry Central Ltd. This is an Open Access article distributed under the terms of the
Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
Gajić-Kvaščev et al. Chemistry Central Journal 2012, 6:102
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as for the recognition of local ceramic production and
its characterisation, distinguishing from objects of pos-
sible trading activities [3], production dating [28], etc.
Even so, discussion on applied dimension reduction
technique regarding its validity from the aspect of infor-
mation 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 prove-
nience as possible.
The objective of this research was to examine the pos-
sibility of using information derived by pEDXRF spec-
trometry to classify ceramics. So, the question arises
whether pattern recognition methods can be applied
to the data obtained by this method in a way as in
provenance studies. The focus of this study was on non-
destructive characterisation of ceramic findings exca-
vated at three Neolithic sites: Vinča-Belo Brdo near
Belgrade, Pločnik near Prokuplje, and Bubanj near Niš,
all in Serbia, and their classification according to elem-
ental compositions and well-known provenance. There
are a few points that must be emphasised. The ceramics
were characterised by means of its elemental compos-
ition obtained using pEDXRF spectrometry. Thirty-two
pottery sherds from the site of Vinča, 21 figurines or
fragments of figurines, 4 fragments of altars, 2 pottery
sherds from the site of Pločnik, and 15 pottery sherds
from the site of Bubanj were organised in three sample
assemblages. The dimensions of the ceramic sherds from
the site of Vinča range from 10 × 5 cm (large pieces) to
5 × 3 cm (the small ones), and the average thickness is
approximately 4–6 mm. The sherds have mostly black to
grey ceramic body. In the archaeological layer of interest,
several figurines had also been found, but only two of
them were available for the analysis. The figurines from
the site of Pločnik are generally about 10–15 cm high
and 5 cm in diameter. Some of the figurines are larger,
while others are much smaller, looking like amulets. The
figurines, pottery sherds and altars have black ceramic
body. The pottery sherds from the site of Bubanj have
black and brownish to red ceramic body. The average
dimension of the fragments from the site of Bubanj is
5 × 5 cm and their thickness is 5–10 mm (see Figure 1.
A more detailed sample description can be found in
[29]). The assemblages were composed of ceramics of
different production quality (but with a homogenous
structure, previously analysed by optical microscopy,
which improved the absence of the tempers of consider-
able grain size and pores whose presences could affect
homogenous elemental distribution around the exam-
ined surface) and usage (pottery, figurines, and altars).
The main characteristic of the ceramic assemblages was
their well-known provenance (on the basis of archaeo-
logical reasons [30,31]). Such an approach was selected
since in archaeometry research, two different approaches
can be followed to determine the origin of production:
comparison with the clay or with the artefacts of well-
known provenance as referred in [32].
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.
Results and discussion
Non-destructive characterisation
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 aver-
age 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 [33]). The uncer-
tainty 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 measure-
ments. 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
Table 1 reports the elemental content of the ceramic
sherds from three Neolithic sites. The net peak area
mean value and standard deviation (SD) are shown for
each element and each group (sampling location) and
for the whole assemblage.
The results of PCA based dimension reduction (per-
formed in MATLAB - version R2010a, Math Works,
Inc. environment and using IBM SPSS Statistics 19, soft-
ware package, both also used for all other calculations)
are presented in Table 2 and Figure 2. Table 2 shows the
principal component (PC) scores for the first two PCs
and the variance explained by each of them. The first
three PCs accounted for more than 75% of the variance
in the TRS, where PC1 explains 49.87% and PC2
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explains 14.12% of the variance. The PC loadings indi-
cate that Fe, Ti and K, dominate the first PC, respect-
ively, while Mn and Ca are the most dominant
parameters in the second PC. The scatter-plot of the
first two PCs (Figure 2) represents three statistical
groups. None of them is clearly separated along the PC
axes to satisfy the required classification. Elements such
as Fe, Ti and K have high loading values (Table 2) and
can be underlined as elements of important variability.
In this context, it may be concluded that some of the
information has been lost, in dimension reduction pro-
cedure that concerns origin of production. High loading
Figure 1 The pEDXRF equipment during the measurement, some representative ceramic fragments from the three archaeological sites
and ceramic body OM picture.
Table 1 Elemental composition of the three ceramic samples groups and the whole assemblage
Variable BUBANJ (n = 13) PLOCNIK (n = 25) VINCA (n = 29) ALL (n = 67)
Mean ± SD Mean ± SD Mean ± SD Mean ± SD
Si 14.46 ± 4.32 8.87 ± 3.85 13.38 ± 4.16 11.91 ± 4.68
K 55.01 ± 9.72 24.31 ± 9.48 37.89 ± 8.98 36.14 ± 14.44
Ca 40.61 ± 12.30 44.00 ± 28.05 56.38 ± 21.44 48.70 ± 23.57
Ti 44.86 ± 11.10 29.19 ± 11.69 37.26 ± 8.82 35.72 ± 11.78
Mn 13.61 ± 6.57 13.47 ± 12.37 10.45 ± 7.23 12.19 ± 9.38
Fe 1223.56 ± 249.18 789.64 ± 280.00 976.99 ± 197.44 954.92 ± 284.80
Zn 14.30 ± 15.79 8.31 ± 5.81 28.21 ± 42.96 18.09 ± 30.41
Rb 12.41 ± 3.46 7.86 ± 2.88 10.18 ± 2.95 9.75 ± 3.42
Sr 14.98± 5.72 11.03 ± 3.15 14.17 ± 4.19 13.16 ± 4.45
Zr 19.47 ± 6.16 15.15 ± 6.28 23.62 ± 5.43 19.65 ± 6.95
The mean intensity is expressed in counts per second (cps) and n denotes the number of samples in each group. An additional table shows dataset in more detail
[see Additional file 1].
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value for Mn might arise from poorer counting statistics
but also provide a clay geochemical signature since it
tends to concentrate in clay fraction. This result may in-
dicate the clay sources or possible technology used for
ceramic manufacturing. High loading value for Mn,
strongly correlated with a high variance of Ca along PC2
axis indicate the influence these elements on within-
group cohesion (see Figure 2). Group spreading could be
caused by that variance in Mn and Ca. This implies a
good knowledge of the clay properties (it can be
assumed that the used clay contained homogeneously
distributed fine-grained CaCO
3
particles, which provided
easier sintering) and the particular clay sources that
were chosen.
Implementing scattering matrices-based dimension re-
duction, the feature vectors from the TRS were projected
from a 10-dimensional into a two-dimensional space,
taking care to minimise information loss (Figure 3). The
newly formed two-dimensional space is defined by a
linear combination of the original features, i.e. two new
features (Feature 1 denoted by y1 and Feature 2 denoted
by y2) were extracted. As dimension reduction was per-
formed in an optimal way, the extracted features y1 and
y2 can be considered as the best features for classifica-
tion purposes [35]. The dependence of y1 and y2 on the
original features and the influence of the original fea-
tures on class separability (i.e. classification) are shown
in Table 3, indicating that K are Zr are the most respon-
sible for class separability along the y1-axis, while Zr
and Si have the most important influence on class separ-
ability along the y2-axis, respectively. Group cohesion is
best preserved for the Pločnik and Vinča groups, while
for the Bubanj group this cohesion is more disturbed. As
the ceramic samples from the site of Vinča and Pločnik
date from two very close periods (first half of the
fifth millennium BC) this result may indicate similar
Table 2 First two PCs of the training dataset: eigenvalues, explained and cumulative variance, and loadings of the
variables
PC Initial eigenvalues Factor loadings
Total % of Variance Cumulative % Si K Ca Ti Mn Fe Zn Rb Sr Zr
1 4.987 49.875 49.875 .884 .901 .337 .917 .055 .918 .232 .766 .703 .678
2 1.412 14.120 63.995 -.139 -.045 .789 -.106 .859 .019 .023 -.129 .022 .013
Figure 2 A score and loadings plot of the first two PCs of the pEDXRF data for Neolithic ceramics.
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technology used for ceramic manufacturing. The ceramic
samples from the site of Bubanj, was tentatively dated
to the end of the seventh millennium BC (Starčevo
group) and the second half of the fifth millennium BC
(Bubanj-Hum I), what might be the reason of decreases
group cohesion caused by some difference in produc-
tion technology.
Following dimension reduction, it was possible to classify
the reduced vector (newly formed vector Y¼y1y2
½
T),
into one of the three classes (Bubanj, Pločnik or Vinča
excavation site). This paper presents a hierarchical classi-
fication method based on one sequentially chosen class
out of two classes. The three classes presented in Figure 3
are not quite separable from each other (especially the
classes representing the sites of Pločnik and Vinča).
The third class (representing the site of Bubanj) is sepa-
rated from the other two in such a way that it is possible
to determine the linear segments which differentiate
from the two patterns without any classification error.
In this case proper classification has been achieved
by designing a linear classifier, based on the desired out-
put (h
1
(Y)). Following the demand that the decision –
making procedure should be rapid, simple and effective
in classification of unknown samples, it is reasonable and
justifiable to perform the second classification of the
Vinča and Pločnik classes using the simplest classifier of
the linear discriminatory function type. The two linear
classifiers based on the desired output are designed and
their dependence on measured variables is as follows (in
matrix representation as more convenient):
h1YðÞ¼VT
1Yþv01 ¼0:0009 0:0001½Y1:0912
h2YðÞ¼VT
2Yþv02 ¼0:0006 0:0007½Yþ1:5116
It is now necessary to decide whether the new vector
Zbelongs to the Bubanj excavation site or not. If it does
not belong to Bubanj (h
1
will have a negative value), the
next step is to choose between the Pločnik and Vinča
excavation sites (h
2
positive value indicates the Pločnik
site while the negative value of h
2
indicates that the ana-
lysed sample belongs to the Vinča group). The classifica-
tion results are presented in Table 4. It is apparent that
ceramic sherds from the site of Bubanj are 100%, from
the site of Pločnik 88%, and from the site of Vinča 86.2%
properly classified. The recognition ability of the present
classification is 89.6% of correctly classified samples of
the TRS. Note that a design of more complex classifiers
(quadratic, for example), instead of the linear classifier
proposed in this paper, would certainly improve the
efficiency of the classification. However, the chosen lin-
ear classifier seemed to be the most convenient type of
classifiers because it not only provides an objective and
Figure 3 Classification results: linear classifiers and test samples shown together with classified training samples.
Table 3 Dependence of extracted features y1 and y2 on
original features
Original feature y1 y2
Si −0.31 −0.42
K0.69 −0.18
Ca −0.10 −0.20
Ti −0.35 0.07
Mn 0.04 0.37
Fe 0.01 0.01
Zn 0.01 −0.07
Rb 0.36 −0.002
Sr 0.08 0.04
Zr −0.39 −0.78
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simple procedure, which addresses all available measure-
ment data in a specific way and makes a decision based
on these data, but also allows a deep insight into the cer-
amic assemblages. The relative position of the points
representing ceramic samples in two-dimensional space
from the classification line can be of importance in
detecting possible trading activities, production technol-
ogy or even measurement irregularities (due to in-situ
conditions).
The success of the classification model was tested by
the leave-one-out cross validation method [36]. 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 classi-
fied. Another test of the classification model was per-
formed. 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 cor-
rectly classified using the model developed during the
training process.
Conclusions
According to the results presented, several conclusions
can be drawn. Algorithm of the proposed decision-
making procedure enables effective classification of cer-
amic 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 forma-
tion 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 deter-
mined by the greatest variance in their elemental composi-
tions 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 min-
imal 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 identifica-
tion of objects based on their well-known provenance
and that the proposed decision-making procedure yields
satisfactory classification results. It should be empha-
sized that the selection of dimension reduction tech-
nique also has to be careful and in accordance with the
aim of data analysis.
There are no previous studies dealing with the investi-
gation 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 pro-
venience 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 cul-
tural 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 expe-
rimental 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.
Methods
Experimental
pEDXRF analysis for non-destructive and non-invasive
characterisation of the ceramic artefacts was performed
Table 4 Classification results for the three site groups
and leave-one-out cross validation results
Predicted Group Membership Total
Bubanj Pločnik Vinča
TRS Count 1 13 0 0 13
2 0 22 3 25
31 3 2529
%1 100 0 0 100
20 88 12 100
3 3.4 10.3 86.2 100
Cross validated Count 1 10 1 2 13
2 0 18 7 25
31 5 2329
%1 76.9 7.7 15.4 100
20 72 28 100
3 3.4 17.2 79.3 100
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using a milli-beam spot XRF spectrometer. The spec-
trometer (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 mm
2
/500 μm, Be window 12.5 μm thick-
ness), 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 ana-
lysis. A 35 kV high voltage, 800 μA, no filter and a 100 s
measuring time were selected as experimental para-
meters 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 [33]) that the high correl-
ation 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 cer-
amic 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 [33], and the aver-
age 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 increas-
ingly frequent requirement [37]. To meet this require-
ment, it is useful to design an efficient and reliable
decision-making procedure [38]. 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) clas-
sification followed by classification success testing.
During the analytical examination and characterisation
of ceramic sherds, the elemental composition was deter-
mined as described above. The result was that 67 differ-
ent 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 para-
meters 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 Xof dimension nonto a vec-
tor Yof dimension m(considerably smaller than the ini-
tial 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 previ-
ous 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 pur-
pose 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 vari-
ables that are linear combinations of the original one re-
sult 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 classifica-
tion, 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 clas-
sifier design approach. Second, it is possible to identify
the important measurements with regard to classifica-
tion. Dimension reduction consists of finding a trans-
formation 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 Ais the explicate solution of
the optimisation criterion J¼tr S1
wSb

, obtained as the
solution for the generalised singular value decompos-
ition of the matrix S1
wSb(where S
w
and S
b
represent the
within-class scatter matrix and between-class scatter
matrix, respectively). The meigenvectors correspond to
the mlargest eigenvalues form the matrix A[35]. Two-
dimensional projection is the most desirable, allowing
examination of the classification results in terms of
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recognition ability (percentage of members of the train-
ing set correctly classified) and prediction ability (per-
centage of members of the test set correctly classified
using the rules developed during the training).
Additional file
Additional file 1: Elemental composition of the three ceramic
samples group. The mean intensity is expressed in counts per
second (cps). Corresponding measurement uncertainties are reported
in the brackets.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
MGK conceived of the study and, together with MMS, participated in its
design and drafted the manuscript. MMS coordinated ceramic sherds
sampling. MGK, MMS and VA participated in all analytical procedures. MGK
and GK took part in the design and performed the statistical analysis. This
project was based on the ideas and carried out under the guidance of MGK,
MMS and GK, in consultation with RJH. All authors have read and approved
the final manuscript.
Acknowledgements
The authors express their gratitude to the archaeologists Dušan Šljivar, Prof.
Dr. Nenad Tasićand Dr. Aleksandar Bulatovićfor making ceramic samples
available. Maja Gajić-Kvaščev especially wishes to thank Prof. Dr. Željko
Đurovićfrom 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).
Author details
1
Vinča Institute of Nuclear Sciences, University of Belgrade, Mike Petrovića
Alasa 12-14, Belgrade, Serbia.
2
National Museum Belgrade, Trg Republike 1a,
Belgrade, Serbia.
3
Faculty of Technology and Metallurgy, University of
Belgrade, Karnegijeva 4, Belgrade, Serbia.
4
Faculty of Electrical Engineering,
University of Belgrade, Bul. kralja Aleksandra 73, Belgrade, Serbia.
Received: 24 June 2012 Accepted: 12 September 2012
Published: 14 September 2012
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doi:10.1186/1752-153X-6-102
Cite this article as: Gajić-Kvaščev et al.:Non-destructive characterisation
and classification of ceramic artefacts using pEDXRF and statistical
pattern recognition. Chemistry Central Journal 2012 6:102.
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