Cultural Heritage Applications: Archaeological Ceramics and Building Restoration - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 136

Table 6.3 Confusion matrix (percentages) by Mixca with 1 PSS ratio

Bronze age Iberian Roman Middle ages

Bronze age 0.79 0 0.07 0.14

Iberian 0 0.89 0.09 0.02

Roman 0.05 0.19 0.69 0.07

Middle Ages 0.02 0 0.05 0.93

Bronze Age pieces 14 % of the time, and Roman pieces cause misclassification of
some pieces from the Bronze Age and the Middle Ages.

6.1.5 Discussion

In order to draw a physical interpretation of the results obtained by ultrasounds, a
diversity of morphological and physiochemical characterization analyses were
carried out using conventional instrumental techniques. A stratified random sam-
pling analysis was made using data from the physical analysis of the pieces: open
porosity and apparent density [ 17 , 18 ]. Thus, a sample of the ceramic pieces for the
different periods was obtained. The raw material composition of the selected
pieces was analyzed using optical microscope and scanning electron microscope
(SEM) [ 19 , 20 ]; and also the processing methods of the pieces were studied. From
those analyses, the differences of the ceramic physical properties for the different
periods and the ultrasound propagation are discussed.

6.1.5.1 Open Porosity and Apparent Density

A sample of the pieces was selected for morphological and physiochemical
characterization based on open porosity and apparent density analyses of the
pieces. For stratified random sampling, the values of these physical properties for
the different periods were considered as random variables that follow Gaussian
distribution. First, an estimation of the variable variance for the different periods
(statistical strata) was made. This estimation was obtained from 45 representative
pieces that were physically tested for open porosity and apparent density. The
results of this prior study are shown in Table 6.4 .
The objective of the sampling was to provide estimators with small variances at
the lowest cost possible (considering that morphological and physiochemical
characterization are costly).To estimate the fraction of the total sample size n
corresponding to the stratum i, we applied the so-called Neyman allocation [ 21 ],
n i
n ¼

N i r i
P

; where L is the number of strata (4 periods for this application), N i is

L

N i r i

i ¼ 1