Fragment Elemental Analysis in Visual Studio .NET

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14.3.1 Fragment Elemental Analysis
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The four selected glass fragments were placed on self-adhesive carbon tabs on an aluminum stub and then carbon coated using an SCD sputter (Bal-Tech, Switzerland). The prepared stub was mounted in the sample chamber of a scanning electron microscope. Analysis of the elemental content of each glass fragment was carried out using a scanning electron microscope (JSM-5800 Jeol, Japan),
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with an energy dispersive X-ray spectrometer (Link ISIS 300, Oxford Instruments Ltd., United Kingdom). Three replicate measurements were taken from different areas on each of the four fragments, making 12 measurements from each glass object but only 4 independent measurements. Four means of the measurements were used for the analysis. The measurement conditions were accelerating voltages 20 kV, life time 50s, magni cation 1000 2000 , and the calibration element was cobalt. The SEMQuant option (part of the software LINK ISIS, Oxford Instruments Ltd., United Kingdom) was used in the process of determining the percentage of particular elements in a fragment. The option applied a ZAF correction procedure that takes into account corrections for the effects of difference in the atomic number (Z), absorption (A), and X-ray uorescence (F ). The selected analytical conditions allowed the determination of all elements except lithium (Li) and boron (B). However, only the concentrations of oxygen (O), sodium (Na), magnesium (Mg), aluminum (Al), silicon (Si), potassium (K), calcium (Ca), and iron (Fe) are considered further here as glass is essentially a
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APPLICATIONS V: FORENSIC GLASS ANALYSIS
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silicon oxide with sodium and/or calcium added to create a commonly produced glass, and potassium, magnesium, aluminum, and iron added to stabilize its structure and modify its physicochemical properties. Histograms of the distributions of the data can be found in Figure 14.2.
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14.3.2 Data Preparation
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As two of the feature evaluation algorithms require fuzzy sets to be de ned for each element in the dataset in order to maximize the use of information contained in the real-valued variables, further processing is required. Note that the attributes still take real values, and hence no discretization is performed. For this set of experiments, ve fuzzy sets per feature were derived automatically based on the mean and standard deviation as seen in Figure 14.3. The value was set at 0.7. There is no theoretical argument as to why ve sets should be chosen, although psychological research suggests that 5, 7, or 9 categories should be used, mimicking human cognition. To minimize computational effort, only ve sets are de ned for this application.
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14.3.3 Feature Selection
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Several feature evaluation methods outlined previously were applied to the processed glass data in order to select a single attribute for use in the univariate LR estimators. The dataset containing the full set of elements was processed by each method, resulting in a ranking of these features. The top ranked feature/element for each method was then selected, and the data reduced to this feature only.
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14.3.4 Estimators
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The performance of four procedures for estimating the likelihood ratio is compared. The procedures estimate the between-group distributions with a normal distribution, an exponential distribution, a normal adaptive kernel, and a biweight kernel with a boundary condition.
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In the experimentation two situations need to be considered: when the control and recovered data are from the same source and when they are from different sources. For same-source comparisons, the control and recovered data are taken from the same group by splitting the group into two equally sized, nonoverlapping halves (containing two measurements each). For different-source comparisons, the control and recovered data are entire groups selected from different sources.
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Aluminium data 100 150 200 250 300 150
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Calcium data
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Frequency
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Frequency 0 1 2 Iron data 3 4
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Magnesium data 250 Frequency
100 200 300 400 500 600
Frequency
0.4 Oxygen data
0 0.0
Potassium data 100 200 300 400 500 600 0 0
100 120
Frequency
Frequency
Silicon data 80 100 120 140 250
Sodium data
Frequency
Frequency
Figure 14.2 Data distributions for the eight elements
APPLICATIONS V: FORENSIC GLASS ANALYSIS
Figure 14.3 Fuzzy set construction
Feature Evaluation
Table 14.1 (summarized in Table 14.2) presents the ordering of features as determined by several leading measures of feature signi cance: fuzzy-rough feature evaluation (FRFS), fuzzy entropy (FuzEnt), 2 , gain ratio (GR), information gain (IG), OneR, Relief-F, and symmetrical uncertainty (SU). It can be seen that FRFS, IG, and OneR select aluminum; FuzEnt and GR select sodium; 2 and SU select potassium; and Relief-F selects magnesium. Based on these selections and corresponding data reductions, the four estimators are applied.