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APPLICATIONS V: FORENSIC GLASS ANALYSIS
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TABLE 14.5 2 and SU)
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Summary of Likelihood Ratios for Potassium (K) Data (Chosen by nn exp 0.0 0.1 0.2 0.5 Within-group comparisons b
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Likelihood Ratio Range
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0 1 1 101 101 102 102 103 103 104 >104 Misclassi cation
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4 174 13 4 2 3 2.0%
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43 138 3 9 4 3 21.5%
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4 181 15 0 0 0 2.0%
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4 181 15 0 0 0 2.0%
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4 181 15 0 0 0 2.0%
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4 181 15 0 0 0 2.0%
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4 170 26 0 0 0 2.0%
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Between-group comparisons 0 1 1 101 101 102 102 103 103 104 >104 Misclassi cation 6463 2722 10696 8 8 3 67.5% 7931 11881 44 33 9 2 60.1% 6989 12869 40 2 0 0 64.9% 6988 12870 41 1 0 0 64.9% 6986 12872 41 1 0 0 64.9% 6971 12887 41 1 0 0 65.0% 7861 11960 78 1 0 0 60.5%
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SUMMARY
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As a type of evidence, glass can be very useful contact trace material in a wide range of offenses including burglaries and robberies, murders, assaults, criminal damage, and thefts of and from motor vehicles. In all these situations there is the potential for glass fragment transfer, providing a link between suspect and crime. Hence the correct interpretation of glass evidence is critical in establishing such connections. Previous work has been based on the use of a normal kernel estimation procedure for evidence evaluation. However, this may be inadequate when the data are positively skewed and an exponential distribution is thought to be a better model [3]. Three techniques that attempt to alleviate this problem were investigated and found to provide better likelihood ratio estimations. In this chapter the role of feature evaluation as an aid to glass analysis was investigated. As the two-level models used were univariate, the task of the evaluation methods was to determine the most informative feature for use in the models. The results have shown that automated feature evaluation techniques can indeed aid the choice of variable for further modeling. This choice is a critical factor in the resulting quality of evidence evaluation. Situations are often encountered where many competing variables co-exist. The manual selection of which variable to use may result in subsequent analysis being too subjective.
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SUMMARY
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TABLE 14.6 Summary of Likelihood Ratios for Sodium (Na) Data (Chosen by FuzEnt and GR) Likelihood Ratio Range nn exp 0.0 0.1 0.2 0.5 b
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Within-group comparisons 0 1 1 101 101 102 102 103 103 104 >104 Misclassi cation 5 179 6 5 5 0 2.5% 3 6 191 0 0 0 1.5% 7 183 10 0 0 0 3.5% 7 183 10 0 0 0 3.5% 7 183 10 0 0 0 3.5% 7 183 10 0 0 0 3.5% 4 183 13 0 0 0 2.0%
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Between-group comparisons 0 1 1 101 101 102 102 103 103 104 >104 Misclassi cation 8540 11239 83 18 20 0 57.1% 6543 2879 10478 0 0 0 67.1% 9414 10452 34 0 0 0 52.7% 9414 10451 35 0 0 0 52.7% 9410 10455 35 0 0 0 52.7% 9345 10519 36 0 0 0 53.0% 7609 6614 5677 0 0 0 61.8%
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TABLE 14.7 Results for Forensic Data Method Features J48 Unreduced 8 83.13 FRFS 8 83.13 Tolerance 6 82.00
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JRip 79.38 79.38 78.25
PART 80.50 80.50 78.00
MODLEM 78.00 78.00 74.13
Through the use of feature evaluation methods, this important decision can be made without expert assistance.
SUPPLEMENTARY DEVELOPMENTS AND INVESTIGATIONS
This chapter presents other developments that have been initiated and future work in the areas of feature selection and rule induction, arising from some of the issues discussed in this book. For feature selection, RSAR-SAT is proposed based on the discernibility matrix approach to nding reducts and employing techniques from propositional satis ability. Additionally the concept of fuzzy universal reducts is proposed as a way of enabling more accurate data reductions. A new decision tree induction method based on the fuzzy-rough metric is suggested, with some initial experimental investigations presented. In addition to these developments, several areas of future work are discussed that utilize the properties of fuzzy-rough sets. A potential mechanism for fuzzy-rough rule induction and fuzzy-rough clustering are proposed. In crisp rough sets, rule induction and clustering a two successful areas of application, but these suffer the same drawbacks as crisp rough set feature selection. It is natural, then, to extend these methods via fuzzy-rough sets. There is also the possibility of using fuzzy-rough sets for the optimization of fuzzi cations.