. "Appendix H: Principal Components Analysis: How Many Elements Should Be Measured?." Forensic Analysis Weighing Bullet Lead Evidence . Washington, DC: The National Academies Press, 2004.
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Forensic Analysis Weighing Bullet Lead Evidence
TABLE H.7 Principal Components Analysis on All Six-Element Subsets of 1,373-Bullet Subset. Elements 1, 2, 3, 4, 5, 6, and 7 are As, Sb, Sn, Cu, Bi, Ag, and Cd, respectively. Row labels 1, 2, 3, 4, 5, and 6 represent the first principal component through sixth, and the rows show the total variation due to each successive element included in the subset.
123456
123457
123467
123567
124567
134567
234567
1
77.172
77.635
77.399
77.620
28.643
74.472
72.411
2
97.157
104.232
103.993
104.216
54.571
101.046
98.887
3
105.322
124.172
123.494
124.159
63.118
113.817
115.215
4
107.934
132.307
131.628
132.294
65.721
116.590
117.872
5
109.605
134.779
133.731
134.494
67.385
118.314
119.543
6
109.946
136.411
134.087
134.951
67.726
118.656
119.885
TABLE H.8 Total Variance (Compare with 136.944 Total Variance) for Six-Component Subsets, in Order of Increasing Variance
124567
123456
134567
234567
123467
123567
123457
67.726
109.946
118.656
119.885
134.087
134.951
136.411
49.45%
80.28%
86.65%
87.54%
97.91%
98.54%
99.61%
TABLE H.9 Principal Components Analysis on all Seven-Element Subsets of 1,373-Bullet Subset. Elements 1, 2, 3, 4, 5, 6, and 7 are As, Sb, Sn, Cu, Bi, Ag, and Cd, respectively. Row labels 1, 2, 3, 4, 5, and 6 represent the first principal component through sixth, and the rows show the total variation due to each successive element included in the subset.
1234567
1
77.64703
2
104.24395
3
124.20241
4
132.33795
5
134.94053
6
136.60234
7
136.94360
Summary:
3 elements: 237
(83.6% of total variance)
4 elements: 1237
(96.07% of total variance)
5 elements: 12357
(98.16% of total variance) or 12347 (97.52%)
6 elements: 123567
(99.61% of total variance) or 123457 (98.54%) (Bi-Ag correlation)
7 elements: 1234567
(100.00% of total variance)
REFERENCES
1. Koons, R. D. and Grant, D. M. J. Foren.. Sci.2002, 47(5), 950.
2. Randich, E.; Duerfeldt, W.; McLendon, W.; and Tobin, W. Foren. Sci. Int.2002, 127, 174–191.
3. Peele, E. R.; Havekost, D. G.; Peters, C. A.; and Riley, J. P. USDOJ (ISBN 0-932115-12-8), 57, 1991.
