Application and Comparison of Weighted Weights of Evidence Models
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摘要: 证据权方法是目前最常用的信息综合方法之一，广泛应用于矿产资源定量预测与评价.然而，它要求变量间相互独立，地质上很难满足这一条件.如何削弱条件不独立对证据权预测结果的影响，已成为当前数学地球科学研究的热点.解决该问题的途径之一是对传统证据权模型进行校正，比如采取加权的方法对原证据权模型计算的证据权重进行修正，以便消除非条件独立性的影响.对近期提出的多种加权证据权模型进行了系统的对比研究，基于同样的应用实例和实验方案，对不同方法的应用效果进行了比较，结果表明，各种加权证据权模型均可不同程度地削弱证据图层条件不独立性的影响，其中，基于逻辑回归的加权证据权模型优于其他加权方法.Abstract: Weights of evidence (WofE) is one of the most widely used methods in prediction and evaluation of mineral resources. It requires the independence of geological variables. However, it is almost impossible to meet the requirement among geological variables. The study of reducing the influence of the independence of variables has become a hot topic. One way to solve the problem is to modify the traditional WofE model such as modifying the weights of each evidential layer by calculating correction factor. In this study, some weighted WofE models proposed in recent years are systematically studied, i.e., the same data of case and the same test program are used to compare these models. The results illustrate that weighted WofE models can reduce the influence of dependence among variables to some extent, and the weighted WofE model based on logistic regression performs better than others.
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表 1 实验数据(据Agterberg et al., 1993)
Table 1. Test data
编号 年龄 高程 接触距离 岩石类型 裂隙距离 通道数 面积 1 0 0 0 0 1 0 10 052 2 0 0 0 0 0 1 3 363 3 0 0 0 1 1 0 3 268 4 0 0 0 1 0 0 1 074 5 0 1 0 0 1 0 5 455 6 0 1 0 0 0 0 25 7 0 0 1 0 1 0 3 482 8 0 1 0 1 1 0 2 518 9 0 0 1 0 0 0 1 474 10 0 1 0 1 0 0 1 371 11 1 0 0 0 1 0 5 12 1 0 0 0 0 0 705 13 0 0 1 1 1 0 5 14 0 0 1 1 0 0 744 15 1 0 0 1 1 0 422 16 1 0 0 1 0 0 58 17 0 1 1 0 1 0 12 18 0 1 1 0 0 0 179 19 1 1 0 0 1 2 1 766 20 1 1 0 0 0 0 119 21 0 1 1 1 1 1 1 055 22 0 1 1 1 0 0 33 23 1 0 1 0 1 0 10 24 1 1 0 1 1 0 146 25 1 0 1 0 0 1 623 26 1 1 0 1 0 0 145 27 1 0 1 1 1 2 504 28 1 0 1 1 0 0 1 29 1 1 1 0 1 2 317 30 1 1 1 0 0 1 277 31 1 1 1 1 1 3 348 32 1 1 1 1 0 0 295 
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表 2 各加权证据权模型加权系数
Table 2. Weighted coefficients of different kinds of weighted WofE model
证据图层 S-K加权 秩相关系数加权 逻辑回归加权 *Deng加权W+ *Deng加权W- 年龄 0.44 0.76 0.84 0.82 0.80 高程 0.14 0.82 0.53 0.67 0.76 接触距离 0.27 0.94 0.84 0.90 0.93 岩石类型 0.21 0.91 0.00 0.71 0.45 裂隙距离 0.05 1.11 5.07 6.67 2.61 注：*Deng的加权方案下，W+和W-加权系数不同.
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表 3 各种证据权模型的权重
Table 3. Weights of different kinds of WofE model
图层 原始权重 S-K加权 秩相关系数加权 逻辑回归加权 Deng加权 W+ W- W+ W- W+ W- W+ W- W+ W- 年龄 1.77 -1.72 0.78 -0.76 1.34 -1.30 1.49 -1.44 1.45 -1.37 高程 0.67 -0.74 0.09 -0.10 0.55 -0.61 0.36 -0.39 0.45 -0.56 接触距离 1.19 -1.20 0.33 -0.33 1.11 -1.12 1.00 -1.01 1.07 -1.12 岩石类型 0.43 -0.26 0.09 -0.05 0.39 -0.24 0.00 0.00 0.30 -0.12 裂隙距离 0.04 -0.13 0.00 -0.01 0.05 -0.15 0.22 -0.67 0.29 -0.34
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表 4 各证据权模型预测后验概率
Table 4. Posterior probabilities using different kinds of WofE model
编号 普通证据权 S-K加权 秩相关系数加权 Deng加权 逻辑回归加权 1 7.00E-06 9.40E-05 1.31E-05 1.83E-05 2.36E-05 2 1.30E-05 1.09E-04 2.45E-05 2.79E-05 2.36E-05 3 1.10E-05 1.08E-04 2.02E-05 1.49E-05 9.76E-06 4 2.80E-05 1.15E-04 4.17E-05 5.04E-05 5.01E-05 5 2.30E-05 1.14E-04 3.44E-05 2.69E-05 2.07E-05 6 7.30E-05 1.82E-04 1.22E-04 1.63E-04 1.77E-04 7 5.60E-05 1.33E-04 7.80E-05 7.67E-05 5.01E-05 8 6.20E-05 1.80E-04 1.00E-04 8.68E-05 7.30E-05 9 4.70E-05 1.32E-04 6.43E-05 4.09E-05 2.07E-05 10 2.21E-04 4.38E-04 1.82E-04 3.08E-04 4.40E-04 11 1.86E-04 4.35E-04 1.51E-04 1.64E-04 1.82E-04 12 1.46E-04 2.10E-04 2.28E-04 2.48E-04 1.77E-04 13 1.23E-04 2.08E-04 1.88E-04 1.32E-04 7.29E-05 14 4.41E-04 5.06E-04 3.42E-04 4.68E-04 4.39E-04 15 3.70E-04 5.02E-04 2.82E-04 2.49E-04 1.82E-04 16 3.03E-04 2.21E-04 3.89E-04 4.48E-04 3.74E-04 17 2.55E-04 2.19E-04 3.20E-04 2.39E-04 1.55E-04 18 7.67E-04 5.29E-04 4.80E-04 4.51E-04 3.85E-04 19 5.07E-04 2.53E-04 6.00E-04 3.63E-04 1.55E-04 20 2.40E-03 8.44E-04 1.70E-03 2.73E-03 3.28E-03 21 1.82E-03 6.15E-04 1.09E-03 1.29E-03 9.31E-04 22 1.53E-03 6.10E-04 8.99E-04 6.86E-04 3.85E-04 23 4.01E-03 9.66E-04 2.62E-03 2.21E-03 1.36E-03 24 1.64E-02 1.17E-03 8.32E-03 6.07E-03 2.87E-03 25 6.00E-06 9.40E-05 1.08E-05 9.76E-06 9.77E-06 26 6.04E-04 2.55E-04 7.27E-04 6.82E-04 3.74E-04 27 2.02E-03 8.37E-04 1.40E-03 1.46E-03 1.36E-03 28 8.27E-03 1.02E-03 4.46E-03 3.99E-03 2.87E-03 29 9.12E-04 5.33E-04 5.82E-04 8.46E-04 9.31E-04 30 4.77E-03 9.73E-04 3.18E-03 4.15E-03 3.28E-03 31 9.83E-03 1.03E-03 5.40E-03 7.47E-03 6.92E-03 32 1.94E-02 1.18E-03 1.01E-02 1.13E-02 6.92E-03
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表 5 各证据权模型预测后验概率排序
Table 5. The rank of posterior probabilities using different kinds of WofE model
编号 普通证据权 S-K加权 秩相关系数加权 Deng加权 逻辑回归加权 1 31 31 31 30 27 2 29 29 29 28 28 3 30 30 30 31 32 4 27 27 27 26 25 5 28 28 28 29 29 6 23 23 23 22 19 7 25 25 25 25 26 8 24 24 24 24 23 9 26 26 26 27 30 10 19 15 21 17 11 11 20 16 22 21 17 12 21 21 19 19 20 13 22 22 20 23 24 14 15 13 16 13 12 15 16 14 18 18 18 16 17 19 15 15 15 17 18 20 17 20 21 18 12 12 14 14 13 19 14 18 12 16 22 20 7 7 7 6 3 21 9 9 9 9 10 22 10 10 10 11 14 23 6 6 6 7 8 24 2 2 2 3 6 25 32 31 32 32 31 26 13 17 11 12 16 27 8 8 8 8 7 28 4 4 4 5 5 29 11 11 13 10 9 30 5 5 5 4 4 31 3 3 3 2 1 32 1 1 1 1 2
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表 6 各证据权模型之间秩相关系数
Table 6. Rank correlation coefficients between posterior probabilities obtained from different WofE models
普通证据权 S-K加权 秩相关系数加权 Deng加权 逻辑回归加权 不加权 1.00 S-K加权 0.99 1.00 秩相关系数加权 0.99 0.96 1.00 Deng加权 0.99 0.98 0.98 1.00 逻辑回归加权 0.94 0.96 0.92 0.97 1.00
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[1] Agterberg, F.P., 1989. Computer programs for mineral exploration. Science, 245(4913): 76-81. doi: 10.1126/science.245.4913.76 [2] Agterberg, F.P., 1992. Combining indicator patterns in weights of evidence modeling for resource evaluation. Nonrenewal Resources, 1(1): 39-50. doi: 10.1007/BF01782111 [3] Agterberg, F.P., 2011. A modified weights-of-evidence method for regional mineral resource estimation. Natural Resources Research, 20(2): 95-101. doi: 10.1007/s11053-011-9138-0 [4] Agterberg, F.P., Cheng, Q.M., 2002. Conditional independence test for weights-of-evidence modeling. Natural Resources Research, 11(4): 249-55. doi: 10.1023/A:1021193827501 [5] Agterberg, F.P., Bonham-Carter, G.F., Cheng, Q.M., et al., 1993. Weights of evidence modeling and weighted logistic regression for mineral potential mapping. In: Davis, J.C., Herzfeld, U.C., eds., Computers in geology—25 years of progress. Oxford University Press, New York, 13-32. [6] Agterberg, F.P., Bonham-Carter, G.F., Wright, D.F., 1990. Statistical pattern integration for mineral exploration. In: Gaál, G., Merriam, D.F., eds., Computer applications in resource estimation prediction and assessment of metals and Petroleum. Pergamon Press, New York, 1-12. [7] Bonham-Carter, G.F., 1994, Geographic information systems for geoscientists: modeling with GIS. Oxford, Pergamon, 398. [8] Bonham-Carter, G.F., Agterberg, F.P., Wright, D.F., 1988. Integration of geological datasets for gold exploration in Nova Scotia. Photogrammetric Engineering & Remote Sensing, 54(11): 1585-1592. doi: 10.1029/SC010p0015/pdf [9] Bonham-Carter, G.F., Agterberg, F.P., Wright, D.F., 1989. Weights of evidence modelling: a new approach to mapping mineral potential. In: Agterberg, F.P., Bonham-Carter, G.F., eds., Statistical applications in the earth sciences. Canadian Government Publishing Centre, Ottawa, 171-183. [10] Cervi, F., Berti, M., Borgatti, L., et al., 2010. Comparing predictive capability of statistical and deterministic methods for landslide susceptibility mapping: a case study in the northern Apennines (Reggio Emilia Province, Italy). Landslides, 7(4): 433-444. doi: 10.1007/s10346-010-0207-y [11] Cheng, Q.M., 2008. Non-linear theory and power-law models for information integration and mineral resources quantitative assessments. Mathematical Geosciences, 40(5): 503-532. doi: 10.1007/s11004-008-9172-6 [12] Cheng, Q.M., 2011. Integration of AdaBoost and weights of evidence model for mineral potential probabilistic mapping. Session MG3 "Geo-process Modeling" at IAMG 2011 Annual Conference, Salzburg, Austria. [13] Cheng, Q.M., 2012. Application of a newly developed boost weights of evidence model (BoostWofE) for mineral resources quantitative assessments. Journal of Jilin University: Earth Science Edition (in press). http://en.cnki.com.cn/Article_en/CJFDTOTAL-CCDZ201206046.htm [14] Cho, S.H., Poudyal, N.C., Roberts, R.K., 2008. Spatial analysis of the amenity value of green open space. Ecological Economics, 66(2-3): 403-416. doi: 10.1016/j.ecolecon.2007.10.012 [15] Deng, M.F., 2009, A conditional dependence adjusted weights of evidence model. Natural Resources Research, 18(4): 249-258. doi: 10.1007/s11053-009-9101-5 [16] Gorney, R.M., Ferris, D.R., Ward, A.D., et al., 2011. Assessing channel-forming characteristics of an impacted headwater stream in Ohio, USA. Ecological Engineering, 37(3): 418-430. doi: 10.1016/j.ecoleng.2010.11.013 [17] Journel, A.G., 2002. Combining knowledge from diverse sources: an alternative to traditional conditional independence hypotheses. Mathematical Geosciences, 34(5): 573-596. doi: 10.1023/A:1016047012594 [18] Krishnan, S., Boucher, A., Journel, A.G., 2005. Evaluating information redundancy through the Tau model. Quantitative Geology and geostatistics, 14(5): 1037-1046. doi: 10.1007/978-1-4020-3610-1_108 [19] Netra, R., Regmi, N.R., Giardino, J.R., et al., 2010. Modeling susceptibility to landslides using the weight of evidence approach: western Colorado, USA. Geomorphology, 115(1-2): 172-187. doi: 10.1016/j.geomorph.2009.10.002 [20] Neuh user, B., Terhorst, B., 2007. Landslide susceptibility assessment using "weights-of-evidence" applied to a study area at the Jurassic escarpment (SW-Germany). Geomorphology, 86(1-2): 12-24. doi: 10.1016/j.geomorph.2006.08.002 [21] Polyakova, E.I., Journel, A.G., 2007. The Nu expression for probabilistic data integration. Mathematical Geology, 39(8): 715-733. doi: 10.1007/s11004-007-9117-5 [22] Romero-Calcerrada, R., Barrio-Parra, F., Millington, J.D.A., et al., 2010. Spatial modelling of socioeconomic data to understand patterns of human-caused wildfire ignition risk in the SW of Madrid (central Spain). Ecological Modelling, 221(1) : 34-45. doi: 10.1016/j.ecolmodel.2009.08.008 [23] Romero-Calcerrada, R., Luque, S., 2006. Habitat quality assessment using weights-of-evidence based GIS modelling: the case of picoides tridactylus as species indicator of the biodiversity value of the finnish forest. Ecological Modelling, 196(1-2): 62-76. doi: 10.1016/j.ecolmodel.2006.02.017 [24] Schaeben, H., 2012. Comparison of mathematical methods of potential modeling. Mathematical Geosciences, 44(1): 101-129. doi: 10.1007/s11004-011-9373-2 [25] Schaeben, H., Boogart, K.G.V.D., 2011. Comment on "a conditional dependence adjusted weights of evidence model" by Minfeng Deng in natural resources research 18(2009), 249-258. Natural Resources Research, 20(4): 401-406. doi: 10.1007/s11053-011-9146-0 [26] Spiegelhalter, D.J., Knill-Jones, R.P., 1984. Statistical and knowledge-based approaches to clinical decision-support systems, with an application in gastroenterology. Journal of the Royal Statistical Society(Ser. A), 147(1): 35-77. doi: 10.2307/2981737 [27] Wang, Z.W., Li, D.Y., Wang, X.G., 2007. Zonation of landslide hazards based on weights of evidence model. Chinese Journal of Geotechnical Engineering, 29(8): 1268-1273 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-YTGC200708028.htm [28] Zhang, S.Y., Cheng, Q.M., Zhang, S.P., et al., 2009. Weighted weights of evidence and stepwise weights of evidence and their application in Sn-Cu mineral potential mapping in Gejiu, Yunnan Province, China. Earth Science—Journal of China University of Geosciences, 34(2): 281-286(in Chinese with English abstract). doi: 10.3799/dqkx.2009.028 [29] Zhang, S.Y., Wu, Q., Cheng, Q.M., et al., 2006. Weights of evidence method based on fuzzy training layer and its application in desertification assessment. Earth Science—Journal of China University of Geosciences, 31(3): 389-393(in Chinese with English abstract). http://www.researchgate.net/publication/286656642_Weights_of_evidence_method_based_on_fuzzy_training_layer_and_its_application_in_desertification_assessment [30] 成秋明, 2012. 增强证据权(BoostWofE)新方法在矿产资源定量评价中的应用. 吉林大学学报: 地球科学版(待刊). https://www.cnki.com.cn/Article/CJFDTOTAL-CCDZ201206046.htm [31] 王志旺, 李端有, 王湘桂, 2007. 证据权法在滑坡危险度区划研究中的应用. 岩土工程学报, 29(8): 1268-1273. doi: 10.3321/j.issn:1000-4548.2007.08.026 [32] 张生元, 成秋明, 张素萍, 等, 2009. 加权证据权模型和逐步证据权模型及其在个旧锡铜矿产资源预测中的应用. 地球科学——中国地质大学学报, 34(2): 281-286. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200902008.htm [33] 张生元, 武强, 成秋明, 等, 2006. 基于模糊预测对象的证据权方法及其在土地沙漠化评价中的应用. 地球科学——中国地质大学学报, 31(3): 389-393. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200603016.htm -
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