A Comparative Analysis of Favorability Mappings by Weights of Evidence, Probabilistic Neural Networks, Discriminant Analysis, and Logistic Regression
Tóm tắt
This study compares the performance of favorability mappings by weights of evidence (WOE), probabilistic neural networks (PNN), logistic regression (LR), and discriminant analysis (DA). Comparisons are made by an objective measure of performance that is based on statistical decision theory. The study further emphasizes out-of-sample inference, and quantifies the extent to which outcome is influenced by optimum variable discretization with classification and regression trees (CARTS). Favorability mapping methodologies are evaluated systematically across three case studies with contrasting scale and geologic information:
$$\begin{gathered} Case{\text{}}Study{\text{}}Carlin{\text{}}Alamos{\text{}}Nevada \hfill \\ {\text{}}Se\dim ent - Hosted{\text{ }}Intrusion - \operatorname{Re} lated{\text{}}Intrusion - \operatorname{Re} leted \hfill \\ {\text{ }}gold{\text{}}copper{\text{}}copper \hfill \\ Scale{\text{}}deposit{\text{}}district{\text{}}regional \hfill \\ Cell{\text{}}Size{\text{}}small{\text{}}(0.01{\text{}}km^2 ){\text{}}medium{\text{}}(1{\text{}}km^2 ){\text{}}l\arg e{\text{}}(7{\text{}}km^2 ) \hfill \\ Information{\text{}}Level{\text{}}high{\text{}}\bmod erate{\text{}}low \hfill \\ Geo\operatorname{var} iables{\text{}}complex{\text{}}simple{\text{}}simple \hfill \\ Variable{\text{}}\operatorname{int} erdependency{\text{}}\bmod erate{\text{}}low{\text{ }}high \hfill \\ Asymmetry{\text{}}in{\text{}}frequency{\text{}}of{\text{}}\bmod est{\text{ }}considerable{\text{}}severe{\text{}} \hfill \\ barren{\text{}}and{\text{}}\min eralized{\text{}}cells{\text{ }} \hfill \\ \end{gathered} $$
Estimated favorabilities for all cells then are represented by computed percent correct classification, and expected loss of optimum decision. The deposit-scale Carlin study reveals that the performances of the various methods from lowest to highest expected decision loss are: PNN, nonparametric DA, binary PNN (WOE variables), LR, and WOE. Moreover, the study indicates that approximately 40% of the increase in expected decision loss using WOE instead of PNN is the result of information loss from variable discretization. The remaining increases in losses using WOE are the result of its lesser inferential power than PNN. The district-scale Alamos study shows that the lowest expected decision loss is not by PNN, but by canonical DA. CARTS discretization improves greatly the performance of WOE. However, PNN and DA perform better than WOE. Unlike findings from the Alamos and Carlin studies, results from the regional-scale Nevada study indicate that decision losses by LR and DA are lower than those by WOE or PNN. Moreover, decision losses by CARTS-based canonical DA are noticeably the lowest of all, including those by LR and DA using the original variables.
Tài liệu tham khảo
Agterberg, F. P., Bonham-Carter, G. F., Cheng, Q. M., and Wright, D. F., 1993, Weights of evidence modeling and weighted logistic regression for mineral potential mapping, in Davis, J. C., and Herzfeld, U. C., eds., Computers in Geology–25 Years of Progress: Oxford Univ. Press, New York, p. 13–32.
Bonham-Carter, G. F., 1994, Geographic Information Systems for geoscientists, Pergamon Press, Oxford, 398p.
Bonham-Carter, G. F., Kerswill, J. A., Shaw, J., and Chorlton, L., 1998, Iron-formation gold and volcanic-associated massive-sulphide base-metal potential in Slave Province by weights of evidence; a preliminary appraisal (abst.) Geol. Assoc. Canada; Mineral. Assoc. Canada; Can. Geophy. Union, Joint Annual Meeting 23 Program with Abstracts p. A20.
Breiman, L., Friedman, J., Olshen, R., and Stone, C. J., 1984, Classification and regression trees: Chapman and Hall, New York, 368p.
Cooley, W. W., and Lohnes, P. R., 1962, Multivariate procedures for the behavioral sciences: John Wiley & Sons, New York, 211p.
Frank, D. G., 1999, Mineral Resources Data System (MRDS) data base: U.S. Geol. Survey digital data series DDS-52, 1 CD-ROM.
Grossman, J. N., 1998, National geochemical atlas: The geochemical landscape of the conterminous United States derived from stream sediment and other solid sample media analyzed by the National Uranium Resource Evaluation (NURE) Program (version 3.01): U.S. Geol. Survey Open-File Rept. 98–0622, 1 CD-ROM.
Harris, D. P., 1984, Mineral resources appraisal; mineral endowment, resources, and potential supply; concepts, methods, and cases: Oxford Univ. Press, New York, 455p.
Harris, D. P., and Pan, G., 1999, Mineral favorability mapping: A comparison of artificial neural networks, logistic regression, and discriminant analysis: Natural Resources Research, v.8, no.2, p. 93–109.
Kemp, L. D., Bonham-Carter, G. F., and Raines, G. L., 1999, Arc-WofE: Arc View extension for weights of evidence mapping: http://gis.nrcan.gc.ca/software/arcview/wofe.
Kucks, R. P., 1999a, Magnetic anomaly data grid: U.S. Geol. Survey digital data series DDS-09, 1 CD-ROM.
Kucks, R. P., 1999b, Gravity anomaly data grid: U.S. Geol. Survey digital data series DDS-09, 1 CD-ROM.
Mihalasky, M. J., and Bonham-Carter, G. F., 2001, Lithodiversity and its spatial association with metallic mineral sites, Great Basin of Nevada: Natural Resources Research, v.10, no.3, p. 209–226.
Pan, G., 1989, Concepts and methods of multivariate information synthesis for mineral resources estimation: unpubl. doctoral dissertation, Univ. Arizona, 302p.
Pan, G., and Harris, D. P., 2000, Information synthesis for mineral exploration: Oxford Univ. Press, New York, 461p.
Phillips, J. D., Duval, J. S., and Ambroziak, R. A., 1993, National geophysical data grids: gamma-ray, gravity, magnetic, and topographic data for the conterminous United States: U.S. Geol. Survey digital data series DDS-09, 1 CD-ROM.
Singer, D. A., and Kouda, R., 1999, A comparison of the weights-of-evidence method and probabilistic neural networks: Natural Resources Research, v.8, no.4, p. 287–298.
Steinberg, D., and Colla, P. L., 1995, CART: Tree-structured non-parametric data analysis: Salford Systems, San Diego, California
Turner, R. M., Bawiec, W. J, and Ambroziak, R. A., 1991, Geology of Nevada; a digital representation of the 1978 geologic map of Nevada: U.S. Geol. Survey digital data series DDS-02, 1 CD-ROM.
Vazquez-Perez, A., 1975, Economic geology of the Alamos mining district, Sonora, Mexico: unpubl. masters thesis, Univ. Arizona, 170p.
Wright, D. F., and Bonham-Carter, G. F., 1996, VHMS favourability mapping with GIS-based integration models, Chisel Lake-Anderson Lake area, in Bonham-Carter, G. F., Galley, A. G., and Hall, G. E. M., eds., EXTECH I; a multidisciplinary approach to massive sulphide research in the Rusty Lake-Snow Lake greenstone belts, Manitoba: Geol. Survey Canada, Bull. p. 339–379.