A prospecting cost-benefit strategy for mineral potential mapping based on ROC curve analysis

Abstract A prospecting cost-benefit strategy is developed by quantitatively defining the prospecting cost and benefit in mineral potential mapping. Suppose that some mineral deposits have been discovered in a study area of a set of grid cells, the prospecting cost and benefit of a “unique” condition can be defined as the percentage of non-deposit-bearing and deposit-bearing cells within the “unique” condition, respectively. By replacing the false positive and true positive rates in the receiver operating characteristic (ROC) curve analysis with the prospecting cost and benefit, the Youden index, likelihood ratio, and lift index can be computed and used to express the mineral potential of the “unique” condition. Thus, the mineral potential mapping in a study area can be implemented by identifying all the possible “unique” conditions and then computing their mineral potential indicators such as the Youden index, likelihood ratio, and lift index. By integrating an automatic “unique” condition searching algorithm with the techniques for computing the mineral potential indicators for each “unique” condition, the following prospecting cost-benefit strategy is developed for mineral potential mapping: (a) select map patterns closely associated with the discovered mineral deposits using their mineral potential indicators, (b) automatically search for all the possible “unique” conditions, (c) evaluate the mineral potential of each “unique” condition using its mineral potential indicators, and (d) assess mineral potential mapping performance using the mineral potential indicator diagrams. For demonstration purposes, the Baishan district in Southern Jilin Province in China, which has a complex geological setting, is chosen as a case study area. The weights of evidence (WofE) modeling posterior probability, Youden index, likelihood ratio, and lift index are applied in the mineral potential mapping and their performance are assessed using their ROC curves, cumulative lift charts, and Youden and likelihood ratio diagrams. The results show that (a) the likelihood ratio and lift index perform similarly well and (b) the posterior probability performs a little bit worse than the likelihood ratio and lift index while a little bit better than the Youden index. Therefore, the prospecting cost-benefit strategy provides a common paradigm for both mineral potential mapping and the performance assessment.

[1]  Yusuf Eshqi Molan,et al.  Prospectivity mapping of Pb–Zn SEDEX mineralization using remote-sensing data in the Behabad area, Central Iran , 2013 .

[2]  Nils P Johnson,et al.  Advantages to transforming the receiver operating characteristic (ROC) curve into likelihood ratio co‐ordinates , 2004, Statistics in medicine.

[3]  F. Agterberg,et al.  Weights of evidence modelling: a new approach to mapping mineral potential , 1990 .

[4]  Maysam Abedi,et al.  ELECTRE III: A knowledge-driven method for integration of geophysical data with geological and geochemical data in mineral prospectivity mapping , 2012 .

[5]  F. Agterberg.  LOGDIA—FORTRAN 77 program for logistic regression with diagnostics , 1989 .

[6]  E. Carranza.  Improved Wildcat Modelling of Mineral Prospectivity , 2010 .

[7]  M. Hale,et al.  Wildcat mapping of gold potential, Baguio District, Philippines , 2002 .

[8]  David I. Groves,et al.  Combined conceptual/empirical prospectivity mapping for orogenic gold in the northern Fennoscandian Shield, Finland , 2008 .

[9]  Qiuming Cheng,et al.  The perimeter-area fractal model and its application to geology , 1995 .

[10]  W. Moon.  Integration of Remote Sensing and Geophysical/geological Data Using Dempster-Shafer Approach , 1989, 12th Canadian Symposium on Remote Sensing Geoscience and Remote Sensing Symposium,.

[11]  S. Wilde,et al.  Nature and significance of the Early Cretaceous giant igneous event in eastern China , 2005 .

[12]  Carlos Roberto de Souza Filho,et al.  Probabilistic neural networks applied to mineral potential mapping for platinum group elements in the Serra Leste region, Carajás Mineral Province, Brazil , 2009, Comput. Geosci..

[13]  Cheng Zhi-jun.  Application of Fuzzy Weights of Evidence Method in Mineral Resource Assessment for Gold in Zhenyuan District, Yunnan Province, China , 2007 .

[14]  Maysam Abedi,et al.  PROMETHEE II: A knowledge-driven method for copper exploration , 2012, Comput. Geosci..

[15]  E. Carranza,et al.  Evidential belief functions for data-driven geologically constrained mapping of gold potential, Baguio district, Philippines , 2003 .

[16]  F. Agterberg,et al.  Integration of Geological Datasets for Gold Exploration in Nova Scotia , 2013 .

[17]  Wang Yu-fen.  Geological characteristics and genesis of Huanggoushan and Banmiaozi gold deposits in Laoling metallogenic belt of southern Jilin , 2010 .

[18]  Wang Wen-lei.  Application of Singularity Theory in Prediction of Tin and Copper Mineral Deposits in Gejiu District,Yunnan,China:Weak Information Extraction and Mixing Information Decomposition , 2009 .

[19]  W. M. Moon,et al.  Information representation and integration of multiple sets of spatial geoscience data , 1995, 1995 International Geoscience and Remote Sensing Symposium, IGARSS '95. Quantitative Remote Sensing for Science and Applications.

[20]  Abbas Bahroudi,et al.  Support vector machine for multi-classification of mineral prospectivity areas , 2012, Comput. Geosci..

[21]  Ziaii Mansour,et al.  A Computational Optimized Extended Model for Mineral Potential Mapping Based on WofE Method , 2009 .

[22]  Q. Cheng,et al.  Conditional Independence Test for Weights-of-Evidence Modeling , 2002 .

[23]  David M. W. Powers,et al.  The Problem with Kappa , 2012, EACL.

[24]  Carlos Roberto de Souza Filho,et al.  Artificial neural networks applied to mineral potential mapping for copper‐gold mineralizations in the Carajás Mineral Province, Brazil , 2009 .

[25]  José Hernández-Orallo,et al.  ROC curves for regression , 2013, Pattern Recognit..

[26]  E. Carranza,et al.  Logistic regression for geologically constrained mapping of gold potential, Baguio district, Philippines , 2001 .

[27]  K. Zou,et al.  Receiver-Operating Characteristic Analysis for Evaluating Diagnostic Tests and Predictive Models , 2007, Circulation.

[28]  E. Carranza,et al.  A Hybrid Fuzzy Weights-of-Evidence Model for Mineral Potential Mapping , 2006 .

[29]  Q. Cheng.  Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments , 2008 .

[30]  Maysam Abedi,et al.  A stable downward continuation of airborne magnetic data: A case study for mineral prospectivity mapping in Central Iran , 2013, Comput. Geosci..

[31]  Renguang Zuo,et al.  Support vector machine: A tool for mapping mineral prospectivity , 2011, Comput. Geosci..

[32]  Yong-Liang Chen.  Indicator Pattern Combination for Mineral Resource Potential Mapping with the General C-F Model , 2003 .

[33]  Q. Cheng.  Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China , 2007 .

[34]  E. Carranza,et al.  Application of Data-Driven Evidential Belief Functions to Prospectivity Mapping for Aquamarine-Bearing Pegmatites, Lundazi District, Zambia , 2005 .

[35]  Wooil M. Moon,et al.  Integration Of Geophysical And Geological Data Using Evidential Belief Function , 1990 .

[36]  F. Agterberg.  Combining indicator patterns in weights of evidence modeling for resource evaluation , 1992 .

[37]  John A. Swets,et al.  Signal Detection Theory and ROC Analysis in Psychology and Diagnostics: Collected Papers , 1996 .

[38]  A. Gałuszka.  A review of geochemical background concepts and an example using data from Poland , 2007 .

[39]  R. Bergmann,et al.  Different Outcomes of the Wilcoxon—Mann—Whitney Test from Different Statistics Packages , 2000 .

[40]  Emmanuel John M. Carranza,et al.  Artificial Neural Networks for Mineral-Potential Mapping: A Case Study from Aravalli Province, Western India , 2003 .

[41]  V. Nykänen.  Radial Basis Functional Link Nets Used as a Prospectivity Mapping Tool for Orogenic Gold Deposits Within the Central Lapland Greenstone Belt, Northern Fennoscandian Shield , 2008 .

[42]  Yongliang Chen.  MRPM: three visual basic programs for mineral resource potential mapping , 2004, Comput. Geosci..

[43]  Alvaro A. Cárdenas,et al.  Optimal ROC Curve for a Combination of Classifiers , 2007, NIPS.

[44]  Guocheng Pan.  Extended weights of evidence modeling for the pseudo-estimation of metal grades , 1996 .

[45]  Wang Wen-lei.  Application of Singularity Theory in Prediction of Tin and Copper Mineral Deposits in Gejiu District,Yunnan,China:Information Integration and Delineation of Mineral Exploration Targets , 2009 .

[46]  Marcus D. Ruopp,et al.  Youden Index and Optimal Cut‐Point Estimated from Observations Affected by a Lower Limit of Detection , 2008, Biometrical journal. Biometrische Zeitschrift.

[47]  Qiuming Cheng,et al.  Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from Gangdese, Tibet, western China , 2009 .

[48]  Tom Gedeon,et al.  Artificial neural networks: A new method for mineral prospectivity mapping , 2000 .

[49]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[50]  Yongliang Chen.  Mineral potential mapping with a restricted Boltzmann machine , 2015 .

[51]  W. M. Moon,et al.  An evidential reasoning structure for integrating geophysical, geological and remote sensing data , 1993, Proceedings of IGARSS '93 - IEEE International Geoscience and Remote Sensing Symposium.

[52]  F. Agterberg,et al.  Statistical Pattern Integration for Mineral Exploration , 1990 .

[53]  H. E. Hawkes,et al.  Geochemistry in Mineral Exploration , 1962 .

[54]  Rakesh Singh,et al.  Supply Chain Integration and Information Technology , 2013 .

[55]  C. Knox-Robinson.  Vectorial fuzzy logic: A novel technique for enhanced mineral prospectivity mapping, with reference to the orogenic gold mineralisation potential of the Kalgoorlie Terrane, Western Australia , 2000 .

[56]  Mohamed Bekkar,et al.  Evaluation Measures for Models Assessment over Imbalanced Data Sets , 2013 .

[57]  D. Groves,et al.  Using fuzzy logic in a Geographic Information System environment to enhance conceptually based prospectivity analysis of Mississippi Valley‐type mineralisation , 2000 .

[58]  Yongliang Chen,et al.  Application of continuous restricted Boltzmann machine to identify multivariate geochemical anomaly , 2014 .

[59]  M. Hale,et al.  Bayesian network classifiers for mineral potential mapping , 2006, Comput. Geosci..

[60]  F. Agterberg,et al.  Automatic contouring of geological maps to detect target areas for mineral exploration , 1974 .

[61]  E. Carranza,et al.  Where Are Porphyry Copper Deposits Spatially Localized? A Case Study in Benguet Province, Philippines , 2002 .

[62]  W. Moon.  On Mathematical Representation and Integration of Multiple Spatial Geoscience Data Sets , 1993 .

[63]  Andrew Skabar,et al.  Mineral potential mapping using feed-forward neural networks , 2003, Proceedings of the International Joint Conference on Neural Networks, 2003..

[64]  M. H. Tangestani,et al.  Porphyry copper potential mapping using the weights of evidence model in a GIS, northern Shahr e Babak, Iran , 2001 .

[65]  Chen Qiu-ming.  Singularity-Generalized Self-Similarity-Fractal Spectrum (3S) Models , 2006 .

[66]  Andrew Skabar,et al.  Mineral Potential Mapping Using Bayesian Learning for Multilayer Perceptrons , 2007 .

[67]  Shahid Anjum.  Composite Indicators for Data Mining: A New Framework for Assessment of Prediction Classifiers , 2014 .

[68]  E. Carranza,et al.  Geologically Constrained Fuzzy Mapping of Gold Mineralization Potential, Baguio District, Philippines , 2001 .

[69]  Wooil M. Moon,et al.  Combination Rules of Spatial Geoscience Data for Mineral Exploration , 1991 .

[70]  Maysam Abedi,et al.  uzzy outranking approach : A knowledge-driven method for mineral rospectivity mapping , 2012 .

[71]  E. Carranza,et al.  Application of Mineral Exploration Models and GIS to Generate Mineral Potential Maps as Input for Optimum Land-Use Planning in the Philippines , 1999 .