A Hybrid Logistic Regression: Gene Expression Programming Model and Its Application to Mineral Prospectivity Mapping

Mineral prospectivity mapping (MPM) is a fundamental task in mineral exploration. The logistic regression (LR) method has been widely used as a data-driven tool for MPM because it is compact and straightforward, and it presents explicit explanations. However, there exists the inherent deficiency of linear assumption in the ordinary LR method. In order to overcome this disadvantage, a hybrid model (i.e., hybrid GEP–LR) that combines LR with gene expression programming (GEP) has been developed. It uses the evolutionary algorithm of GEP to discover automatically the symbolic function defined in the logit transformation of the ordinary LR method without any assumption. To investigate the performance of the hybrid GEP–LR hybrid method, a synthetic data modeling and a case study of prospectivity mapping for porphyry Cu–Mo polymetallic deposits (PCMPDs) in the Eastern Tianshan region, northwestern China are presented here. In the synthetic data modeling, two different datasets, namely linearly separable dataset and nonlinearly separable dataset, were generated by Monte Carlo simulation. By defining the area under the receiver operating characteristic curve (AUC) as a fitness function, these two datasets were used to validate the efficiency of the hybrid GEP–LR method in classification of both linearly and nonlinearly separable datasets. In the case study, 15 hybrid GEP–LR models were designed using 15 different evolutionary strategies of the GEP algorithm including the number of genes, the head length of every gene, and the set of functions. Binary maps of prospectivity for PCMPDs derived using these 15 hybrid GEP–LR models with the fitness function of AUC were compared and contrasted with the one derived using the ordinary LR method. The results demonstrate that the proposed hybrid GEP–LR method is a robust data-driven tool that can deal with both linear and nonlinear problems in data mining. It outperforms the ordinary LR method in predicting target areas for mineral prospecting. GEP provides an inspiring way to combine other machine learning methods in addressing challenges associated with supervised or unsupervised classification issues with respect to complex nonlinearly distributed geodata.