Mining Implicit Equations from Data using Gene Expression Programming

Symbolic regression is an active research topic that has various applications in data mining and knowledge discovery. Existing methods for symbolic regression mainly focus on mining explicit equations. In contrast, implicit equations are more flexible and powerful than explicit equations with regard to describing the relationships between variables in the given dataset. However, evaluating the quality of an implicit equation is more difficult than evaluating an explicit equation. The traditional method for implicit equation evaluation is based on derivative calculation, which requires much time consumption and dense training data. To address the above issues, this paper proposes a new evolutionary framework to efficiently mine implicit equations from data. In the proposed framework, a new mechanism (named CL-FEM) is proposed to evaluate implicit equations, and it can efficiently evaluate the accuracy and validity of implicit equations. In addition, a multiple sub-chromosome encoding method based on a least-squares estimator is proposed in the framework to further improve its search efficiency. Based on the proposed evolutionary framework, an efficient algorithm named gene expression programming with a least-squares estimator (LSE-GEP) is developed to mine implicit equations from data. Experimental results demonstrate that the proposed LSE-GEP method performs much better than the recently published methods, in terms of its success rate, accuracy and readability.