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ROC is usually used to analyze the performance of classifiers in data mining.ROC convex hull (ROCCH) is the least convex major-ant (LCM) of the empiricalROC curve, and covers potential optima for the given set of classifiers.Generally, ROC performance maximization could be considered to maximize theROCCH, which also means to maximize the true positive rate (tpr) and minimizethe false positive rate (fpr) for each classifier in the ROC space. However,tpr and fpr are conflicting with each other in the ROCCH optimization process.Though ROCCH maximization problem seems like a multi-objective optimizationproblem (MOP), the special characters make it different from traditional MOP.In this work, we will discuss the difference between them and propose convexhull-based multi-objective genetic programming (CH-MOGP) to solve ROCCHmaximization problems. Convex hull-based sort is an indicator based selectionscheme that aims to maximize the area under convex hull, which serves as aunary indicator for the performance of a set of points. A selection procedureis described that can be efficiently implemented and follows similar designprinciples than classical hyper-volume based optimization algorithms. It ishypothesized that by using a tailored indicator-based selection scheme CH-MOGPgets more efficient for ROC convex hull approximation than algorithms whichcompute all Pareto optimal points. To test our hypothesis we compare the newCH-MOGP to MOGP with classical selection schemes, including NSGA-II, MOEA/D)and SMS-EMOA. Meanwhile, CH-MOGP is also compared with traditional machinelearning algorithms such as C4.5, Naive Bayes and Prie. Experimental resultsbased on 22 well-known UCI data sets show that CH-MOGP outperformssignificantly traditional EMOAs.

Convex Hull-Based Multi-objective Genetic Programming for Maximizing ROC Performance