  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 empirical
ROC curve, and covers potential optima for the given set of classifiers.
Generally, ROC performance maximization could be considered to maximize the
ROCCH, which also means to maximize the true positive rate (tpr) and minimize
the 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 optimization
problem (MOP), the special characters make it different from traditional MOP.
In this work, we will discuss the difference between them and propose convex
hull-based multi-objective genetic programming (CH-MOGP) to solve ROCCH
maximization problems. Convex hull-based sort is an indicator based selection
scheme that aims to maximize the area under convex hull, which serves as a
unary indicator for the performance of a set of points. A selection procedure
is described that can be efficiently implemented and follows similar design
principles than classical hyper-volume based optimization algorithms. It is
hypothesized that by using a tailored indicator-based selection scheme CH-MOGP
gets more efficient for ROC convex hull approximation than algorithms which
compute all Pareto optimal points. To test our hypothesis we compare the new
CH-MOGP to MOGP with classical selection schemes, including NSGA-II, MOEA/D)
and SMS-EMOA. Meanwhile, CH-MOGP is also compared with traditional machine
learning algorithms such as C4.5, Naive Bayes and Prie. Experimental results
based on 22 well-known UCI data sets show that CH-MOGP outperforms
significantly traditional EMOAs.
