Least squares support vector machines with fast leave-one-out AUC optimization on imbalanced prostate cancer data

© 2020, Springer-Verlag GmbH Germany, part of Springer Nature. Quite often, the available pre-biopsy data for early prostate cancer detection are imbalanced. When the least squares support vector machines (LS-SVMs) are applied to such scenarios, it becomes naturally desirable for us to introduce the well-known AUC performance index into the LS-SVMs framework to avoid bias towards majority classes. However, this may result in high computational complexity for the minimal leave-one-out error. In this paper, by introducing the parameter λ, a generalized Area under the ROC curve (AUC) performance index RAUCLS is developed to theoretically guarantee that RAUCLS linearly depends on the classical AUC performance index RAUC. Based on both RAUCLS and the classical LS-SVM, a new AUC-based least squares support vector machine called AUC-LS-SVMs is proposed for directly and effectively classifying imbalanced prostate cancer data. The distinctive advantage of the proposed classifier AUC-LS-SVMs exists in that it can achieve the minimal leave-one-out error by quickly optimizing the parameter λ in RAUCLS using the proposed fast leave-one-out cross validation (LOOCV) strategy. The proposed classifier is first evaluated using generic public datasets. Further experiments are then conducted on a real-world prostate cancer dataset to demonstrate the efficacy of our proposed classifier for early prostate cancer detection.