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

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 \(\lambda \), a generalized Area under the ROC curve (AUC) performance index \(R_{AUCLS}\) is developed to theoretically guarantee that \(R_{AUCLS}\) linearly depends on the classical AUC performance index \(R_{AUC}\). Based on both \(R_{AUCLS}\) 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 \(\lambda \) in \(R_{AUCLS}\) 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.