There have been many attempts to classify imbalanced data, since this classification is critical in a wide variety of applications related to the detection of anomalies, failures, and risks. Many conventional methods, which can be categorized into sampling, cost-sensitive, or ensemble, include heuristic and task dependent processes. In order to achieve a better classification performance by formulation without heuristics and task dependence, we propose confusion-matrix-based kernel logistic regression (CM-KLOGR). Its objective function is the harmonic mean of various evaluation criteria derived from a confusion matrix, such criteria as sensitivity, positive predictive value, and others for negatives. This objective function and its optimization are consistently formulated on the framework of KLOGR, based on minimum classification error and generalized probabilistic descent (MCE/GPD) learning. Due to the merits of the harmonic mean, KLOGR, and MCE/GPD, CM-KLOGR improves the multifaceted performances in a well-balanced way. This paper presents the formulation of CM-KLOGR and its effectiveness through experiments that comparatively evaluated CM-KLOGR using benchmark imbalanced datasets.

Imbalanced data classification, which is a common and important problem in various fields related to the detection of anomaly, failure, and risk, has been studied intensively. Conventional methods are based on sampling, misclassification costs, or ensemble of classifiers, and many of them are heuristic and task dependent. Aiming at a higher classification performance with the solution of such problems, we propose a confusion-matrix-based kernel logistic regression (CM-KLOGR). After pretraining with a cross-entropy error function, CM-KLOGR retrains its parameters using the harmonic mean of the various evaluation criteria, including sensitivity, positive predictive value, and others, which are derived from a confusion matrix. CM-KLOGR inherits the advantages of kernel logistic regression, and it has the potential to raise the values of all the evaluation criteria in a well-balanced way. This paper presents the concept and formulation of CM-KLOGR, accompanied by the results of an exploratory experiment using an imbalanced biomedical dataset.