LRID: A new metric of multi-class imbalance degree based on likelihood-ratio test

In this paper, we introduce a new likelihood ratio imbalance degree (LRID) to measure the class-imbalance extent of multi-class data. Imbalance ratio (IR) is usually used to measure class-imbalance extent in imbalanced learning problems. However, IR cannot capture the detailed information in the class distribution of multi-class data, because it only utilises the information of the largest majority class and the smallest minority class. Imbalance degree (ID) has been proposed to solve the problem of IR for multi-class data. However, we note that improper use of distance metric in ID can have harmful effect on the results. In addition, ID assumes that data with more minority classes are more imbalanced than data with less minority classes, which is not always true in practice. Thus ID cannot provide reliable measurement when the assumption is violated. In this paper, we propose a new metric based on the likelihood-ratio test, LRID, to provide a more reliable measurement of class-imbalance extent for multi-class data. Experiments on both simulated and real data show that LRID is competitive with IR and ID, and can reduce the negative correlation with F1 scores by up to 0.55.