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Recent studies have shown that imbalance ratio is not the only cause of theperformance loss of a classifier in imbalanced data classification. In fact,other data factors, such as small disjuncts, noises and overlapping, also playthe roles in tandem with imbalance ratio, which makes the problem difficult.Thus far, the empirical studies have demonstrated the relationship between theimbalance ratio and other data factors only. To the best of our knowledge,there is no any measurement about the extent of influence of class imbalance onthe classification performance of imbalanced data. Further, it is also unknownfor a dataset which data factor is actually the main barrier forclassification. In this paper, we focus on Bayes optimal classifier and studythe influence of class imbalance from a theoretical perspective. Accordingly,we propose an instance measure called Individual Bayes Imbalance Impact Index($IBI^3$) and a data measure called Bayes Imbalance Impact Index ($BI^3$).$IBI^3$ and $BI^3$ reflect the extent of influence purely by the factor ofimbalance in terms of each minority class sample and the whole dataset,respectively. Therefore, $IBI^3$ can be used as an instance complexity measureof imbalance and $BI^3$ is a criterion to show the degree of how imbalancedeteriorates the classification. As a result, we can therefore use $BI^3$ tojudge whether it is worth using imbalance recovery methods like sampling orcost-sensitive methods to recover the performance loss of a classifier. Theexperiments show that $IBI^3$ is highly consistent with the increase ofprediction score made by the imbalance recovery methods and $BI^3$ is highlyconsistent with the improvement of F1 score made by the imbalance recoverymethods on both synthetic and real benchmark datasets.

Bayes Imbalance Impact Index: A Measure of Class Imbalanced Dataset for Classification Problem