  Recent studies have shown that imbalance ratio is not the only cause of the
performance loss of a classifier in imbalanced data classification. In fact,
other data factors, such as small disjuncts, noises and overlapping, also play
the roles in tandem with imbalance ratio, which makes the problem difficult.
Thus far, the empirical studies have demonstrated the relationship between the
imbalance 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 on
the classification performance of imbalanced data. Further, it is also unknown
for a dataset which data factor is actually the main barrier for
classification. In this paper, we focus on Bayes optimal classifier and study
the 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 of
imbalance in terms of each minority class sample and the whole dataset,
respectively. Therefore, $IBI^3$ can be used as an instance complexity measure
of imbalance and $BI^3$ is a criterion to show the degree of how imbalance
deteriorates the classification. As a result, we can therefore use $BI^3$ to
judge whether it is worth using imbalance recovery methods like sampling or
cost-sensitive methods to recover the performance loss of a classifier. The
experiments show that $IBI^3$ is highly consistent with the increase of
prediction score made by the imbalance recovery methods and $BI^3$ is highly
consistent with the improvement of F1 score made by the imbalance recovery
methods on both synthetic and real benchmark datasets.
