  Although a great methodological effort has been invested in proposing
competitive solutions to the class-imbalance problem, little effort has been
made in pursuing a theoretical understanding of this matter.
  In order to shed some light on this topic, we perform, through a novel
framework, an exhaustive analysis of the adequateness of the most commonly used
performance scores to assess this complex scenario. We conclude that using
unweighted H\"older means with exponent $p \leq 1$ to average the recalls of
all the classes produces adequate scores which are capable of determining
whether a classifier is competitive.
  Then, we review the major solutions presented in the class-imbalance
literature. Since any learning task can be defined as an optimisation problem
where a loss function, usually connected to a particular score, is minimised,
our goal, here, is to find whether the learning tasks found in the literature
are also oriented to maximise the previously detected adequate scores. We
conclude that they usually maximise the unweighted H\"older mean with $p = 1$
(a-mean).
  Finally, we provide bounds on the values of the studied performance scores
which guarantee a classifier with a higher recall than the random classifier in
each and every class.
