  Evaluation often aims to reduce the correctness or error characteristics of a
system down to a single number, but that always involves trade-offs. Another
way of dealing with this is to quote two numbers, such as Recall and Precision,
or Sensitivity and Specificity. But it can also be useful to see more than
this, and a graphical approach can explore sensitivity to cost, prevalence,
bias, noise, parameters and hyper-parameters.
  Moreover, most techniques are implicitly based on two balanced classes, and
our ability to visualize graphically is intrinsically two dimensional, but we
often want to visualize in a multiclass context. We review the dichotomous
approaches relating to Precision, Recall, and ROC as well as the related LIFT
chart, exploring how they handle unbalanced and multiclass data, and deriving
new probabilistic and information theoretic variants of LIFT that help deal
with the issues associated with the handling of multiple and unbalanced
classes.
