I really would like to ask some intelligent question but after a first reading I still don't understand anything about this paper. I've limited experience with ROC curves in general and no experience with most of the metrics in the paper. I do like the thought of a unifying structure as it seems that different definitions are misleading when looking at results.

I found this to be a good review of ROC curves, covering a few of the less-common performance measures. It would be interesting to know more of the logic behind choosing one metric over another.

It's very interesting that they are able to unify several different metrics through the 3D ROC. But I don't think it is anything more than a theoretical exercise. If the metrics generally used for your sub-field/problem work well enough, why would you bother trying to extrapolate metrics that are consistent over a whole bunch of fields?

To follow up on Anup's remark, does the ROC space provide a clear advantage to the f-measure or metircs used for decision tree splitting - i.e. does the unification of these different metrics give more insight? Also, has this been used in some application that would make its strengths apparent?

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