ROC Convex Hull Algorithm

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A ROC Convex Hull Algorithm is a Convex Hull Algorithm that constructs the convex hull of an ROC curve.



References

2017

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve Retrieved:2015-7-18.
    • … It is also common to calculate the Area Under the ROC Convex Hull (ROC AUCH = ROCH AUC) as any point on the line segment between two prediction results can be achieved by randomly using one or other system with probabilities proportional to the relative length of the opposite component of the segment. Interestingly, it is also possible to invert concavities – just as in the figure the worse solution can be reflected to become a better solution; concavities can be reflected in any line segment, but this more extreme form of fusion is much more likely to overfit the data. ...

2005

2005 RepairingConcavitiesinROCCurves Fig3.png
Figure 3: A probabilistic ROC curve and its convex hull.
Four points of the ROC curve (point a, b, c and d) are located on the convex hull. Each of these points corresponds to a probability threshold, and thus each segment of the convex hull corresponds to a probability interval. For instance, the convex hull in Figure 3 has three segments corresponding to three disjoint probability intervals. (...) It is interesting to note that if this procedure is followed for all concavities, this corresponds to constructing the convex hull by discretising the probability scores. (...) by applying this algorithm to the model corresponding to threshold $c_2$, this point would be point-mirrored through the midpoint on line segment $c_d$ to the other side of the convex hull.

(...) The AUC of the repaired curve is therefore larger than both the AUC of the original curve and the AUC of its convex hull.

  1. For illustration purposes, the test set contains only a few examples and the resolution of the ROC curve is low. In practical circumstances a step curve with much higher resolution is obtained.

2001