Statistics 4240 - Data Mining

If we are analyzing the accuracy of a multi class classifier such as linear discriminant analysis, would it make sense to construct an ROC curve of the specificity and sensitivity for each class? For example, treat the false positive rate as the number of observations that the classifier determined to be in the class divided by the number of actual observations that are not in the class.

You certainly can use ROC on each class individually. There are a number
of suggestions for multi-class ROC extensions - see for example
http://portal.acm.org/citation.cfm?id=1279009.1279176&coll=GUIDE&dl=GUIDE