I am looking for a metric to evaluate the quality of a classifier which answers the question for a class of an object with a probability per known class. Say I use the classifier to classify an object of class A and the classifier classifies the object with 75% probability as A and 25% probability as C.
One option is, just to pick the probabilities, in this case the 75%. Are there any other metrics?
The Classifier uses a database of classes with different objects but not all objects of one class share the same properties found in an query object, so not all objects of a class may be relevant.