We find that oblique decision trees represent a good compromise between the demands of computational efficiency, classification accuracy, and analytical value of the results. Noise is common in astronomical data. In the presence of noise, classification becomes a statistical estimation problem. Objects should not be classified as either stars or galaxies, but should be assigned probabilities of being in one or the other class. All of the above methods can be modified to give a probabilistic estimate of class rather than a simple yes or no answer.
Neural nets can have an output parameter that represents probability.
The nearest-neighbor method can be generalized to use the K nearest neighbors to an object, which can vote for the object's class. If the vote is not unanimous, it gives an estimate of the uncertainty of the object's majority classification. The same approach can be applied to decision trees. For decision trees, it is also possible to use known noise estimates for the parameters to determine at each node the probability that an object belongs on the left branch or the right branch. These probabilities, multiplied down to the leaf nodes and summed over all the leaves belonging to a particular class, give a probability that an object belongs that class.