In this paper I have briefly reviewed methods for object classification, focusing on the problem of distinguishing stars from galaxies. There are several methods available for classification; the oblique decision tree method is well-suited for our problem, but the other methods are also useful and may be better for other problems. Choice of parameters and the construction of high quality training/test data sets are important steps in the problem.
A new method has been described for scaling feature values based on ranks to make the features more robust. This approach should be generally applicable to many classification problems and is especially useful when the data being classified are not completely homogeneous.
There are several interesting avenues for future work. Two topics related to this conference come to mind. First, since the use of ranks (borrowed from statistical methods) looks like a powerful tool for classification, perhaps there are other transformation methods from robust or non-parametric statistics that should be explored for similar applications. Second, most of the classifiers discussed here do not view the classification as a statistical estimation problem. When the object features are noisy, though, classification really is a statistical problem. All the classification methods we have used may be adapted to utilize noise estimates on parameters (§ 2.5), but there has been relatively little work on this problem to date.
Acknowledgements: This project is an outgrowth of an on-going collaboration with Steven Salzberg, Holland Ford, Rupali Chandar, and Sreerama Murthy on applications of classification methods to astronomical problems. Thanks to all of them for many useful discussions. I am especially grateful to Murthy and Steven for freely distributing the OC1 decision tree program, which I have used extensively in this work. The development of the high quality training sets was done with my GSC-II colleague, Andrea Zacchei, whose participation in the project is supported by the Italian Council for Research in Astronomy. Marc Postman's CCD galaxy catalog has proved invaluable in this effort.