I had a discussion today with Huppenkothen about the qualitatively different states of accreting black-hole GRS 1915. The behavior of the star has been classified into some dozen-ish different states, based on time behavior and spectral properties. We figured out at least three interesting approaches. The first is to do old-school (meaning, normal) machine learning, based on a training set of classified time periods, and try to classify all the unclassified periods. It would be interesting to find out what features are most informative, and whether or not there are any classes that the machine has trouble with; these would be candidates for deletion.
The second approach is to do old-school (meaning, normal) clustering, and see if the clusters correspond to the known states, or whether it splits some and merges others. This would generate candidates for deletion or addition. It also might give us some ideas about whether the states are really discrete or whether there is a continuum of intermediate states.
The third approach is to try to build a generative model of the path the system takes through states, using a markov model or something similar. This might reveal patterns of state switches. It could even work at a lower level and try to predict the detailed time-domain behavior, which is incredibly rich and odd. This is a great set of projects, and easy (at least to get started).