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Echoes from patches of fish fluctuate significantly from ping to ping as the sonar beam is swept across the patches. The fluctuations can be strongly non-Rayleigh because 1) there can be a small number of targets in the beam at a time, 2) the distribution of fish can be inhomogeneous, or "patchy", and 3) the echoes are weighted by the non-uniform response of the sonar beam. We have previously identified several distributions to describe the statistical behavior of non-Rayleigh echoes from fish - the K-distribution for multiple patches of unresolved fish, a mix distribution composed of two Rayleigh distributions for the patches, and a distribution that explicitly accounts for the beampattern when the fish are resolved. We have demonstrated good agreement between these PDF's and corresponding sets of data. In this new study, we investigate classification approaches and how they best suit the problem specific to patches of fish. In particular, we apply standard classifiers to fish echo data using our theoretical PDF's. We compare the performance of the different classifiers and make recommendations as to which type of classifier might best be suited to the fish application. Our initial results show that a classifier using the Kullback-Leibler (KL) distance is better than a L-2 norm approach, as the KL approach emphasizes differences in the tail of the distribution. One key aspect to this problem is that parameters of the theoretical PDF's are physics-based.