In classification, the goal is to assign an input vector to a discrete number of output classes. Classifier design has a long history and they have been put to a large number of uses. In this paper we continue the task of categorizing classifiers by their computational complexity as begun. In particular, we derive analytical formulas for the number of arithmetic operations in the probabilistic neural network (PNN) and its polynomial expansion, also known as the polynomial discriminant method (PDM) and the mixture model neural network (M$+2$/N$+2$/). In addition we perform tests of the classification accuracy of the PDM with respect to the PNN and the M$+2$/N$+2$/ find that all three are close in accuracy. Based on this research we now have the ability to choose one or the other based on the computational complexity, the memory requirements and the size of the training set. This is a great advantage in an operational environment. We also discus the extension of such methods to hyperspectral data and find that only the M$+2$/N$+2$/ is suitable for application to such data.
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