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Model Overview

The model chosen is a modified version of ``Cluster Weighted Modelling'', a mixture of E-M experts system described by Neil Gershenfeld.

Each expert(c_m) attempts to predict the probability of a particular state, s (attacking or not) and a particular vector x in the input space. This is factored as:

Each expert's input authority, p(x|c_m) is implemented as a seperable Gaussian. Normally, each expert may predict any state, however, for speed purposes, and to avoid certain pathological cases, each expert was fixed to predict a particular state. That is, p(s_m|x,c_m) = 1.

The experts are initialized with random initial means in the range of the input space and variances equal to that of the input sample. Using E-M, the posteriors are calculated:

Similarly, the means, variances, and p(c_m)'s are updated. Given this, the forward values, p(x,s) are calculated and the process repeated.