The table look-up rule

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Abstract
The table look-up rule problem can be described by the question: what is a good way for the table to represent the decision regions in the N-dimensional measurement space. This paper describes a quickly implementable table look-up rule based on Ashby’s representation of sets in his constraint analysis. A decision region for category c in the N-dimensional measurement space is considered to be the intersection of the inverse projections of the decision regions determined for category c by Bayes rules in smaller dimensional projection spaces. Error bounds for this composite decision rule are derived: any entry in the confusion matrix for the composite decision rule is bounded above by the minimum of that entry taken over all the confusion matrices of the Bayes decision rules in the smaller dimensional projection spaces. On simulated Gaussian Data, probability of error with the table look-up rule is comparable to the optimum Bayes rule.

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