Capacity and Efficiency of Decision Functions

Two criteria for comparing the performance of dedision functions are discussed. The first is the capacity as defined by Cover. We extend his definition to allow the calculation of the capacity of hyperboxes (interval complexes), which are shown to have asymptotically lower capacity than hyperplanes. The second criterion is the efficiency. We calculate the efficiency for polynomial functions. The efficiency sharply decreases as the degree of the polynomial increases. This calculation is also done for hyperboxes, which are shown to be more efficient than hyperplanes.