Reduced Perplexity: Uncertainty measures without entropy

C. Shannon revolutionized the design of information systems by showing that the logarithm of independent probabilities were additive and constituted a unit of measure for information. Because ln p  is additive, basic analytics could be applied to information, such as the average which forms entropy and the average difference which forms divergence. Unnecessarily neglected in this formative framework for information theory, is the equally important fact that translating entropy back into probability space gives the geometric mean of the distribution, . i p i i p  This is also the inverse of the perplexity, but