Exponential Negation of a Probability Distribution
This work addresses a theoretical problem in intelligent information processing, but it appears incremental as it builds on existing negation concepts without clear practical applications.
The paper tackles the problem of defining a negation operation for probability distributions by proposing an exponential negation, which is a geometric approach that increases entropy and causes all distributions to converge to the uniform distribution after multiple iterations, with convergence speed inversely proportional to the number of elements.
Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation is investigated, we find that the fix point is the uniform probability distribution. The negation is an entropy increase operation and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation.