On the scaled Rényi entropy and application

Rényi entropy has been widely used in many applications. However, the significance of the parameter α in Rényi entropy and how to determine the value of α is still an open issue. To explore the significance of α, a scaled Rényi entropy is proposed in this article, where α is a scaled constant. Based on the information dimension of mass function in a power set whose uncertainty is measured by Deng entropy, the scale of α in Rényi entropy of the probability distribution is determined. One numerical example is given to show its properties. The scaled Rényi entropy and Rényi entropy are then applied to the C 4.5 decision tree and active learning to compare the usefulness of scaled Rényi and Rényi entropy.