An information fractal dimensional relative entropy

Abstract

Shannon entropy is used to measure information uncertainty, while the information dimension is used to measure information complexity. Given two probability distributions, the difference can be measured by relative entropy. However, the existing relative entropy does not consider the effect of information dimension. To improve the existing entropy, a new relative entropy is presented in this paper. The information fractal dimension is considered in the proposed relative entropy. The new relative entropy is more generalized than the initial relative entropy. When dimension is not considered, it will degenerate to the initial relative entropy. Another interesting point is that the new relative entropy may have negative values when calculating. The physical meaning is still under exploration. Finally, some application examples are provided to exemplify the utilization of the proposed relative entropy.