Multi-scale information content measurement method based on Shannon information

Abstract: In this paper, we present a new multi-scale information content calculation method based on Shannon information (and Shannon entropy). The original method described by Claude E. Shannon and based on the logarithm of the probability of elements gives an upper limit to the information content of discrete patterns, but in many cases (for example, in the case of repeating patterns) it is inaccurate and does not approximate the true information content of the pattern well enough. The new mathematical method presented here provides a more accurate estimate of the (internal) information content of any discrete pattern based on Shannon's original function. The method is tested on different data sets and the results are compared with the results of other methods like compression algorithms.