Research on entropy and similarity measures for high dimensional data was carried out with spatial information. General definition such as distance measure was also applied to high dimensional data. Designed entropy and similarity measure are applied to fuzzy data that has uncertainty. We also derived the summation of similarity measure and entropy between fuzzy set and the corresponding ordinary set, and the summation constitutes degree of uncertainty and certainty of data. As a result, we derived a similarity measure from entropy realization, and showed the maximum similar value can be obtained using minimum entropy by simple example.
Keywords:
Similarity measure, Entropy, Spatial information, High dimension data