Prediction of social tag frequency´s power law distribution with RGF model

The power law distribution of social tag frequency is one of the most important statistic characteristics in social tagging system. Researchers have proposed several models to predict this distribution, but these models depend on specific system. What´s more, data fitting methods were failed to describe the raw data precisely compared with a mathematical model. Random Group Formation (RGF) model is a newly proposed mathematical model which could predict the power law distribution precisely. This model does not depend on the specific system. It could predict the power law distribution precisely using only three values: total number of elements, groups and the number of elements in the largest group. In this paper, RGF model is employed to predict the power law distribution of tag frequency. The experiments show that the power law distribution of tag frequency can be predicted precisely by three values, and the distribution is independent on specific system. The analysis of the tag dataset using RGF model shows that the exponent of power law decreases with the increasing of the dataset´s size.