Data structure comparison using fractal analysis

Fractal analysis is useful to describe complex structures. We directed our attention to the complexity of the structure of a dataset including many thousands of samples, and introduced fractal analysis to the comparison of dataset structures. The fractal dimensions of representative subsets of the datasets that were selected using nonhierachical clustering technique (combination of leader algorithm and MacQueenʹs k-means method) and randomly selected subsets were estimated using a box counting method. We compared fractal dimensions of all subsets with the fractal dimension of the original dataset. The representative subsets selected by the clustering method showed more similar fractal dimensions to those of the original dataset when compared to randomly selected subsets.