Fractal Dimension for Data Mining

In this project, we introduce the concept of intrinsic "fractal" dimension of a data set and show how this can be used to aid in several data mining tasks. We are interested in answering questions about the performance of a method and also in comparing between the methods quickly. In particular, we discuss two specific problems -- dimensionality reduction and vector quantization. In each of these problems, we show how the performance of a method is related to the fractal dimension of the data set. Using real and synthetic data sets, we validate these relationships and show how we can use this for faster evaluation and comparison of the methods