Fast feature selection using fractal dimension

Dimensionality curse and dimensionality reduction are two issues that have retained high interest for data mining, machine learning, multimedia indexing, and clustering. We present a fast, scalable algorithm to quickly select the most important attributes (dimensions) for a given set of n-dimensional vectors. In contrast to older methods, our method has the following desirable properties: (a) it does not do rotation of attributes, thus leading to easy interpretation of the resulting attributes; (b) it can spot attributes that have nonlinear correlations; (c) it requires a constant number of passes over the dataset; (d) it gives a good estimate on how many attributes we should keep. The idea is to use the ‘fractal’ dimension of a dataset as a good approximation of its intrinsic dimension, and to drop attributes that do not affect it. We applied our method on real and synthetic datasets, where it gave fast and good results.