An improved algorithm for feature selection using fractal dimension

Dimensionality reduction is an important issue in data mining and machine learning. Traina[1] proposed a feature selection algorithm to select the most important attributes for a given set of n-dimensional vectors based on correlation fractal dimension. The author used a kind of multi-dimensional “quad-tree” structure to compute the fractal dimension. Inspired by his work, we propose a new and simpler algorithm to compute the fractal dimension, and design a novel and faster feature selection algorithm using correlation fractal dimension, whose time complexity is lower than that of Traina’s. The main idea is when computing the fractal dimension of (d-1)-dimensional data, the intermediate generated results of the extended d-dimensional data is reused. It inherits the desirable properties described as in [1]. Also, Our algorithm does not require the grid sizes decrease by half as the original “quad-tree” algorithm. Experiments show our feature selection algorithm has a good efficiency over the test dataset.