Unsupervised Sequential Forward Dimensionality Reduction Based on Fractal

Dimensionality reduction has long been an active research topic within statistics, pattern recognition, machine learning and data mining. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. In this paper, we transform the attribute selection problem into the optimization problem which tries to find the attribute subset with the maximal fractal dimension and the attribute number restriction simultaneously. In order to avoid exhaustive search in the huge attribute subset space we integrate the individual attribute priority with attribute subset evaluation for dimensionality reduction and propose the unsupervised Sequential Forward Fractal Dimensionality Reduction(SFFDR) algorithm. Our experiments on synthetic and real datasets show that the algorithm proposed can get the satisfied resulting attribute subset with a rather low time complexity.