Fast estimation of fractal dimension and correlation integral on stream data

Authors:
Angeline Wong;Leejay Wu;Phillip B. Gibbons;Christos Faloutsos
Affiliations:
Department of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA;Department of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA;Intel Research, 417 South Craig Str., Suite 300, Pittsburgh, PA;Department of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA
Venue:
Information Processing Letters
Year:
2005

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Abstract

In this paper we give a very space-efficient, yet fast method for estimating the fractal dimensionality of the points in a data stream. Algorithms to estimate the fractal dimension exist, such as the straightforward quadratic algorithm and the faster O(N log N) or even O(N) box-counting algorithms. However, the sub-quadratic algorithms require Ω(N) space. In this paper, we propose an algorithm that computes the fractal dimension in a single pass, using a constant amount of memory relative to data cardinality. Experimental results on synthetic and real world data sets demonstrate the effectiveness of our algorithm.