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Fast estimation of fractal dimension and correlation integral on stream data. (English) Zbl 1173.68873
Summary: 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 \(\Omega (N)\) 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.

MSC:
68W25 Approximation algorithms
68P15 Database theory
68W20 Randomized algorithms
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