Sixth International Conference on Data Mining (ICDM'06) (2006)

Hong Kong

Dec. 18, 2006 to Dec. 22, 2006

ISSN: 1550-4786

ISBN: 0-7695-2701-9

pp: 603-612

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.167

Nikolaj Tatti , University of Helsinki and Helsinki University of Technology, Finland

Taneli Mielikainen , University of Helsinki and Helsinki University of Technology, Finland

Aristides Gionis , University of Helsinki and Helsinki University of Technology, Finland

Heikki Mannila , University of Helsinki and Helsinki University of Technology, Finland

ABSTRACT

Many 0/1 datasets have a very large number of variables; however, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust measure of dimension for 0/1 datasets, and show that the basic idea of fractal dimension can be adapted for binary data. However, as such the fractal dimension is difficult to interpret. Hence we introduce the concept of normalized fractal dimension. For a dataset D, its normalized fractal dimension counts the number of independent columns needed to achieve the unnormalized fractal dimension of D. The normalized fractal dimension measures the degree of dependency structure of the data. We study the properties of the normalized fractal dimension and discuss its computation. We give empirical results on the normalized fractal dimension, comparing it against PCA.

INDEX TERMS

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CITATION

H. Mannila, A. Gionis, T. Mielikainen and N. Tatti, "What is the Dimension of Your Binary Data?,"

*Sixth International Conference on Data Mining (ICDM'06)(ICDM)*, Hong Kong, 2006, pp. 603-612.

doi:10.1109/ICDM.2006.167

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