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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
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.
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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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