Fractal Mining
 Daniel Barbara,
 Ping Chen
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Abstract
Selfsimilarity is the property of being invariant with respect to the scale used to look at the data set. Selfsimilarity can be measured using the fractal dimension. Fractal dimension is an important charactaristics for many complex systems and can serve as a powerful representation technique. In this chapter, we present a new clustering algorithm, based on selfsimilarity properties of the data sets, and also its applications to other fields in Data Mining, such as projected clustering and trend analysis. Clustering is a widely used knowledge discovery technique. The new algorithm which we call Fractal Clustering (FC) places points incrementally in the cluster for which the change in the fractal dimension after adding the point is the least. This is a very natural way of clustering points, since points in the same clusterhave a great degree of selfsimilarity among them (and much less selfsimilarity with respect to points in other clusters). FC requires one scan of the data, is suspendable at will, providing the best answer possible at that point, and is incremental. We show via experiments that FC effectively deals with large data sets, highdimensionality and noise and is capable of recognizing clusters of arbitrary shape.
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 Title
 Fractal Mining
 Book Title
 Data Mining and Knowledge Discovery Handbook
 Book Part
 V
 Pages
 pp 627647
 Copyright
 2005
 DOI
 10.1007/038725465X_28
 Print ISBN
 9780387244358
 Online ISBN
 9780387254654
 Publisher
 Springer US
 Copyright Holder
 Springer Science+Business Media, Inc.
 Additional Links
 Topics
 Keywords

 selfsimilarity
 clustering
 projected clustering
 trend analysis
 Industry Sectors
 eBook Packages
 Editors

 Oded Maimon ^{(1)}
 Lior Rokach ^{(1)}
 Editor Affiliations

 1. Dept. of Industrial Engineering, TelAviv University
 Authors

 Daniel Barbara ^{(2)}
 Ping Chen ^{(3)}
 Author Affiliations

 2. George Mason University, Fairfax, VA, 22030, USA
 3. University of HoustonDowntown, Houston, TX, 77002, USA
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