Results in Mathematics

, Volume 63, Issue 3–4, pp 779–803 | Cite as

Predictive tools in data mining and k-means clustering: Universal Inequalities

  • Hamzeh Agahi
  • A. Mohammadpour
  • S. Mansour Vaezpour


Grouping data into meaningful clusters is very important in data mining. K-means clustering is a fast method for finding clusters in data. The integral inequalities are a predictive tool in data mining and k-means clustering. Many papers have been published on speeding up k-means or nearest neighbor search using inequalities that are specific for Euclidean distance. An extended inequality related to Hölder type for universal integral is obtained in a rather general form. Previous results of Agahi et al. (Results Math, 61:179–194, 2012) are generalized by relaxing some of their requirements, thus closing the series of papers on this topic. Chebyshev’s, Hölder’s, Minkowski’s, Stolarsky’s, Jensen’s and Lyapunov’s type inequalities for the universal integral are obtained.

Mathematics Subject Classification (2000)

Primary 60E15 Secondary 39B62 


Monotone measure Universal integral Data mining Chebyshev’s inequality Stolarsky’s inequality Minkowski’s inequality Jensen’s inequality Lyapunov’s inequality Hölder’s inequality 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Hamzeh Agahi
    • 1
    • 2
  • A. Mohammadpour
    • 1
  • S. Mansour Vaezpour
    • 1
  1. 1.Department of Mathematics and Computer ScienceAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.Statistical Research and Training Center (SRTC)TehranIran

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