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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., 15914, Tehran, Iran

    Hamzeh Agahi, A. Mohammadpour & S. Mansour Vaezpour

  2. Statistical Research and Training Center (SRTC), Tehran, Iran

    Hamzeh Agahi

Authors
  1. Hamzeh Agahi
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  2. A. Mohammadpour
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  3. S. Mansour Vaezpour
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Correspondence to A. Mohammadpour.

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Agahi, H., Mohammadpour, A. & Mansour Vaezpour, S. Predictive tools in data mining and k-means clustering: Universal Inequalities. Results. Math. 63, 779–803 (2013). https://doi.org/10.1007/s00025-012-0233-2

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  • DOI: https://doi.org/10.1007/s00025-012-0233-2

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