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Statistical Models for Data Analysis pp 27–35Cite as

Data Stream Summarization by Histograms Clustering

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Abstract

In this paper we introduce a new strategy for summarizing a fast changing data stream. Evolving data streams are generated by non stationary processes which require to adapt the knowledge discovery process to the new emerging concepts. To deal with this challenge we propose a clustering algorithm where each cluster is summarized by a histogram and data are allocated to clusters through a Wasserstein derived distance. Histograms are a well known graphical tool for representing the frequency distribution of data and are widely used in data stream mining, however, unlike to existing methods, we discover a set of histograms where each one represents a main concept in the data. In order to evaluate the performance of the method, we have performed extensive tests on simulated data.

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References

  • Aggarwal, C. C., Han, J., Wang, J., & Philip, S. (2003). A framework for clustering evolving data streams. In: 29th int. conf. on very large data bases.

    Google Scholar 

  • Babcock, B., Babu, S., Datar, M., Motwani, R., & Widom J. (2002). Models and issues in data stream systems. In: 21th ACM SIGMOD-SIGACT-SIGART symposium PODS ’02 (pp. 1–16).

    Google Scholar 

  • Balzanella, A. (2009). Clustering and summarizing massive data streams. PHD Thesis, http://www.fedoa.unina.it/4184(2009).

  • Balzanella, A., Irpino, A., & Verde, R. (2010). Dimensionality reduction techniques for streaming time series: a new symbolic approach. Studies in classification, data analysis, and knowledge organization (pp. 381–389). Heidelberg, Berlin: Springer.

    Google Scholar 

  • Balzanella, A., Romano, E., & Verde, R. (2011). Summarizing and mining streaming data via a functional data approach. Classification and multivariate analysis for complex data structures (pp. 409–416). Heidelberg, Berlin: Springer

    Google Scholar 

  • Gama, J., & Gaber, M. M. (2007). Learning from data stream. Techniques in sensor networks. Heidelberg, Berlin: Springer

    Google Scholar 

  • Guha, S., Koudas, N., & Shim, K. (2001). Data-streams and histograms. In: 33th annual ACM symposium on theory of computing (pp. 471–475). New York: ACM.

    Google Scholar 

  • Irpino, A., & Verde, R. (2006). Dynamic clustering of histograms using Wasserstein metric. In A. Rizzi, & M. Vichi (Eds.) COMPSTAT 2006 - Advances in computational statistics (pp. 869–876). Heidelberg: Physica-Verlag.

    Google Scholar 

  • Mallows, C. L. (1972). A note on asymptotic joint normality. Annals of Mathematical Statistics, 43(2), 508–515.

    Article  MathSciNet  MATH  Google Scholar 

  • Sebastiao, R., & Gama, J. (2007). Change detection in learning histograms from data streams. Progress in Artificial Intelligence. Lecture Notes in Computer Science. Springer Berlin Heidelberg. ISBN: 978-3-540-77000-8

    Google Scholar 

  • Verde, R., & Irpino, A. (2007). Dynamic clustering of histogram data: using the right metric. Studies in Classification, Data Analysis, and Knowledge Organization, Part I, 123–134, doi: 10.1007/978-3-540-73560-1 12.

  • Verde, R., & Irpino, A. (2010). Ordinary least squares for histogram data based on wasserstein distance. In Y. Lechevallier, & G. Saporta (Eds.) COMPSTAT 2010 (pp. 581588). Berlin: PhysicaVerlag.

    Google Scholar 

  • Vitter, J. S. (1985). Random sampling with a reservoir. ACM Transactions on Mathematical Software, 11(1), 37–57.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Second University of Naples, Naples, Italy

    Antonio Balzanella & Rosanna Verde

  2. University of Naples Federico II, Naples, Italy

    Lidia Rivoli

Authors
  1. Antonio Balzanella
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  2. Lidia Rivoli
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  3. Rosanna Verde
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Corresponding author

Correspondence to Antonio Balzanella .

Editor information

Editors and Affiliations

  1. Department of Economics, and Management, University of Pavia, Via San Felice 7, Pavia, 27100, Italy

    Paolo Giudici

  2. Department of Economics, and Business, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Ingrassia

  3. , Department of Statistics, University of Rome "La Sapienza", Piazzale Aldo Moro 5, Rome, 00185, Italy

    Maurizio Vichi

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Balzanella, A., Rivoli, L., Verde, R. (2013). Data Stream Summarization by Histograms Clustering. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_4

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