On-Line Clustering of Functional Boxplots for Monitoring Multiple Streaming Time Series

  • Elvira RomanoEmail author
  • Antonio Balzanella
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In this paper we introduce a micro-clustering strategy for functional boxplots. The aim is to summarize a set of streaming time series split in non-overlapping windows. It is a two-step strategy which performs at first, an on-line summarization by means of functional data structures, named Functional Boxplot micro-clusters; then, it reveals the final summarization by processing, off-line, the functional data structures. Our main contribute consists in providing a new definition of micro-cluster based on Functional Boxplots and in defining a proximity measure which allows to compare and update them. This allows to get a finer graphical summarization of the streaming time series by five functional basic statistics of data. The obtained synthesis will be able to keep track of the dynamic evolution of the multiple streams.


  1. Adelfio, G., Chiodi, M., D’alessandro, A., Luzio, D., D’anna, G., & Mangano, G. (2012). Simultaneous seismic wave clustering and registration. Computers Geosciences, 44, 60–69. ISSN: 0098-3004. doi: 10.1016/j.cageo.2012.02.017.Google Scholar
  2. Aggarwal, C. C., Han, J., Wang, J., & Yup, S. (2003). A framework for clustering evolving data stream. In Proceedings of the 29th VLDB Conference.Google Scholar
  3. Balzanella, A., Lechevallier, Y., & Verde, R. (2011). Clustering multiple data streams. In New perspectives in statistical modeling and data analysis. Heidelberg: Springer. ISBN: 978-3-642-11362-8. doi:  10.1007/978-3-642-11363-5-28.
  4. Dai, B. R., Huang, J. W., Yeh M. Y., & Chen, M. S. (2006). Adaptive clustering for multiple evolving streams. IEEE Transactions on Knowledge and Data Engineering, 18(9), 1166–1180.CrossRefGoogle Scholar
  5. Guha, S., Meyerson, A., Mishra, N., & Motwani, R. (2003). Clustering data streams: Theory and practice. IEEE Transactions on Knowledge and Data Engineering, 15(3), 515–528.CrossRefGoogle Scholar
  6. Lopez-Pintado, S., & Romo, J. (2009). On the concept of depth for functional data. Journal of the American Statistical Association, 104, 718–734.CrossRefMathSciNetGoogle Scholar
  7. Ramsay, J. E., & Silverman, B. W. (2005). Functional data analysis, 2nd ed. New York: Springer.Google Scholar
  8. Romano, E., Balzanella, A., & Rivoli, L. (2011). Functional boxplots for summarizing and detecting changes in environmental data coming from sensors. In Electronic Proceedings of Spatial 2, Spatial Data Methods for Environmental and Ecological Processes 2nd Edition. Foggia, 1–3 Settembre.Google Scholar
  9. Sangalli, L. M., Secchi, P., Vantini, S., & Vitelli, V. (2010). K-mean alignment for curve clustering. Computational Statistics and Data Analysis, 54(5), 1219–1233. ISSN 0167-9473. 10.1016/j.csda.2009.12.008.Google Scholar
  10. Sun, Y., & Genton, M. G. (2011). Functional boxplots. Journal of Computational and Graphical Statistics, 20, 316–334.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Political Science “Jean Monnet”Second University of NaplesCasertaItaly

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