Kalman Filters and Adaptive Windows for Learning in Data Streams

  • Albert Bifet
  • Ricard Gavaldà
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4265)


We study the combination of Kalman filter and a recently proposed algorithm for dynamically maintaining a sliding window, for learning from streams of examples. We integrate this idea into two well-known learning algorithms, the Naïve Bayes algorithm and the k-means clusterer. We show on synthetic data that the new algorithms do never worse, and in some cases much better, than the algorithms using only memoryless Kalman filters or sliding windows with no filtering.


Kalman Filter Data Stream Synthetic Data Linear Estimator Concept Drift 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and issues in data stream systems. In: Proc. 21st ACM Symposium on Principles of Database Systems (2002)Google Scholar
  2. 2.
    Bifet, A., Gavaldà, R.: Learning from time-changing data with adaptive windowing. Technical report, Universitat Politècnica de Catalunya (2006), Available from:
  3. 3.
    Datar, M., Gionis, A., Indyk, P., Motwani, R.: Maintaining stream statistics over sliding windows. SIAM Journal on Computing 14(1), 27–45 (2002)MathSciNetGoogle Scholar
  4. 4.
    Gama, J., Medas, P., Castillo, G., Rodrigues, P.: Learning with drift detection. In: SBIA Brazilian Symposium on Artificial Intelligence, pp. 286–295 (2004)Google Scholar
  5. 5.
    Hulten, G., Spencer, L., Domingos, P.: Mining time-changing data streams. In: 7th ACM SIGKDD Intl. Conf. on Knowledge Discovery and Data Mining, San Francisco, CA, pp. 97–106. ACM Press, New York (2001)CrossRefGoogle Scholar
  6. 6.
    Jacobsson, K., Möller, N., Johansson, K.-H., Hjalmarsson, H.: Some modeling and estimation issues in control of heterogeneous networks. In: 16th Intl. Symposium on Mathematical Theory of Networks and Systems (MTNS 2004) (2004)Google Scholar
  7. 7.
    Kifer, D., Ben-David, S., Gehrke, J.: Detecting change in data streams. In: Proc. 30th VLDB Conf., Toronto, Canada (2004)Google Scholar
  8. 8.
    Muthukrishnan, S.: Data streams: Algorithms and applications. In: Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (2003)Google Scholar
  9. 9.
    Ordonez, C.: Clustering binary data streams with k-means. In: ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery (2003)Google Scholar
  10. 10.
    Page, E.S.: Continuous inspection schemes. Biometrika 41(1/2), 100–115 (1954)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Schön, T., Eidehall, A., Gustafsson, F.: Lane departure detection for improved road geometry estimation. Technical Report LiTH-ISY-R-2714, Dept.of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden (December 2005)Google Scholar
  12. 12.
    Severo, M., Gama, J.: Change detection with Kalman Filter applied to apnoeas disorder. In: 2nd. Intl. Workshop on Knowledge Discovery from Data Streams, Porto (Portugal) (2005)Google Scholar
  13. 13.
    Welch, G., Bishop, G.: An introduction to the Kalman Filter. Technical report, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Albert Bifet
    • 1
  • Ricard Gavaldà
    • 1
  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations