Evaluation of Summarization Schemes for Learning in Streams

  • Alec Pawling
  • Nitesh V. Chawla
  • Amitabh Chaudhary
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4213)


Traditional discretization techniques for machine learning, from examples with continuous feature spaces, are not efficient when the data is in the form of a stream from an unknown, possibly changing, distribution. We present a time-and-memory-efficient discretization technique based on computing ε-approximate exponential frequency quantiles, and prove bounds on the worst-case error introduced in computing information entropy in data streams compared to an offline algorithm that has no efficiency constraints. We compare the empirical performance of the technique, using it for feature selection, with (streaming adaptations of) two popular methods of discretization, equal width binning and equal frequency binning, under a variety of streaming scenarios for real and artificial datasets. Our experiments show that ε-approximate exponential frequency quantiles are remarkably consistent in their performance, in contrast to the simple and efficient equal width binning that perform quite well when the streams are from stationary distributions, and quite poorly otherwise.


Feature Selection Data Stream Information Gain Memory Usage Information Entropy 
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.


  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 (PODS), pp. 1–16 (2002)Google Scholar
  2. 2.
    Dougherty, J., Kohavi, R., Sahami, M.: Supervised and unsupervised discretization of continuous features. In: Prieditis, A., Russell, S. (eds.) Proc. 12th International Conference on Machine Learning (ICML), pp. 194–202. Morgan Kaufmann, San Francisco (1995)Google Scholar
  3. 3.
    Gupta, A., Zane, F.X.: Counting inversions in lists. In: Proc. 14th ACM-SIAM Symposium on Discrete algorithms (SODA), pp. 253–254 (2003)Google Scholar
  4. 4.
    Gehrke, J., Ganti, V., Ramakrishnan, R., Loh, W.Y.: BOAT — optimistic decision tree construction. In: Proc. ACM SIGMOD International Conference on Management of Data, pp. 169–180 (1999)Google Scholar
  5. 5.
    Domingos, P., Hulten, G.: Mining high-speed data streams. In: Proc. 6th International Conference on Knowledge Discovery and Data Mining (KDD), pp. 71–80. ACM Press, New York (2000)CrossRefGoogle Scholar
  6. 6.
    Street, W.N., Kim, Y.: A streaming ensemble algorithm (sea) for large-scale classification. In: Proc. 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 377–382. ACM Press, New York (2001)CrossRefGoogle Scholar
  7. 7.
    Hulten, G., Spencer, L., Domingos, P.: Mining time-changing data streams. In: Proc. 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), San Francisco, CA, pp. 97–106. ACM Press, New York (2001)CrossRefGoogle Scholar
  8. 8.
    Gama, J., Pinto, C.: Discretization from data streams: Applications to histograms and data mining. In: 2nd International Workshop on Knowledge Discovery from Data Streams (2005)Google Scholar
  9. 9.
    Guha, S., McGregor, A., Venkatasubramanian, S.: Streaming and sublinear approximation of entropy and information distances. In: Proc. ACM SIAM Symposium on Discrete Algorithms (SODA), pp. 733–742 (2006)Google Scholar
  10. 10.
    Pawling, A., Chawla, N.V., Chaudhary, A.: Evaluation of summarization schemes for learning in streams. Technical Report 2006-08, University of Notre Dame (2006),
  11. 11.
    Pawling, A., Chawla, N.V., Chaudhary, A.: Computing information gain in data streams. In: ICDM Workshop on Temporal Data Mining: Algorithms, Theory, and Applications (2005)Google Scholar
  12. 12.
    Chawla, N.V., Hall, L.O.: Modifying MUSTAFA to capture salient data. Technical report, University of South Florida, Computer Science and Engineering Department (1999)Google Scholar
  13. 13.
    Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J.: UCI repository of machine learning databases (1998),
  14. 14.
    UCSD: UCSD student data mining competition (2006),

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alec Pawling
    • 1
  • Nitesh V. Chawla
    • 1
  • Amitabh Chaudhary
    • 1
  1. 1.University of Notre Dame 

Personalised recommendations