CCM: Controlling the Change Magnitude in High Dimensional Data

  • Cesare Alippi
  • Giacomo Boracchi
  • Diego CarreraEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 529)


The effectiveness of change-detection algorithms is often assessed on real-world datasets by injecting synthetically generated changes. Typically, the magnitude of the introduced changes is not controlled, and most of experimental practices lead to results that are difficult to reproduce and compare with. This problem becomes particularly relevant when the data-dimension scales, as it happens in big data applications.

To enable a fair comparison among change-detection algorithms, we have designed “Controlling Change Magnitude” (CCM), a rigorous method to introduce changes in multivariate datasets. In particular, we measure the change magnitude as the symmetric Kullback-Leibler divergence between the pre- and post-change distributions, and introduce changes by applying a roto-translation directly to the data. We present an algorithm to identify the parameters yielding the desired change magnitude, and analytically prove its convergence. Our experiments show the effectiveness of the proposed method and the limitations of tests run on high-dimensional datasets when changes are injected following traditional approaches. The MATLAB framework implementing the proposed method is made publicly available for download.


Bisection Method Change Magnitude Realistic Monitoring Multivariate Dataset Popular Machine Learning 
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.
    Alippi, C.: Intelligence for Embedded Systems, A Methodological Approach. Springer, Switzerland (2014)Google Scholar
  2. 2.
    Alippi, C., Boracchi, G., Carrera, D., Roveri, M.: Change detection in multivariate datastreams: Likelihood and detectability loss. In: Proceedings of IJCAI (2016)Google Scholar
  3. 3.
    Alippi, C., Boracchi, G., Roveri, M.: A Just-In-Time adaptive classification system based on the Intersection of Confidence Intervals rule. Neural Netw. 24(8), 791–800 (2011)CrossRefGoogle Scholar
  4. 4.
    Alippi, C., Boracchi, G., Roveri, M.: Just-in-time classifiers for recurrent concepts. IEEE Trans. Neural Netw. Learn. Syst. 24(4) (2013)Google Scholar
  5. 5.
    Alippi, C., Boracchi, G., Roveri, M.: Hierarchical change-detection tests. IEEE Trans. Neural Netw. Learn. Syst. PP(99), 1–13 (2016)CrossRefGoogle Scholar
  6. 6.
    Bauer, H.: Measure and Integration Theory. Walter de Gruyter, Berlin (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Boracchi, G., Roveri, M.: Exploiting self-similarity for change detection. In: Proceedings of IEEE International Joint Conference on Neural Networks (IJCNN) (2014)Google Scholar
  8. 8.
    Burden, R.L., Faires, J.D.: Numerical Analysis. Brooks/Cole, USA (2001)zbMATHGoogle Scholar
  9. 9.
    Chandola, V., Banerjee, A., Kumar, V.: Anomaly detection: a survey. ACM Comput. Surv. 41(3), 15:1–15:58 (2009)CrossRefGoogle Scholar
  10. 10.
    Gama, J., Medas, P., Castillo, G., Rodrigues, P.: Learning with drift detection. In: Proceedings of Brazilian Symposium on Artificial Intelligence (SBIA) (2004)Google Scholar
  11. 11.
    Gama, J., Žliobaitė, I., Bifet, A., Pechenizkiy, M., Bouchachia, A.: A survey on concept drift adaptation. ACM Comput. Surv. (CSUR) 46(4) (2014)Google Scholar
  12. 12.
    Harel, M., Mannor, S., El-yaniv, R., Crammer, K.: Concept drift detection through resampling. In: Proceedings of ICML, pp. 1009–1017 (2014)Google Scholar
  13. 13.
    Kuncheva, L.I.: Change detection in streaming multivariate data using likelihood detectors. IEEE Trans. Knowl. Data Eng. 25(5) (2013)Google Scholar
  14. 14.
    Lichman, M.: UCI machine learning repository.
  15. 15.
    McLachlan, G., Peel, D.: Finite Mixture Models. Wiley, New York (2004)zbMATHGoogle Scholar
  16. 16.
    Pimentel, M.A., Clifton, D.A., Clifton, L., Tarassenko, L.: A review of novelty detection. Sig. Process. 99, 215–249 (2014)CrossRefGoogle Scholar
  17. 17.
    Ross, G.J., Tasoulis, D.K., Adams, N.M.: Nonparametric monitoring of data streams for changes in location and scale. Technometrics 53(4) (2011)Google Scholar
  18. 18.
    Rudin, W.: Principles of Mathematical Analysis. McGraw-Hill, New York (1964)zbMATHGoogle Scholar
  19. 19.
    Street, W.N., Kim, Y.: A streaming ensemble algorithm (sea) for large-scale classification. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2001)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Cesare Alippi
    • 1
    • 2
  • Giacomo Boracchi
    • 1
  • Diego Carrera
    • 1
    Email author
  1. 1.Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di MilanoMilanoItaly
  2. 2.Università della Svizzera ItalianaLuganoSwitzerland

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