Classification of high-dimensional evolving data streams via a resource-efficient online ensemble


A novel online ensemble strategy, ensemble BPegasos (EBPegasos), is proposed to solve the problems simultaneously caused by concept drifting and the curse of dimensionality in classifying high-dimensional evolving data streams, which has not been addressed in the literature. First, EBPegasos uses BPegasos, an online kernelized SVM-based algorithm, as the component classifier to address the scalability and sparsity of high-dimensional data. Second, EBPegasos takes full advantage of the characteristics of BPegasos to cope with various types of concept drifts. Specifically, EBPegasos constructs diverse component classifiers by controlling the budget size of BPegasos; it also equips each component with a drift detector to monitor and evaluate its performance, and modifies the ensemble structure only when large performance degradation occurs. Such conditional structural modification strategy makes EBPegasos strike a good balance between exploiting and forgetting old knowledge. Lastly, we first prove experimentally that EBPegasos is more effective and resource-efficient than the tree ensembles on high-dimensional data. Then comprehensive experiments on synthetic and real-life datasets also show that EBPegasos can cope with various types of concept drifts significantly better than the state-of-the-art ensemble frameworks when all ensembles use BPegasos as the base learner.

This is a preview of subscription content, log in to check access.

Fig. 1


  1. 1.

  2. 2.

  3. 3.

    ASHTBag is excluded here since its ensemble strategy is dedicated to Hoeffding trees.

  4. 4.

    The scripts for generating these datasets are available at

  5. 5.

    It can be downloaded from

  6. 6.

    It can be downloaded from


  1. Abdulsalam H, Skillicorn DB, Martin P (2007) Streaming random forests. In: 11th international database engineering and applications symposium, pp 225–232

  2. Abdulsalam H, Skillicorn DB, Martin P (2011) Classification using streaming random forests. IEEE Trans Knowl Data Eng 23(1):22–36

    Article  Google Scholar 

  3. Abe S (2005) Support vector machines for pattern classification. Springer, London

    Google Scholar 

  4. Aggarwal CC, Yu PS (2008) Locust: an online analytical processing framework for high dimensional classification of data streams. In: Proceedings of the 24th IEEE international conference on data engineering, pp 426–435

  5. Bifet A, Frank E (2010) Sentiment knowledge discovery in twitter streaming data. In: International conference on discovery science, pp 1–15

  6. Bifet A, Gavalda R (2007) Learning from time-changing data with adaptive windowing. In: Proceedings of the 7th SIAM international conference on data mining, pp 443–448

  7. Bifet A, Holmes G, Pfahringer B, Kirkby R, Gavaldà R (2009) New ensemble methods for evolving data streams. In: Proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining, pp 139–148

  8. Bifet A, Holmes G, Kirkby R, Pfahringer B (2010a) Moa: massive online analysis. J Mach Learn Res 11:1601–1604

    Google Scholar 

  9. Bifet A, Holmes G, Pfahringer B (2010b) Leveraging bagging for evolving data streams. In: Joint European conference on machine learning and knowledge discovery in databases, pp 135–150

  10. Bifet A, Holmes G, Pfahringer B, Frank E (2010c) Fast perceptron decision tree learning from evolving data streams. In: Pacific-Asia conference on knowledge discovery and data mining, pp 299–310

  11. Bifet A, Pfahringer B, Read J, Holmes G (2013) Efficient data stream classification via probabilistic adaptive windows. In: Proceedings of the 28th annual ACM symposium on applied computing, pp 801–806

  12. Brzeziński D, Stefanowski J (2011) Accuracy updated ensemble for data streams with concept drift. In: International conference on hybrid artificial intelligence systems, pp 155–163

  13. Brzezinski D, Stefanowski J (2014a) Combining block-based and online methods in learning ensembles from concept drifting data streams. Inf Sci 265:50–67

    MathSciNet  Article  MATH  Google Scholar 

  14. Brzezinski D, Stefanowski J (2014b) Reacting to different types of concept drift: the accuracy updated ensemble algorithm. IEEE Trans Neural Netw Learn Syst 25(1):81–94

    Article  Google Scholar 

  15. Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  MATH  Google Scholar 

  16. Denil M, Matheson D, De Freitas N (2013) Consistency of online random forests. In: Proceedings of the 30th international conference on machine learning, pp 1256–1264

  17. Do TN, Lenca P, Lallich S, Pham NK (2010) Classifying very-high-dimensional data with random forests of oblique decision trees. In: Guillet F, Ritschard G, Zighed DA, Briand H (eds) Advances in knowledge discovery and management. Springer, Berlin, Heidelberg, pp 39–55

    Google Scholar 

  18. Domingos P, Hulten G (2000) Mining high-speed data streams. In: Proceedings of the 6th ACM SIGKDD international conference on knowledge discovery and data mining, pp 71–80

  19. Elwell R, Polikar R (2011) Incremental learning of concept drift in nonstationary environments. IEEE Trans Neural Netw 22(10):1517–1531

    Article  Google Scholar 

  20. Gama J, Fernandes R, Rocha R (2006) Decision trees for mining data streams. Intell Data Anal 10(1):23–45

    Google Scholar 

  21. Gama J, Sebastiao R, Rodrigues PP (2013) On evaluating stream learning algorithms. Mach Learn 90(3):317–346

    MathSciNet  Article  MATH  Google Scholar 

  22. Gama J, Zliobaite I, Bifet A, Pechenizkiy M, Bouchachia A (2014) A survey on concept drift adaptation. ACM Comput Surv 46(4):44

    Article  MATH  Google Scholar 

  23. Holmes G, Kirkby R, Pfahringer B (2005) Stress-testing hoeffding trees. In: European conference on principles of data mining and knowledge discovery, pp 495–502

  24. Hosseini MJ, Gholipour A, Beigy H (2015) An ensemble of cluster-based classifiers for semi-supervised classification of non-stationary data streams. Knowl Inf Syst 46:1–31

    Google Scholar 

  25. Hsu CW, Chang CC, Lin CJ, et al (2003) A practical guide to support vector classification.

  26. Katakis I, Tsoumakas G, Banos E, Bassiliades N, Vlahavas I (2009) An adaptive personalized news dissemination system. J Intell Inf Syst 32(2):191–212

    Article  Google Scholar 

  27. Katakis I, Tsoumakas G, Vlahavas I (2010) Tracking recurring contexts using ensemble classifiers: an application to email filtering. Knowl Inf Syst 22(3):371–391

    Article  Google Scholar 

  28. Kolter JZ, Maloof MA (2007) Dynamic weighted majority: an ensemble method for drifting concepts. J Mach Learn Res 8:2755–2790

    MATH  Google Scholar 

  29. Krempl G, Žliobaite I, Brzeziński D, Hüllermeier E, Last M, Lemaire V, Noack T, Shaker A, Sievi S, Spiliopoulou M, Stefanowski J (2014) Open challenges for data stream mining research. SIGKDD Explor 16(1):1–10

    Article  Google Scholar 

  30. Lakshminarayanan B, Roy DM, Teh YW (2014) Mondrian forests: efficient online random forests. In: Advances in neural information processing systems 27: annual conference on neural information processing systems 2014, Montreal, Quebec, Canada, pp 3140–3148

  31. Liu Y, Zhou Y (2014) Online detection of concept drift in visual tracking. In: International conference on neural information processing, pp 159–166

  32. McCallum A, Nigam K et al (1998) A comparison of event models for naive bayes text classification. In: AAAI-98 workshop on learning for text categorization, vol 752, pp 41–48

  33. Minku LL, Yao X (2012) Ddd: A new ensemble approach for dealing with concept drift. IEEE Trans Knowl Data Eng 24(4):619–633

    Article  Google Scholar 

  34. Minku LL, White AP, Yao X (2010) The impact of diversity on online ensemble learning in the presence of concept drift. IEEE Trans Knowl Data Eng 22(5):730–742

    Article  Google Scholar 

  35. Oza NC (2005) Online bagging and boosting. In: 2005 IEEE international conference on systems, man and cybernetics, vol 3, pp 2340–2345

  36. Pappu V, Pardalos PM (2014) High-dimensional data classification. In: Aleskerov F, Goldengorin B, Pardalos PM (eds) Clusters, orders, and trees: methods and applications. Springer, New York, pp 119–150

    Google Scholar 

  37. Rutkowski L, Pietruczuk L, Duda P, Jaworski M (2013) Decision trees for mining data streams based on the McDiarmid’s bound. IEEE Trans Knowl Data Eng 25(6):1272–1279

    Article  Google Scholar 

  38. Saffari A, Leistner C, Santner J, Godec M, Bischof H (2009) On-line random forests. In: 2009 IEEE 12th international conference on computer vision workshops, pp 1393–1400

  39. Shalev-Shwartz S, Singer Y, Srebro N, Cotter A (2011) Pegasos: primal estimated sub-gradient solver for SVM. Math Program 127(1):3–30

    MathSciNet  Article  MATH  Google Scholar 

  40. Tomasev N, Radovanovic M, Mladenic D, Ivanovic M (2014) The role of hubness in clustering high-dimensional data. IEEE Trans Knowl Data Eng 26(3):739–751

    Article  Google Scholar 

  41. Wang Z, Crammer K, Vucetic S (2012) Breaking the curse of kernelization: budgeted stochastic gradient descent for large-scale SVM training. J Mach Learn Res 13(1):3103–3131

    MathSciNet  MATH  Google Scholar 

  42. Wang D, Wu P, Zhao P, Wu Y, Miao C, Hoi SC (2014) High-dimensional data stream classification via sparse online learning. In: 2014 IEEE international conference on data mining, pp 1007–1012

  43. Ye Y, Wu Q, Huang JZ, Ng MK, Li X (2013) Stratified sampling for feature subspace selection in random forests for high dimensional data. Pattern Recognit 46(3):769–787

    Article  Google Scholar 

  44. Zhang X, Furtlehner C, Germain-Renaud C, Sebag M (2014) Data stream clustering with affinity propagation. IEEE Trans Knowl Data Eng 26(7):1644–1656

    Article  Google Scholar 

  45. Zliobaite I, Gabrys B (2014) Adaptive preprocessing for streaming data. IEEE Trans Knowl Data Eng 26(2):309–321

    Article  Google Scholar 

  46. Zliobaite I, Bifet A, Read J, Pfahringer B, Holmes G (2015) Evaluation methods and decision theory for classification of streaming data with temporal dependence. Mach Learn 98(3):455–482

    MathSciNet  Article  MATH  Google Scholar 

Download references


This work is supported by the National NSF of China (Nos. 61432008, 61503178), NSF and Primary R&D Plan of Jiangsu Province, China (Nos. BE2015213, BK20150587), and the Collaborative Innovation Center of Novel Software Technology and Industrialization.

Author information



Corresponding author

Correspondence to Yang Gao.

Additional information

Responsible editor: Thomas Gärtner, Mirco Nanni, Andrea Passerini and Céline Robardet.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhai, T., Gao, Y., Wang, H. et al. Classification of high-dimensional evolving data streams via a resource-efficient online ensemble. Data Min Knowl Disc 31, 1242–1265 (2017).

Download citation


  • High dimensionality
  • Concept drift
  • Data stream classification
  • Online ensemble