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On-line elimination of local redundancies in evolving fuzzy systems

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Abstract

In this paper, we examine approaches for reducing the complexity of evolving fuzzy systems (EFSs) by eliminating local redundancies during training, evolving the models on on-line data streams. Thus, the complexity reduction steps should support fast incremental single-pass processing steps. In EFSs, such reduction steps are important due to several reasons: (1) originally distinct rules representing distinct local regions in the input/output data space may move together over time and get significantly over-lapping as data samples are filling up the gaps in-between these, (2) two or several fuzzy sets in the fuzzy partitions may become redundant because of projecting high-dimensional clusters onto the single axes, (3) they can be also seen as a first step towards a better readability and interpretability of fuzzy systems, as unnecessary information is discarded and the models are made more transparent. One technique is performing a new rule merging approach directly in the product cluster space using a novel concept for calculating the similarity degree between an updated rule and the remaining ones. Inconsistent rules elicited by comparing the similarity of two redundant rule antecedent parts with the similarity of their consequents are specifically handled in the merging procedure. The second one is operating directly in the fuzzy partition space, where redundant fuzzy sets are merged based on their joint α-cut levels. Redundancy is measured by a novel kernel-based similarity measure. The complexity reduction approaches are evaluated based on high-dimensional noisy real-world measurements and an artificially generated data stream containing 1.2 million samples. Based on this empirical comparison, it will be shown that the novel techniques are (1) fast enough in order to cope with on-line demands and (2) produce fuzzy systems with less structural components while at the same time achieving accuracies similar to EFS not integrating any reduction steps.

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References

  • Abraham W, Robins A (2005) Memory retention—the synaptic stability versus plasticity dilemma. Trends Neurosci 28(2):73–78

    Article  Google Scholar 

  • Angelov P (2010) Evolving takagi-sugeno fuzzy systems from streaming data, eTS+. In: Angelov P, Filev D, Kasabov N (eds) Evolving intelligent systems: methodology and applications. Wiley, New York, pp 21–50

  • Angelov P, Filev D (2005) Simpl_eTS: A simplified method for learning evolving Takagi-Sugeno fuzzy models. In: Proceedings of FUZZ-IEEE 2005. Reno, Nevada, USA, pp 1068–1073

  • Angelov P, Kordon A (2010) Evolving inferential sensors in the chemical process industry. In: Angelov P, Filev D, Kasabov N (eds) Evolving intelligent systems: methodology and applications. Wiley, New York, pp 313–336

  • Babuska R (1998) Fuzzy modeling for control. Kluwer, Norwell

  • Baturone I, Moreno-Velo F, Gersnoviez A (2006) A cad approach to simplify fuzzy system descriptions. In: Proceedings of the 2006 IEEE international conference on fuzzy systems. Vancouver, pp 2392–2399

  • Bifet A, Holmes G, Kirkby R, Pfahringer B (2010) MOA: massive online analysis. J Mach Learning Res 11:1601–1604

    Google Scholar 

  • Breiman L, Friedman J, Stone C, Olshen R (1993) Classification and regression trees. Chapman & Hall, Boca Raton

  • Burger M, Haslinger J, Bodenhofer U, Engl HW (2002) Regularized data-driven construction of fuzzy controllers. J Inverse Ill Posed Probl 10(4):319–344

    MathSciNet  MATH  Google Scholar 

  • Casillas J, Cordon O, Herrera F, Magdalena L (2003) Interpretability issues in fuzzy modeling. Springer, Berlin

  • Chen M, Linkens D (2004) Rule-base self-generation and simplification for data-driven fuzzy models. Fuzzy Sets Syst 142(2):243–265

    Article  MathSciNet  MATH  Google Scholar 

  • Destercke S, Guillaume S, Charnomordic B (2007) Building an interpretable fuzzy rule base from data using orthogonal least squares—application to a depollution problem. Fuzzy Sets Syst 158(18):2078–2094

    Article  MathSciNet  MATH  Google Scholar 

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

  • Espinosa J, Vandewalle J (2000) Constructing fuzzy models with linguistic intergrity from numerical data—AFRELI algorithm. IEEE Trans Fuzzy Syst 8(5):591–600

    Article  Google Scholar 

  • Groißböock W, Lughofer E, Klement E (2004) A comparison of variable selection methods with the main focus on orthogonalization. In: Lopéz-Díaz M, Gil M, Grzegorzewski P, Hryniewicz O, Lawry J (eds) Soft methodology and random information systems. Advances in soft computing. Springer, Berlin, pp 479–486

  • Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference and prediction, 2nd edn. Springer, Berlin

  • Hathaway R, Bezdek J (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1(3):195–204

    Article  Google Scholar 

  • Jimenez F, Gomez-Skarmeta AF, Sanchez G, Roubos H, Babuska R (2003) Accurate, transparent and compact fuzzy models by multi-objective evolutionary algorithms. In: Casillas J, Cordón O, Herrera F, Magdalena L (eds) Interpretability issues in fuzzy modeling. Studies in fuzziness and soft computing, vol 128. Springer, Berlin, pp 431–451

  • Kasabov N (2007) Evolving connectionist systems: the knowledge engineering approach, 2nd edn. Springer, London

  • Kasabov NK, Song Q (2002) DENFIS: dynamic evolving neural-fuzzy inference system and its application for time-series prediction. IEEE Trans Fuzzy Syst 10(2):144–154

    Article  Google Scholar 

  • Klement E, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht

  • Kordon A, Smits G, Kalos A, Jordaan E (2003) Robust soft sensor development using genetic programming. In: Leardi R (ed) Nature-inspired methods in chemometrics, pp 69–108

  • Kurzhanskiy AA, Varaiya P (2006) Ellipsoidal toolbox. Tech. rep. UCB/EECS-2006-46, EECS Department, University of California, Berkeley. http://code.google.com/p/ellipsoids

  • Lima E, Hell M, Ballini R, Gomide F (2010) Evolving fuzzy modeling using participatory learning. In: Angelov P, Filev D, Kasabov N (eds) Evolving intelligent systems: methodology and applications. Wiley, New York, pp 67–86

  • Lughofer E (2006) Process safety enhancements for data-driven evolving fuzzy models. In: Proceedings of 2nd symposium on evolving fuzzy systems. Lake District, UK, pp 42–48

  • Lughofer E (2008a) Extensions of vector quantization for incremental clustering. Pattern Recogn 41(3):995–1011

    Article  MATH  Google Scholar 

  • Lughofer E (2008b) FLEXFIS: a robust incremental learning approach for evolving TS fuzzy models. IEEE Trans Fuzzy Syst 16(6):1393–1410

    Article  Google Scholar 

  • Lughofer E (2010) Towards robust evolving fuzzy systems. In: Angelov P, Filev D, Kasabov N (eds) Evolving intelligent systems: methodology and applications. Wiley, New York, pp 87–126

  • Lughofer E (2011) Evolving fuzzy systems-Methodologies, advanced concepts and applications. Springer, Berlin. ISBN: 978-3-642-18086-6

  • Lughofer E, Angelov P (2011) Handling drifts and shifts in on-line data streams with evolving fuzzy systems. Applied Soft Computing 11(2):2057–2068

    Article  Google Scholar 

  • Lughofer E, Hüllermeier E, Klement E (2005) Improving the interpretability of data-driven evolving fuzzy systems. In: Proceedings of EUSFLAT 2005. Barcelona, Spain, pp 28–33

  • Lughofer E, Macian V, Guardiola C, Klement E (2010) Data-driven design of takagi-sugeno fuzzy systems for predicting NOx emissions. In: Hüllermeier E, Kruse R, Hoffmann F (eds) Proc. of the 13th international conference on information processing and management of uncertainty, IPMU 2010, part II (applications), CCIS, vol 81. Springer, Dortmund, pp 1–10

  • Mikut R, Mäkel J, Gröll L (2005) Interpretability issues in data-based learning of fuzzy systems. Fuzzy Sets Syst 150(2):179–197

    Article  MATH  Google Scholar 

  • Moser B A similarity measure for images and volumetric data based on Hermann Weyl’s discrepancy. IEEE Trans Pattern Anal Mach Intell (2010). doi:10.1109/TPAMI.2009.50

  • Nelles O (2001) Nonlinear system identification. Springer, Berlin

  • Oliveira JVD (1999) Semantic constraints for membership function optimization. IEEE Trans Syst Man Cybern Part A Syst Hum 29(1):128–138

    Article  Google Scholar 

  • Pang S, Ozawa S, Kasabov N (2005) Incremental linear discriminant analysis for classification of data streams. IEEE Trans Syst Man Cybern Part B Cybern 35(5):905–914

    Article  Google Scholar 

  • Qin S, Li W, Yue H (2000) Recursive PCA for adaptive process monitoring. J Process Control 10:471–486

    Article  Google Scholar 

  • Quinlan JR (1993) C4.5: programs for machine learning. Morgan Kaufmann, San Francisco

  • Ramos J, Dourado A (2006) Pruning for interpretability of large spanned eTS. In: Proceedings of the 2006 international symposium on evolving fuzzy systems. Ambleside, UK, pp 55–60

  • Rong HJ, Sundararajan N, Huang GB, Saratchandran P (2006) Sequential adaptive fuzzy inference system (SAFIS) for nonlinear system identification and prediction. Fuzzy Sets Syst 157(9):1260–1275

    Article  MathSciNet  MATH  Google Scholar 

  • Rong HJ, Sundararajan N, Huang GB, Zhao GS (2011) Extended sequential adaptive fuzzy inference system for classification problems. Evol Syst (in press). doi:10.1007/s12530-010-9023-9

  • Ros L, Sabater A, Thomas F (2002) An ellipsoidal calculus based on propagation and fusion. IEEE Trans Syst Man Cybern Part B Cybern 32(4):430–442

    Article  Google Scholar 

  • Setnes M (2003) Simplification and reduction of fuzzy rules. In: Casillas J, Cordón O, Herrera F, Magdalena L (eds) Interpretability issues in fuzzy modeling. Studies in fuzziness and soft computing, vol 128. Springer, Berlin, pp 278–302

  • Setnes M, Babuska R, Kaymak U, Lemke H (1998a) Similarity measures in fuzzy rule base simplification. IEEE Trans Syst Man Cybern Part B Cybern 28(3):376–386

    Article  Google Scholar 

  • Setnes M, Babuska R, Verbruggen H (1998b) Complexity reduction in fuzzy modeling. Math Comput Simul 46(5-6):509–518

    Article  Google Scholar 

  • Shaker A, Senge R, Hüllermeier E (2011) Evolving fuzzy pattern trees for binary classification on data streams. Inf Sci (in press)

  • Stone M (1974) Cross-validatory choice and assessment of statistical predictions. J R Stat Soc 36:111–147

    MATH  Google Scholar 

  • Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    MATH  Google Scholar 

  • Wang L (1992) Fuzzy systems are universal approximators. In: Proceedings of the 1st IEEE conf. fuzzy systems. San Diego, CA, pp 1163–1169

  • Wang L, Mendel J (1992) Fuzzy basis functions, universal approximation and orthogonal least-squares learning. IEEE Trans Neural Netw 3(5):807–814

    Article  Google Scholar 

  • Yager RR (1990) A model of participatory learning. IEEE Trans Syst Man Cybern 20:1229–1234

    Article  MathSciNet  Google Scholar 

  • Yen J, Wang L, Gillespie C (1998) Improving the interpretability of TSK fuzzy models by combining global learning and local learning. IEEE Trans Fuzzy Syst 6(4):530–537

    Article  Google Scholar 

  • Zhou S, Gan J (2008) Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy systems modelling. Fuzzy Seta Syst 159(23):3091–3131

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was funded by the Austrian and German fund for promoting scientific research (FWF and DFG, contract number I328-N23, acronym IREFS). It reflects only the authors’ views. The residential premise data set was provided by Bogdan and Krysztof Trawinski. The authors also acknowledge Eyke Hüllermeier for providing valuable comments and suggestions on the manuscript.

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Authors and Affiliations

  1. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University of Linz, Linz, Austria

    Edwin Lughofer & Jean-Luc Bouchot

  2. Department of Mathematics and Computer Science, Philipps-University Marburg, Marburg, Germany

    Ammar Shaker

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  1. Edwin Lughofer
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  2. Jean-Luc Bouchot
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  3. Ammar Shaker
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Correspondence to Edwin Lughofer.

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Lughofer, E., Bouchot, JL. & Shaker, A. On-line elimination of local redundancies in evolving fuzzy systems. Evolving Systems 2, 165–187 (2011). https://doi.org/10.1007/s12530-011-9032-3

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