Skip to main content
SpringerLink
Log in

Logistic regression-based pattern classifiers for symbolic interval data

  • Theoretical Advances
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

This paper introduces different pattern classifiers for interval data based on the logistic regression methodology. Four approaches are considered. These approaches differ according to the way of representing the intervals. The first classifier considers that each interval is represented by the centres of the intervals and performs a classic logistic regression on the centers of the intervals. The second one assumes each interval as a pair of quantitative variables and performs a conjoint classic logistic regression on these variables. The third one considers that each interval is represented by its vertices and a classic logistic regression on the vertices of the intervals is applied. The last one assumes each interval as a pair of quantitative variables, performs two separate classic logistic regressions on these variables and combines the results in some appropriate way. Experiments with synthetic data sets and an application with a real interval data set demonstrate the usefulness of these classifiers.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Bock HH, Diday E (2000) Analysis of symbolic data: exploratory methods for extracting statistical information from complex data. Springer, Berlin

    Google Scholar 

  2. Ichino M, Yaguchi H, Diday E (1996) A fuzzy symbolic pattern classifier. In: Diday E et al (eds) Ordinal and symbolic data analysis. Springer, Berlin, pp 92–102

    Google Scholar 

  3. de Souza RMCR, De Carvalho FAT, Frery AC (1999) Symbolic approach to SAR image classification. In: IEEE international geoscience and remote sensing symposium, Hamburgo

  4. D’Oliveira S, De Carvalho FAT, de Souza RMCR (2004) Classification of SAR images through a convex hull region oriented approach. In: Pal NR et al (eds) 11th International conference on neural information processing (ICONIP-2004). Lectures notes in computer science—LNCS, vol 3316. Springer, Berlin, pp 769–774

    Google Scholar 

  5. Ciampi A, Diday E, Lebbe J, Perinel E, Vignes R (2000) Growing a tree classifier with imprecise data. Pattern Recognit Lett 21:787–803

    Article  Google Scholar 

  6. Rossi F, Conan-Guez B (2004) Multi-layer perceptron interval data. In: Bock HH (ed) Classification, clustering and data analysis (IFCS2002). Springer, Berlin, pp 427–434

    Google Scholar 

  7. Mali K, Mitra S (2005) Symbolic classification, clustering and fuzzy radial basis function network. Fuzzy Sets Syst 152:553–564

    Article  MathSciNet  MATH  Google Scholar 

  8. Appice A, D’Amato C, Esposito F, Malerba D (2006) Classification of symbolic objects: a lazy learning approach. Intell Data Anal 10(4):301–324

    Google Scholar 

  9. Silva APD, Brito P (2006) Linear discriminant analysis for interval data. Comput Stat 21:289–308

    Article  MATH  Google Scholar 

  10. Roque AMS, Mate C, Arroyo J, Sarabia A (2007) iMLP: applying multi-layer perceptrons to interval-valued data. Neural Process Lett 25:157–169

    Article  Google Scholar 

  11. Hosmer D, Stanley L (2000) Applied logistic regression, 2nd edn. Wiley, New York

    Book  MATH  Google Scholar 

  12. Billard L, Diday E (2000) Regression analysis for interval-valued data. In: Data analysis, classification and related methods. Proceedings of the seventh conference of the international federation of classification societies (IFCS00). Springer, Belgium, pp 369–374

  13. Chouakria A, Cazes P, Diday E (2000) Symbolic principal component analysis in analysis of symbolic data. In: Bock HH, Diday E (eds) Exploratory methods for extracting statistical information from complex data. Springer, Heidelberg, pp 200–212

    Google Scholar 

  14. Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning, data mining, inference and prediction. Springer, Berlin

    MATH  Google Scholar 

  15. Fahrmeir L, Tutz G (2001) Multivariate Statistical Modelling Based on Generalized Linear Models. 2nd Edition. Springer

  16. Duda RO, Hart PE, Stork DG (2001) Pattern classification, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  17. Alexandre LA, Campilho AC, Kamel M (2001) On combining classifiers using product and sum rules. Pattern Recognit Lett 22:1283–1289

    Article  MATH  Google Scholar 

  18. Gowda KC, Diday E (1991) Symbolic clustering using a new dissimilarity measure. Pattern Recognit 24(6):567–578

    Article  Google Scholar 

  19. De Carvalho FAT (2007) Fuzzy c-means clustering methods for symbolic interval data. Pattern Recognit Lett 28:423–437

    Article  Google Scholar 

  20. De Carvalho FAT, Brito P, Bock H. H (2006) Dynamic clustering for interval data based on L2 distance. Comput Stat (Zeitschrift), Heidelberg (Alemanha) 21:231–250

    MATH  Google Scholar 

  21. De Carvalho FAT, Pimentel JT, Bezerra LXT, de Souza RMCR (2007) Clustering symbolic interval data based on a single adaptive Hausdorff distance. In: 2007 IEEE international conference on systems, man and cybernetics, Montreal. Proceedings of the 2007 IEEE international conference on systems, man and cybernetics (IEEE SMC 2007), pp. 451–455

  22. de Souza RMCR, De Carvalho FAT, Pizzato DF (2006) A Partitioning method for mixed feature-type symbolic data using a squared Euclidean distance. In: Proceedings of the 29th Annual German conference on artificial intelligence (KI2006), Bremen (Alemanha). Lecture notes on artificial intelligence—LNAI, vol 4314. Springer, Berlin, pp 260–273

  23. De Carvalho FAT, de Souza RMCR, Bezerra LXT (2006) A dynamical clustering method for symbolic interval data based on a single adaptive Euclidean distance. In: Brazilian symposium on artificial neural networks Ribeiro Preto (SP). Proceedings of the symposium on artificial neural networks (SBRN 2006), vol 8

Download references

Acknowledgments

The authors would like to thank National Counsel of Technological and Scientific Development (Brazilian Agency) for its financial support.

Author information

Authors and Affiliations

  1. Centro de Informática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitária, CEP 50740-540, Recife, PE, Brazil

    Renata M. C. R. de Souza & Diego C. F. Queiroz

  2. Departamento de Estatística, CCEN, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitaria, CEP 50740-540, Recife, PE, Brazil

    Francisco José A. Cysneiros

Authors
  1. Renata M. C. R. de Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diego C. F. Queiroz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francisco José A. Cysneiros
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renata M. C. R. de Souza.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Souza, R.M.C.R., Queiroz, D.C.F. & Cysneiros, F.J.A. Logistic regression-based pattern classifiers for symbolic interval data. Pattern Anal Applic 14, 273–282 (2011). https://doi.org/10.1007/s10044-011-0222-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-011-0222-1

Keywords

Search

Navigation