Skip to main content
Log in

Experimenting multiresolution analysis for identifying regions of different classification complexity

  • Short Paper
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

Systems for assessing the classification complexity of a dataset have received increasing attention in research activities on pattern recognition. These systems typically aim at quantifying the overall complexity of a domain, with the goal of comparing different datasets. In this work, we propose a method for partitioning a dataset into regions of different classification complexity, so to highlight sources of complexity inside the dataset. Experiments have been carried out on relevant datasets, proving the effectiveness of the proposed method.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Notes

  1. Of course, a similar definition can also be given for the dataset \(\mathbf {D}\).

References

  1. Singh S (2003) Multiresolution estimates of classification complexity. IEEE Trans Pattern Anal Mach Intell 25:1534–1539

    Article  Google Scholar 

  2. Ho TK, Basu M (2002) Complexity measures of supervised classification problems. IEEE Trans Pattern Anal Mach Intell 24:289–300

    Article  Google Scholar 

  3. Ho TK, Baird HS (1994) Estimating the intrinsic difficulty of a recognition problem. In: Proceedings of the 12th International Conference on Pattern Recognition, pp. 178–183

  4. Loftsgaardne D, Quesenberry C (1965) A non-parametric estimate of multivariate density functiond.o. loftsgaardne. Ann Math Stat 36:1049–1051

  5. Fix E (1951) Discriminatory analysis: nonparametric discrimination: consistency properties. Technical Report. Project 21–49-004, Report Number 4, USAF School of Aviation Medicine, Randolf Field, Texas

  6. Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33(3):1065–1076

    Article  MathSciNet  MATH  Google Scholar 

  7. Alessandro S-JK, Magnani A, Boyd SP (2006) Robust fisher discriminant analysis. Advances in neural information processing systems. MIT Press, Cambridge

    Google Scholar 

  8. Ho TK, Baird HS (1998) Pattern classification with compact distribution maps. Comput Vis Image Underst 70:101–110

    Article  Google Scholar 

  9. Smith F (1968) Pattern classifier design by linear programming. IEEE Trans Comput 17:367–372

    Article  Google Scholar 

  10. Smith S, Jain A (1988) A test to determine the multivariate normality of a data set. IEEE Trans Pattern Anal Mach Intell 10:757–761

    Article  Google Scholar 

  11. Hoekstra A, Duin RP (1996) On the nonlinearity of pattern classifiers. In: Proceedings of the 13th International Conference on Pattern Recognition (ICPR 96), pp. 271–275

  12. Kohn A, Nakano L, Silva M (1996) A class discriminability measure based on feature space partitioning. Pattern Recognit 29(5):873–887

    Article  Google Scholar 

  13. Li J, Han G, Wen J, Gao X (2011) Robust tensor subspace learning for anomaly detection. Int J Mach Learn Cybern 2(2):89–98

    Article  Google Scholar 

  14. Li N, Guo G-D, Chen L-F, Chen S (2012) Optimal subspace classification method for complex data. Int J Mach Learn Cybern 4:163–171

    Article  Google Scholar 

  15. Bernado-Mansilla E, Ho TK (2005) Domain of competence of xcs classifier system in complexity measurement space. Trans Evol Comput 9:82–104

    Article  Google Scholar 

  16. Luengo J, Herrera F (2012) Shared domains of competence of approximate learning models using measures of separability of classes. Inf Sci 185(1):43–65

    Article  MathSciNet  Google Scholar 

  17. Sotoca JM, Mollineda RA, Sánchez JS (2006) A meta-learning framework for pattern classification by means of data complexity measures. Intel Artif 10(29):31–38

    Google Scholar 

  18. Luengo J, Fernández A, García S, Herrera F (2011) Addressing data complexity for imbalanced data sets: analysis of smote-based oversampling and evolutionary undersampling. Soft Comput 15(10):1909–1936

    Article  Google Scholar 

  19. Sohn SY (1999) Meta analysis of classification algorithms for pattern recognition. IEEE Trans Pattern Anal Mach Intell 21:1137–1144

    Article  Google Scholar 

  20. Armano G, Mascia F (2013) A novel method for partitioning feature spaces according to their inherent classification complexity. Int J Pattern Recognit Artif Intell 27(02):1350007

    Article  MathSciNet  Google Scholar 

  21. Alcalá-Fdez J, Fernández A, Luengo J, Derrac J, García S (2011) Keel data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. Multiple-Valued Logic Soft Comput 17(2–3):255–287

    Google Scholar 

  22. Bache K, Lichman M (2013) UCI machine learning repository. University of California, Irvine

    Google Scholar 

  23. Hall M, Frank E, Holmes G, Pfahringer B, Reutemann P, Witten IH (2009) The weka data mining software: an update. SIGKDD Explor Newsl 11:10–18

    Article  Google Scholar 

Download references

Acknowledgments

Emanuele Tamponi gratefully acknowledges Sardinia Regional Government for the financial support of his PhD scholarship (P.O.R. Sardegna F.S.E. Operational Programme of the Autonomous Region of Sardinia, European Social Fund 2007–2013 - Axis IV Human Resources, Objective l.3, Line of Activity l.3.1.).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Tamponi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Armano, G., Tamponi, E. Experimenting multiresolution analysis for identifying regions of different classification complexity. Pattern Anal Applic 19, 129–137 (2016). https://doi.org/10.1007/s10044-014-0446-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-014-0446-y

Keywords

Navigation