Marginality: A Numerical Mapping for Enhanced Exploitation of Taxonomic Attributes

  • Josep Domingo-Ferrer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7647)

Abstract

Hierarchical attributes appear in taxonomic or ontology- based data (e.g. NACE economic activities, ICD-classified diseases, animal/plant species, etc.). Such taxonomic data are often exploited as if they were flat nominal data without hierarchy, which implies losing substantial information and analytical power. We introduce marginality, a numerical mapping for taxonomic data that allows using on those data many of the algorithms and analytical techniques designed for numerical data. We show how to compute descriptive statistics like the mean, the variance and the covariance on marginality-mapped data. Also, we define a mathematical distance between records including hierarchical attributes that is based on marginality-based variances. Such a distance paves the way to re-using on taxonomic data clustering and anonymization techniques designed for numerical data.

Keywords

Hierarchical attributes Classification Taxonomic data Ontologies Descriptive statistics Numerical mapping Anonymization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Domingo-Ferrer, J., Mateo-Sanz, J.M.: Practical data-oriented microaggregation for statistical disclosure control. IEEE Transactions on Knowledge and Data Engineering 14(1), 189–201 (2002)CrossRefGoogle Scholar
  2. 2.
    Domingo-Ferrer, J., Torra, V.: Ordinal, continuous and heterogeneous k-anonymity through microaggregation. Data Mining and Knowledge Discovery 11(2), 195–212 (2005)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Domingo-Ferrer, J., Sánchez, D., Rufian-Torrell, G.: Anonymization of clinical data based on semantic marginality (manuscript, 2012)Google Scholar
  4. 4.
    Domingo-Ferrer, J., Solanas, A.: A measure of nominal variance for hierarchical nominal attributes. Information Sciences 178(24), 4644–4655 (2008); Erratum in Information Sciences 179(20), 3732 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Duncan, G.T., Elliot, M., Salazar-González, J.-J.: Statistical Confidentiality: Principles and Practice. Springer, New York (2011)MATHCrossRefGoogle Scholar
  6. 6.
    Hundepool, A., Domingo-Ferrer, J., Franconi, L., Giessing, S., Lenz, R., Longhurst, J., Schulte-Nordholt, E., Seri, G., DeWolf, P.-P.: Handbook on Statistical Disclosure Control (version 1.2). ESSNET SDC Project (2010), http://neon.vb.cbs.nl/casc
  7. 7.
    Hundepool, A., Domingo-Ferrer, J., Franconi, L., Giessing, S., Schulte Nordholt, E., Spicer, K., De Wolf, P.P.: Statistical Disclosure Control. Wiley, New York (2012)Google Scholar
  8. 8.
    ICD9 - International Classification of Diseases, 9th Revision, Clinical Modification, 6th edn., October 1 (2008), http://icd9cm.chrisendres.com/
  9. 9.
    ISIC Rev. 4 - International Standard Industrial Classification of All Economic Activities, United Nations Statistics Division, http://unstats.un.org/unsd/cr/registry/regcst.asp?Cl=27&prn=yes
  10. 10.
    Lenz, R.: Methoden der Geheimhaltung wirtschaftsstatistischer Einzeldaten und ihre Schutzwirkung. Statistik und Wissenschaft, vol. 18. Statistisches Bundesamt, Wiesbaden (2010)Google Scholar
  11. 11.
    McNeill, J., et al. (eds.): International Code of Botanical Nomenclature (Vienna Code). International Association for Plant Taxonomy (2006), http://ibot.sav.sk/icbn/main.htm
  12. 12.
    NACE Rev. 2 - Statistical Classification of Economic Activities in the European Community, Rev. 2. Eurostat, European Commission (2008), http://epp.eurostat.ec.europa.eu/cache/ITY_OFFPUB/KS-RA-07-015/EN/KS-RA-07-015-EN.PDF
  13. 13.
    Reid, K.B.: Centrality measures in trees. In: Kaul, H., Mulder, H.M. (eds.) Advances in Interdisciplinary Applied Discrete Mathematics, pp. 167–197. World Scientific eBook (2010)Google Scholar
  14. 14.
    Ride, W.D.L., et al. (eds.): International Code of Zoological Nomenclature, 4th edn., January 1. International Union of Biological Sciences (2000), http://www.nhm.ac.uk/hosted-sites/iczn/code/
  15. 15.
    Samarati, P.: Protecting respondents’ identities in microdata release. IEEE Transactions on Knowledge and Data Engineering 13(6), 1010–1027 (2001)CrossRefGoogle Scholar
  16. 16.
    Sánchez, D., Batet, M., Isern, D., Valls, A.: Ontology-based semantic similarity: a new feature-based approach. Expert Systems with Applications 39(9), 7718–7728 (2012)CrossRefGoogle Scholar
  17. 17.
    Willenborg, L., DeWaal, T.: Elements of Statistical Disclosure Control. Springer, New York (2001)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Josep Domingo-Ferrer
    • 1
  1. 1.Dept. of Computer Engineering and Mathematics UNESCO Chair in Data PrivacyUniversitat Rovira i VirgiliTarragonaSpain

Personalised recommendations