Similarity and Dissimilarity Measures for Mixed Feature-Type Symbolic Data

  • Manabu Ichino
  • Kadri Umbleja
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 227)


This paper presents some preliminary results for the similarity and dissimilarity measures based on the Cartesian System Model (CSM) that is a mathematical model to manipulate mixed feature-type symbolic data. We define the notion of concept size for the description of each object in the feature space. By extending the notion to the concept sizes of the Cartesian join and the Cartesian meet of the descriptions for objects, we can obtain various similarity and dissimilarity measures. We present especially asymmetric and symmetric similarity measures useful for pattern recognition problems.


Cartesian system model Symbolic data Concept size Pattern recognition 



The authors thank anonymous referees for their helpful comments. This work was supported by JSPS KAKENHI (Grants–in–Aid for Scientific Research) Grant Number 25330268.


  1. 1.
    Johnson, S.C.: Hierarchical clustering schemes. Psychometrika 32(3), 241–254 (1967)CrossRefzbMATHGoogle Scholar
  2. 2.
    Hubert, L.: Some extensions of Johnson’s hierarchical clustering algorithms. Psychometrika 37(3) 261–27 L. 4 (1972)Google Scholar
  3. 3.
    Tversky, A.: Features of similarity. Psychol. Rev. 84(4) (1977)Google Scholar
  4. 4.
    Michalski, R., Stepp, R.: Learning from observation: Conceptual clustering. In: Michalski, R.S., Carbonell, J.G., Mitchel, T.M. (eds.) Machine Learning, An Artificial Intelligence Approach, vol. II, pp. 331–363. TIOGA Publishing Co., Palo Alto (1983)Google Scholar
  5. 5.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999)CrossRefGoogle Scholar
  6. 6.
    Bock, H.-H., Diday, E.: Analysis of Symbolic Data. Exploratory Methods for Extracting Statistical Information from Complex Data. Springer, Berlin, Heidelberg (2000)zbMATHGoogle Scholar
  7. 7.
    Billard, L., Diday, E.: Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester (2007)zbMATHGoogle Scholar
  8. 8.
    Diday, E., Noirhomme-Fraiture, M.: Symbolic Data Analysis and the SODAS Software. Wiley, Chichester (2008)zbMATHGoogle Scholar
  9. 9.
    De Carvalho, F.D.A.T., De Souza, M.C.R.: Unsupervised pattern recognition models for mixed feature-type data. Pattern Recognit. Lett. 31, 430–443 (2010)Google Scholar
  10. 10.
    Ichino, M., Yaguchi, H.: Generalized Minkowski metrics for mixed feature-type data analysis. IEEE Trans. Syst. Man Cybern. 24(4), 698–708 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Guru, D.S., Kiranagi, B.B., Nagabhushan, P.: Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns. Pattern Recognit. 25, 1203–1213 (2004)CrossRefGoogle Scholar
  12. 12.
    Ichino, M.: The quantile method of symbolic principal component analysis 4, 184–198 (2011)Google Scholar
  13. 13.
    Ono, Y., Ichino, M.: A new feature selection method based on geometrical thickness. Int. J. Off. Stat. 1(2), 19–38 (1998)Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tokyo Denki UniversityTokyoJapan
  2. 2.Tallinn University of TechnologyTallinnEstonia

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