Abstract
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.
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References
Johnson, S.C.: Hierarchical clustering schemes. Psychometrika 32(3), 241–254 (1967)
Hubert, L.: Some extensions of Johnson’s hierarchical clustering algorithms. Psychometrika 37(3) 261–27 L. 4 (1972)
Tversky, A.: Features of similarity. Psychol. Rev. 84(4) (1977)
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)
Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999)
Bock, H.-H., Diday, E.: Analysis of Symbolic Data. Exploratory Methods for Extracting Statistical Information from Complex Data. Springer, Berlin, Heidelberg (2000)
Billard, L., Diday, E.: Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester (2007)
Diday, E., Noirhomme-Fraiture, M.: Symbolic Data Analysis and the SODAS Software. Wiley, Chichester (2008)
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)
Ichino, M., Yaguchi, H.: Generalized Minkowski metrics for mixed feature-type data analysis. IEEE Trans. Syst. Man Cybern. 24(4), 698–708 (1994)
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)
Ichino, M.: The quantile method of symbolic principal component analysis 4, 184–198 (2011)
Ono, Y., Ichino, M.: A new feature selection method based on geometrical thickness. Int. J. Off. Stat. 1(2), 19–38 (1998)
Acknowledgements
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.
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Ichino, M., Umbleja, K. (2018). Similarity and Dissimilarity Measures for Mixed Feature-Type Symbolic Data. In: Perna, C., Pratesi, M., Ruiz-Gazen, A. (eds) Studies in Theoretical and Applied Statistics. SIS 2016. Springer Proceedings in Mathematics & Statistics, vol 227. Springer, Cham. https://doi.org/10.1007/978-3-319-73906-9_12
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DOI: https://doi.org/10.1007/978-3-319-73906-9_12
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