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Classification of Multivariate Objects Using Interval Quantile Classes

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Abstract

The paper contains a proposal of interval data clustering related to given social and economic objects characterized by many interval variables. This multivariate approach is based on an original conception of interval quantiles constructed using a special definition derived from the notion of the Hausdorff distance. In order to improve the quality of classification, the obtained interval quantile classes can be next aggregated into larger merged classes. The efficiency of our method can be assessed using especially defined indices of entropy and volume coefficients. The second notion replaces the classical concept of area, which is not applicable in this case.

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Authors and Affiliations

  1. Statistical Office in Poznań, Branch in Kalisz, pl. J. Kilińskiego 13, 62-800, Kalisz, Poland

    Andrzej Młodak

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  1. Andrzej Młodak
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Correspondence to Andrzej Młodak.

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Dedicated to the Memory of Prof. Dr. Wiesław Wagner and Dr. Piotr Błażczak.

I would like to express my gratitude to Mrs. Paula Brito, Associate Professor in Statistics and Data Analysis at the Faculty of Economics (Group of Mathematics and Informatics) of the University of Porto as well as to three anonymous referees for careful reading of my paper and for very detailed and useful comments and suggestions.

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Młodak, A. Classification of Multivariate Objects Using Interval Quantile Classes. J Classif 28, 327–362 (2011). https://doi.org/10.1007/s00357-011-9088-6

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