Abstract
In addition to our first publication about measures of incomparability/inequality (Bartel and Mucha, Measures of incomparability and of inequality and their applications. In: Multi-indicator systems and modeling in partial order. Springer, New York, 2014), a new weighted measure is proposed. In particular, on the basis of these proposed pairwise distance measures, partitional graph clustering techniques are applied to real datasets. In the case of the OCR dataset of handwritten digits “0” and “1”, the error rates are low, i.e., the performance of our proposed measures is very good. In an application to archaeometry, the results are quite similar to the K-means method. Concerning additional interesting archaeological interpretation, we postpone to our ongoing research that will be published soon (Bartel and Mucha, Applications of measures of incomparability and of inequality to archaeometry. Berliner Beiträge zur Archäometrie, Kunsttechnologie und Konservierungswissenschaft, 2016).
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Notes
- 1.
The Egyptologist Fritz Hintze (18 April 1915 to 30 March 1993) was Professor in Egyptology at Humboldt University Berlin, “his principal interest lay in the study of the Meroitic civilization and the application of mathematical methods, seriation, and cluster analysis in archaeology” (Dawson and Uphill 1995). The Coptologist Martin Krause characterizes his colleague in a similar manner: “[…] his later interests on Meroitic studies, the archaeology of the Sudan, and the application of mathematical and statistical analysis to the study of language and archaeological material, are well known.” (Krause 2010: 69), and the mathematician Peter Ihm emphasized: “[Regarding the use of methods of mathematical statistics and computer science in Egyptian, Meroitic, Nubian philology and archaeology, Fritz Hintze may] auf seinem wissenschaftlichen Gebiet als einer der Pioniere ansehen werden (be viewed as one of the pioneers on his scientific field.)” (Ihm 2003: 39).
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Acknowledgement
Dedicated to the 100th birthday of Fritz Hintze.Footnote 1
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Bartel, HG., Mucha, HJ. (2017). Incomparability/Inequality Measures and Clustering. In: Fattore, M., Bruggemann, R. (eds) Partial Order Concepts in Applied Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-45421-4_2
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DOI: https://doi.org/10.1007/978-3-319-45421-4_2
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