Abstract
This paper focuses on the problem to find an ultrametric whose distortion is close to optimal. We introduce the Minkowski ultrametric distances of the n statistical units obtained by a hierarchical Cluster method (single linkage). We consider the distortion matrix which measures the difference between the initial dissimilarity and the ultrametric approximation. We propose an algorithm which by the application of the Minkowski ultrametrics reaches a minimum approximation. The convergence of the algorithm allows us to identify when the ultrametric approximation is at the local minimum. The validity of the algorithm is confirmed by its application to sets of real data.
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Notes
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This indicator shows the number of rooms that each person in a household has in his disposal by tenure status of the household.
- 2.
At current prices (% of total household consumption expenditure). Household final at current prices consumption expenditure consists of the expenditure, including imputed expenditure, incurred by resident households on individual consumption goods and services, including those sold at prices that are not economically significant.
- 3.
The indicator gives the change in percentage from one year to another of the total number of employed persons on the economic territory of the country or the geographical area.
- 4.
Apparent human consumption per capita is obtained by dividing human consumption by the number of inhabitants (resident population stated in official statistics as at 30 June).
- 5.
A data set with 150 random samples of flowers from the iris species setosa, versicolor, and virginica collected by Anderson (1935). From each species there are 50 observations for sepal length, sepal width, petal length, and petal width in centimeter.
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Scippacercola, S. (2010). The Progressive Single Linkage Algorithm Based on Minkowski Ultrametrics. In: Palumbo, F., Lauro, C., Greenacre, M. (eds) Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03739-9_7
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DOI: https://doi.org/10.1007/978-3-642-03739-9_7
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