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In compositional data, an observation is a vector with non-negativecomponents which sum to a constant, typically 1. Data of this type arise inmany areas, such as geology, archaeology, biology, economics and politicalscience among others. The goal of this paper is to extend the taxicab metricand a newly suggested metric for compositional data by employing a powertransformation. Both metrics are to be used in the k-nearest neighboursalgorithm regardless of the presence of zeros. Examples with real data areexhibited.

The k-NN algorithm for compositional data: a revised approach with and without zero values present