Density estimates on the unit simplex and calculation of the mode of a sample |
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Authors: | Maia Angelova Gleb Beliakov Sergiy Shelyag Ye Zhu |
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Affiliation: | School of Information Technology, Deakin University, Burwood, Australia |
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Abstract: | This paper addresses reliable and efficient calculation of the mode of a multivariate sample, which is a classical fusion function. In particular, we focus on the inputs given on the unit simplex, when aggregating elements of Atanassov intuitionistic fuzzy sets, interval-valued fuzzy sets and their extensions, as well as compositional data. We outline the use of a specially designed 2-additive fuzzy measures and the Choquet integral for the purposes of reducing computational complexity in higher dimensions. We present computational analysis and benchmark four different methods of density-based mode estimation. |
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Keywords: | aggregation functions delaunay triangulation density estimate interval valued fuzzy sets mode nearest neighbours |
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