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    Proximity curves for potential-based clustering

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    Neagu_et_al_Journal_of_Classification (1.768Mb)
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    Publication date
    2019
    Author
    Csenki, Attila
    Neagu, Daniel
    Torgunov, Denis
    Micic, Natasha
    Keyword
    Clustering
    Physical model
    Anisotropic potential
    Cauchy class of distributions
    Steepest descent
    Probabilistic dendogram
    Proximity curve
    Iris data set
    Rights
    © The Author(s) 2019. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
    Peer-Reviewed
    Yes
    
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    Abstract
    The concept of proximity curve and a new algorithm are proposed for obtaining clusters in a finite set of data points in the finite dimensional Euclidean space. Each point is endowed with a potential constructed by means of a multi-dimensional Cauchy density, contributing to an overall anisotropic potential function. Guided by the steepest descent algorithm, the data points are successively visited and removed one by one, and at each stage the overall potential is updated and the magnitude of its local gradient is calculated. The result is a finite sequence of tuples, the proximity curve, whose pattern is analysed to give rise to a deterministic clustering. The finite set of all such proximity curves in conjunction with a simulation study of their distribution results in a probabilistic clustering represented by a distribution on the set of dendrograms. A two-dimensional synthetic data set is used to illustrate the proposed potential-based clustering idea. It is shown that the results achieved are plausible since both the ‘geographic distribution’ of data points as well as the ‘topographic features’ imposed by the potential function are well reflected in the suggested clustering. Experiments using the Iris data set are conducted for validation purposes on classification and clustering benchmark data. The results are consistent with the proposed theoretical framework and data properties, and open new approaches and applications to consider data processing from different perspectives and interpret data attributes contribution to patterns.
    URI
    http://hdl.handle.net/10454/17596
    Version
    Published version
    Citation
    Csenki A, Neagu D, Torgunov D et al (2019) Proximity curves for potential-based clustering. Journal of Classification. Accepted for Publication.
    Link to publisher’s version
    https://doi.org/10.1007/s00357-019-09348-y
    Type
    Article
    Collections
    Engineering and Informatics Publications

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