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On ill-conceived initialization in archetypal analysis

Author

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  • Abdul Suleman

    (ISCTE-IUL Instituto Universitário de Lisboa, Business Research Unit (BRU-IUL))

Abstract

We show that an improper initialization of the matrix of prototypes, $${\mathbf {V}}$$ V , can be misleading, and potentially gives rise to a degenerate fuzzy partition when performing fuzzy clustering by means of an archetypal analysis. Subsequently, we propose an algorithm to correct the initial guess for $${\mathbf {V}}$$ V , which is grounded in two theoretical results on convex hulls. A numerical experiment carried out to assess its accuracy, and involving more than 200,000 initializations, shows a failure rate of below 0.8%.

Suggested Citation

  • Abdul Suleman, 2017. "On ill-conceived initialization in archetypal analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 785-808, December.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:4:d:10.1007_s11634-017-0303-0
    DOI: 10.1007/s11634-017-0303-0
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    References listed on IDEAS

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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Eugster, Manuel J. A. & Leisch, Friedrich, 2009. "From Spider-Man to Hero — Archetypal Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i08).
    3. Dorit S. Hochbaum & David B. Shmoys, 1985. "A Best Possible Heuristic for the k -Center Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 180-184, May.
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    Cited by:

    1. Flavia Esposito, 2021. "A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments," Mathematics, MDPI, vol. 9(9), pages 1-17, April.

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