Advances in Data Analysis and Classification

, Volume 11, Issue 4, pp 785–808 | Cite as

On ill-conceived initialization in archetypal analysis

Regular Article
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Abstract

We show that an improper initialization of the matrix of prototypes, \({\mathbf {V}}\), 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 \({\mathbf {V}}\), 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%.

Keywords

Matrix factorization Fuzzy clustering Archetypal analysis Initialization Polytopes 

Mathematics Subject Classification

62H30 62H86 

Notes

Acknowledgements

The author is indebted to Günter M. Ziegler and C. Bradford Barber for their advice which significantly contributed to this research work. However, the work is the exclusive responsibility of the author. He also thanks the three anonymous reviewers for their comments, suggestions and careful reading of an earlier version of this manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

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

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