On ill-conceived initialization in archetypal analysis

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

Advances in Data Analysis and Classification, 2017, vol. 11, issue 4, No 7, 785-808

Abstract: 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%.

Keywords: Matrix factorization; Fuzzy clustering; Archetypal analysis; Initialization; Polytopes; 62H30; 62H86 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-017-0303-0

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