Probabilistic archetypal analysis

Sohan Seth*, Manuel J. A. Eugster

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

24 Citations (Scopus)

Abstract

Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be real-valued. This, unfortunately, is not compatible with many practical situations. In this paper we revisit archetypal analysis from the basic principles, and propose a probabilistic framework that accommodates other observation types such as integers, binary, and probability vectors. We corroborate the proposed methodology with convincing real-world applications on finding archetypal soccer players based on performance data, archetypal winter tourists based on binary survey data, archetypal disaster-affected countries based on disaster count data, and document archetypes based on term-frequency data. We also present an appropriate visualization tool to summarize archetypal analysis solution better.

Original languageEnglish
Pages (from-to)85-113
Number of pages29
JournalMachine Learning
Volume102
Issue number1
DOIs
Publication statusPublished - Jan 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Archetypal analysis
  • Probabilistic modeling
  • Majorization-minimization
  • Visualization
  • Convex hull
  • Binary observation
  • NONNEGATIVE MATRIX FACTORIZATION

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