Cutoff for Exact Recovery of Gaussian Mixture Models

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We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a K-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the K-means clustering method achieves such sharp threshold for exact recovery without assuming the symmetry of cluster centers.

Original languageEnglish (US)
Article number9366690
Pages (from-to)4223-4238
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2021


  • Gaussian mixture models
  • K-means
  • exact recovery
  • optimality
  • semidefinite relaxation
  • sharp threshold

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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