Detecting the number of clusters in n-way probabilistic clustering

Zhaoshui He, Andrzej Cichocki, Shengli Xie, Kyuwan Choi

Research output: Contribution to journalArticlepeer-review

146 Citations (Scopus)


Recently, there has been a growing interest in multiway probabilistic clustering. Some efficient algorithms have been developed for this problem. However, not much attention has been paid on how to detect the number of clusters for the general n-way clustering (n≥ 2). To fill this gap, this problem is investigated based on n-way algebraic theory in this paper. A simple, yet efficient, detection method is proposed by eigenvalue decomposition (EVD), which is easy to implement. We justify this method. In addition, its effectiveness is demonstrated by the experiments on both simulated and real-world data sets.

Original languageEnglish
Article number5383365
Pages (from-to)2006-2021
Number of pages16
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number11
Publication statusPublished - 2010
Externally publishedYes


  • affinity arrays
  • enumeration of clusters
  • estimation of PARAFAC components
  • higher order tensor
  • hypergraph
  • model order selection
  • multiway array
  • Multiway clustering
  • parallel factor analysis (PARAFAC)
  • principal components enumeration
  • probabilistic clustering
  • supersymmetric tensors


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