Block-Relaxation Approaches for Fitting the INDCLUS Model

Tom F. Wilderjans, Dirk Depril, Iven van Mechelen

Research output: Contribution to JournalArticleAcademicpeer-review


A well-known clustering model to represent I × I × J data blocks, the J frontal slices of which consist of I × I object by object similarity matrices, is the INDCLUS model. This model implies a grouping of the I objects into a prespecified number of overlapping clusters, with each cluster having a slice-specific positive weight. An INDCLUS model is fitted to a given data set by means of minimizing a least squares loss function. The minimization of this loss function has appeared to be a difficult problem for which several algorithmic strategies have been proposed. At present, the best available option seems to be the SYMPRES algorithm, which minimizes the loss function by means of a block-relaxation algorithm. Yet, SYMPRES is conjectured to suffer from a severe local optima problem. As a way out, based on theoretical results with respect to optimally designing block-relaxation algorithms, five alternative block-relaxation algorithms are proposed. In a simulation study it appears that the alternative algorithms with overlapping parameter subsets perform best and clearly outperform SYMPRES in terms of optimization performance and cluster recovery.

Original languageEnglish
Pages (from-to)277-296
Number of pages20
JournalJournal of Classification
Issue number3
Publication statusPublished - 1 Oct 2012
Externally publishedYes


  • Additive clustering
  • Alternating least squares
  • Block-Relaxation algorithms
  • Overlapping clusters
  • Proximity data
  • Three-Way data


Dive into the research topics of 'Block-Relaxation Approaches for Fitting the INDCLUS Model'. Together they form a unique fingerprint.

Cite this