NMF with feature relationship preservation penalty term for clustering problems

Rachid Hedjam*, Abdelhamid Abdesselam, Farid Melgani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


The method proposed in this paper belongs to the family of orthogonal non-negative matrix factorization (ONMF) methods designed to solve clustering problems. Unlike some existing ONMF methods that explicitly constrain the orthogonality of the coefficient matrix in the cost function to derive their clustering models, the proposed method integrates it implicitly, so that it results in a new optimization model with a penalty term. The latter is added to impose a scale relationship between the scatter of the cluster centroids and that of the data points. The solution of the new model involves deriving a new parametrized update scheme for the basis matrix, which makes it possible to improve the performance of the clustering by adjusting a parameter. The proposed clustering algorithm, which we call “pairwise Feature Relationship preservation-based NMF” (FR-NMF), is evaluated on several real-life and synthetic datasets and compared to eight existing NMF-based clustering models. The results obtained show the effectiveness of the proposed algorithm.

Original languageEnglish
Article number107814
JournalPattern Recognition
Publication statusPublished - Apr 2021


  • Clustering
  • Low-rank matrix factorization
  • NMF
  • Orthogonal NMF
  • Unsupervised learning

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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