Nonnegative matrix factorization with integrated graph and feature learning

Chong Peng, Zhao Kang, Yunhong Hu, Jie Cheng, Qiang Cheng

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Matrix factorization is a useful technique for data representation in many data mining andmachine learning tasks. Particularly, for data sets with all nonnegative entries, matrix factorization often requires that factor matrices be nonnegative, leading to nonnegative matrix factorization (NMF). One important application of NMF is for clustering with reduced dimensions of the data represented in the new feature space. In this paper, we propose a new graph regularized NMF method capable of feature learning and apply it to clustering. Unlike existing NMF methods that treat all features in the original feature space equally, our method distinguishes features by incorporating a feature-wise sparse approximation error matrix in the formulation. It enables important features to be more closely approximated by the factor matrices. Meanwhile, the graph of the data is constructed using cleaner features in the feature learning process, which integrates feature learning andmanifold learning procedures into a unifiedNMFmodel. This distinctly differs from applying the existing graph-based NMF models after feature selection in that, when these two procedures are independently used, they often fail to align themselves toward obtaining a compact and most expressive data representation. Comprehensive experimental results demonstrate the effectiveness of the proposed method, which outperforms state-of-the-art algorithms when applied to clustering.

Original languageEnglish
Article number42
JournalACM Transactions on Intelligent Systems and Technology
Issue number3
StatePublished - Jan 2017

Bibliographical note

Publisher Copyright:
© 2017 ACM.


  • Clustering
  • Feature learning
  • Manifold learning
  • Non-negative matrix factorization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Artificial Intelligence


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