mlsanityData to 14 Oct 2026

k-Means Clustering Is Matrix Factorization

arXiv 1512.07548 ↗First posted 23 Dec 2015stat.MLcited by 11

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Abstract (arXiv)

We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Dec 2015.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 2; 2024: 2; 2025: 3; 2026: 1.

11 papers.

  1. 2023GCFAgg: Global and Cross-view Feature Aggregation for Multi-view Clusteringcited by 30
  2. 2025Forget the Data and Fine-Tuning! Just Fold the Network to Compresscited by 7
  3. 2026Cut Less, Fold More: Model Compression through the Lens of Projection Geometrycited by 4
  4. 2024Trusted Mamba Contrastive Network for Multi-View Clusteringcited by 3
  5. 2023A Restarted Large-Scale Spectral Clustering with Self-Guiding and Block Diagonal Representationcited by 2
  6. 2021Improving Spectral Clustering Using Spectrum-Preserving Node Aggregationcited by 1
  7. 2024Deep Contrastive Multi-view Clustering under Semantic Feature Guidancecited by 1
  8. 2025Vocabulary-free few-shot learning for Vision-Language Modelscited by 1
  9. 2022Binary Orthogonal Non-negative Matrix Factorizationcited by 0
  10. 2022On the Global Solution of Soft k-Meanscited by 0
  11. 2025A Unified Matrix Factorization Framework for Classical and Robust Clusteringcited by 0