The DOI matches its Crossref record.
On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering
Abstract
Current nonnegative matrix factorization (NMF) deals with X = FGT type. We provide a systematic analysis and extensions of NMF to the symmetric W = HHT, and the weighted W = HSHT. We show that (1) W = HHT is equivalent to Kernel if-means clustering and the Laplacian-based spectral clustering. (2) X = FGT is equivalent to simultaneous clustering of rows and columns of a bipartite graph. Algorithms are given for computing these symmetric NMFs.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Convex and Semi-Nonnegative Matrix Factorizations
Ding, C. H. Q., Li, T., & Jordan, M. I. (2010) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.277 · Cited by 1,317
Self-citationThe Constrained Laplacian Rank Algorithm for Graph-Based Clustering
Nie, F., Wang, X., Jordan, M., & Huang, H. (2016) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v30i1.10302 · Cited by 837
Imaging-based parcellations of the human brain
Eickhoff, S. B., Yeo, B. T. T., & Genon, S. (2018) · Nature reviews. Neuroscience · doi:10.1038/s41583-018-0071-7 · Cited by 484
Frequency-specific directed interactions in the human brain network for language
Schoffelen, J.-M., Hultén, A., Lam, N., Marquand, A. F., Uddén, J., & Hagoort, P. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1703155114 · Cited by 128
Neural correlates of sparse coding and dimensionality reduction
Beyeler, M., Rounds, E. L., Carlson, K. D., Dutt, N., & Krichmar, J. L. (2019) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1006908 · Cited by 104
Metadata
- Authors
- Ding, C., He, X., & Simon, H. D.
- Venue
- Proceedings of the 2005 SIAM International Conference on Data Mining
- Published
- 2005-01-09
- Pages
- 606-610
- OpenAlex
- W2571268788
- Cited by
- 985
- References
- 0
- FWCI
- 17.71
- Type
- conference paper
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering. https://app.cochat.ai/papers/10.1137/1.9781611972757.70
- The paper
- Ding, C., He, X., & Simon, H. D. (2005). On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering. Proceedings of the 2005 SIAM International Conference on Data Mining. https://doi.org/10.1137/1.9781611972757.70
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
