IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v62y2015i3p545-574.html
   My bibliography  Save this article

SymNMF: nonnegative low-rank approximation of a similarity matrix for graph clustering

Author

Listed:
  • Da Kuang
  • Sangwoon Yun
  • Haesun Park

Abstract

Nonnegative matrix factorization (NMF) provides a lower rank approximation of a matrix by a product of two nonnegative factors. NMF has been shown to produce clustering results that are often superior to those by other methods such as K-means. In this paper, we provide further interpretation of NMF as a clustering method and study an extended formulation for graph clustering called Symmetric NMF (SymNMF). In contrast to NMF that takes a data matrix as an input, SymNMF takes a nonnegative similarity matrix as an input, and a symmetric nonnegative lower rank approximation is computed. We show that SymNMF is related to spectral clustering, justify SymNMF as a general graph clustering method, and discuss the strengths and shortcomings of SymNMF and spectral clustering. We propose two optimization algorithms for SymNMF and discuss their convergence properties and computational efficiencies. Our experiments on document clustering, image clustering, and image segmentation support SymNMF as a graph clustering method that captures latent linear and nonlinear relationships in the data. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Da Kuang & Sangwoon Yun & Haesun Park, 2015. "SymNMF: nonnegative low-rank approximation of a similarity matrix for graph clustering," Journal of Global Optimization, Springer, vol. 62(3), pages 545-574, July.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:3:p:545-574
    DOI: 10.1007/s10898-014-0247-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-014-0247-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-014-0247-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Ma, Xiaoke & Gao, Lin & Yong, Xuerong & Fu, Lidong, 2010. "Semi-supervised clustering algorithm for community structure detection in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 187-197.
    3. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    4. Abilio Lucena & Celso Ribeiro & Andréa Santos, 2010. "A hybrid heuristic for the diameter constrained minimum spanning tree problem," Journal of Global Optimization, Springer, vol. 46(3), pages 363-381, March.
    5. Jingu Kim & Yunlong He & Haesun Park, 2014. "Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework," Journal of Global Optimization, Springer, vol. 58(2), pages 285-319, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xin, Xuri & Liu, Kezhong & Loughney, Sean & Wang, Jin & Li, Huanhuan & Ekere, Nduka & Yang, Zaili, 2023. "Multi-scale collision risk estimation for maritime traffic in complex port waters," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    2. Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2016. "Clustering of heterogeneous networks with directional flows based on “Snake” similarities," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 250-269.
    3. Radu-Alexandru Dragomir & Alexandre d’Aspremont & Jérôme Bolte, 2021. "Quartic First-Order Methods for Low-Rank Minimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 341-363, May.
    4. Rundong Du & Barry Drake & Haesun Park, 2019. "Hybrid clustering based on content and connection structure using joint nonnegative matrix factorization," Journal of Global Optimization, Springer, vol. 74(4), pages 861-877, August.
    5. Arnaud Vandaele & François Glineur & Nicolas Gillis, 2018. "Algorithms for positive semidefinite factorization," Computational Optimization and Applications, Springer, vol. 71(1), pages 193-219, September.
    6. Rundong Du & Da Kuang & Barry Drake & Haesun Park, 2017. "DC-NMF: nonnegative matrix factorization based on divide-and-conquer for fast clustering and topic modeling," Journal of Global Optimization, Springer, vol. 68(4), pages 777-798, August.
    7. He, Chaobo & Zhang, Qiong & Tang, Yong & Liu, Shuangyin & Zheng, Jianhua, 2019. "Community detection method based on robust semi-supervised nonnegative matrix factorization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 279-291.
    8. Srinivas Eswar & Ramakrishnan Kannan & Richard Vuduc & Haesun Park, 2021. "ORCA: Outlier detection and Robust Clustering for Attributed graphs," Journal of Global Optimization, Springer, vol. 81(4), pages 967-989, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Takehiro Sano & Tsuyoshi Migita & Norikazu Takahashi, 2022. "A novel update rule of HALS algorithm for nonnegative matrix factorization and Zangwill’s global convergence," Journal of Global Optimization, Springer, vol. 84(3), pages 755-781, November.
    2. Duy Khuong Nguyen & Tu Bao Ho, 2017. "Accelerated parallel and distributed algorithm using limited internal memory for nonnegative matrix factorization," Journal of Global Optimization, Springer, vol. 68(2), pages 307-328, June.
    3. Lu, Hong & Sang, Xiaoshuang & Zhao, Qinghua & Lu, Jianfeng, 2020. "Community detection algorithm based on nonnegative matrix factorization and pairwise constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Flavia Esposito, 2021. "A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments," Mathematics, MDPI, vol. 9(9), pages 1-17, April.
    5. Ning, Yi-Zi & Liu, Xin & Cheng, Hui-Min & Zhang, Zhong-Yuan, 2020. "Effects of social network structures and behavioral responses on the spread of infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    6. Rundong Du & Da Kuang & Barry Drake & Haesun Park, 2017. "DC-NMF: nonnegative matrix factorization based on divide-and-conquer for fast clustering and topic modeling," Journal of Global Optimization, Springer, vol. 68(4), pages 777-798, August.
    7. Ma, Xiaoke & Li, Dongyuan & Tan, Shiyin & Huang, Zhihao, 2019. "Detecting evolving communities in dynamic networks using graph regularized evolutionary nonnegative matrix factorization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 530(C), pages 1-1.
    8. Eustace, Justine & Wang, Xingyuan & Cui, Yaozu, 2015. "Overlapping community detection using neighborhood ratio matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 510-521.
    9. Zhang, Zhong-Yuan & Gai, Yujie & Wang, Yu-Fei & Cheng, Hui-Min & Liu, Xin, 2018. "On equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 687-697.
    10. Chen, Zigang & Li, Lixiang & Peng, Haipeng & Liu, Yuhong & Yang, Yixian, 2018. "Attributed community mining using joint general non-negative matrix factorization with graph Laplacian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 324-335.
    11. Chen, Chunchun & Zhu, Wenjie & Peng, Bo, 2022. "Differentiated graph regularized non-negative matrix factorization for semi-supervised community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    12. Norikazu Takahashi & Jiro Katayama & Masato Seki & Jun’ichi Takeuchi, 2018. "A unified global convergence analysis of multiplicative update rules for nonnegative matrix factorization," Computational Optimization and Applications, Springer, vol. 71(1), pages 221-250, September.
    13. Ma, Xiaoke & Wang, Bingbo & Yu, Liang, 2018. "Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 786-802.
    14. Srinivas Eswar & Ramakrishnan Kannan & Richard Vuduc & Haesun Park, 2021. "ORCA: Outlier detection and Robust Clustering for Attributed graphs," Journal of Global Optimization, Springer, vol. 81(4), pages 967-989, December.
    15. Yan, Chao & Chang, Zhenhai, 2020. "Modularized convex nonnegative matrix factorization for community detection in signed and unsigned networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    16. Wu, Xunlian & Zhang, Han & Quan, Yining & Miao, Qiguang & Sun, Peng Gang, 2023. "Graph embedding based on motif-aware feature propagation for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    17. Rafael Teixeira & Mário Antunes & Diogo Gomes & Rui L. Aguiar, 2024. "Comparison of Semantic Similarity Models on Constrained Scenarios," Information Systems Frontiers, Springer, vol. 26(4), pages 1307-1330, August.
    18. Del Corso, Gianna M. & Romani, Francesco, 2019. "Adaptive nonnegative matrix factorization and measure comparisons for recommender systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 164-179.
    19. P Fogel & C Geissler & P Cotte & G Luta, 2022. "Applying separative non-negative matrix factorization to extra-financial data," Working Papers hal-03689774, HAL.
    20. Xiao-Bai Li & Jialun Qin, 2017. "Anonymizing and Sharing Medical Text Records," Information Systems Research, INFORMS, vol. 28(2), pages 332-352, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:62:y:2015:i:3:p:545-574. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.