IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v132y2019icp46-69.html
   My bibliography  Save this article

Spectral clustering via sparse graph structure learning with application to proteomic signaling networks in cancer

Author

Listed:
  • Banerjee, Sayantan
  • Akbani, Rehan
  • Baladandayuthapani, Veerabhadran

Abstract

Clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables are presented. As opposed to standard approaches for graph clustering that assume known graph structures, the edge structure of the unknown graph is first estimated using sparse regression based approaches for sparse graph structure learning. Subsequently, graph clustering on the lower dimensional projections of the graph is performed based on Laplacian embeddings using a penalized k-means approach, motivated by Dirichlet process mixture models in Bayesian nonparametrics. In contrast to standard algorithmic approaches for known graphs, the proposed method allows estimation and inference for both graph structure learning and clustering. More importantly, the arguments for Laplacian embeddings as suitable projections for graph clustering are formalized by providing theoretical support for the consistency of the eigenspace of the estimated graph Laplacians. Fast computational algorithms are proposed to scale the method to large number of nodes. Extensive simulations are presented to compare the clustering performance with standard methods. The methods are applied to a novel pan-cancer proteomic data set, and protein networks and clusters are evaluated across multiple different cancer types.

Suggested Citation

  • Banerjee, Sayantan & Akbani, Rehan & Baladandayuthapani, Veerabhadran, 2019. "Spectral clustering via sparse graph structure learning with application to proteomic signaling networks in cancer," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 46-69.
  • Handle: RePEc:eee:csdana:v:132:y:2019:i:c:p:46-69
    DOI: 10.1016/j.csda.2018.08.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301920
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2018.08.009?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. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Betzel, Richard F. & Griffa, Alessandra & Avena-Koenigsberger, Andrea & Goñi, Joaquín & Thiran, Jean-Philippe & Hagmann, Patric & Sporns, Olaf, 2013. "Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity," Network Science, Cambridge University Press, vol. 1(3), pages 353-373, December.
    3. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2011. "Joint estimation of multiple graphical models," Biometrika, Biometrika Trust, vol. 98(1), pages 1-15.
    4. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    5. Y. Yu & T. Wang & R. J. Samworth, 2015. "A useful variant of the Davis–Kahan theorem for statisticians," Biometrika, Biometrika Trust, vol. 102(2), pages 315-323.
    6. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    7. Michael T Schaub & Jean-Charles Delvenne & Sophia N Yaliraki & Mauricio Barahona, 2012. "Markov Dynamics as a Zooming Lens for Multiscale Community Detection: Non Clique-Like Communities and the Field-of-View Limit," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-11, February.
    8. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    9. Michele Guindani & Wesley O. Johnson, 2018. "More nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 239-251, June.
    10. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    11. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
    12. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
    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. Sayantan Banerjee & Kousik Guhathakurta, 2019. "Change-point Analysis in Financial Networks," Papers 1911.05952, arXiv.org.

    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. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    2. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    3. Kang, Xiaoning & Wang, Mingqiu, 2021. "Ensemble sparse estimation of covariance structure for exploring genetic disease data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. Avagyan, Vahe & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Zamar, Rubén, 2015. "Ranking Edges and Model Selection in High-Dimensional Graphs," DES - Working Papers. Statistics and Econometrics. WS ws1511, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    7. Guanghui Cheng & Zhengjun Zhang & Baoxue Zhang, 2017. "Test for bandedness of high-dimensional precision matrices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 884-902, October.
    8. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    9. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.
    10. Tan, Kean Ming & Witten, Daniela & Shojaie, Ali, 2015. "The cluster graphical lasso for improved estimation of Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 23-36.
    11. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Ziqi Chen & Chenlei Leng, 2016. "Dynamic Covariance Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1196-1207, July.
    13. Avagyan, Vahe & Nogales, Francisco J., 2014. "Improving the graphical lasso estimation for the precision matrix through roots ot the sample convariance matrix," DES - Working Papers. Statistics and Econometrics. WS ws141208, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Xingqi Du & Subhashis Ghosal, 2018. "Bayesian Discriminant Analysis Using a High Dimensional Predictor," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 112-145, December.
    15. Choi, Young-Geun & Lim, Johan & Roy, Anindya & Park, Junyong, 2019. "Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 234-249.
    16. Lafit, Ginette & Nogales Martín, Francisco Javier, 2017. "Robust and sparse estimation of high-dimensional precision matrices via bivariate outlier detection," DES - Working Papers. Statistics and Econometrics. WS 24534, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    18. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    19. Benjamin Poignard & Manabu Asai, 2023. "Estimation of high-dimensional vector autoregression via sparse precision matrix," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 307-326.
    20. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.

    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:eee:csdana:v:132:y:2019:i:c:p:46-69. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.