IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v107y2012i499p1119-1128.html
   My bibliography  Save this article

A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs

Author

Listed:
  • Daniel L. Sussman
  • Minh Tang
  • Donniell E. Fishkind
  • Carey E. Priebe

Abstract

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedding associates each node with a vector; these vectors are clustered via minimization of a square error criterion. We prove that this method is consistent for assigning nodes to blocks, as only a negligible number of nodes will be misassigned. We prove consistency of the method for directed and undirected graphs. The consistent block assignment makes possible consistent parameter estimation for a stochastic blockmodel. We extend the result in the setting where the number of blocks grows slowly with the number of nodes. Our method is also computationally feasible even for very large graphs. We compare our method with Laplacian spectral clustering through analysis of simulated data and a graph derived from Wikipedia documents.

Suggested Citation

  • Daniel L. Sussman & Minh Tang & Donniell E. Fishkind & Carey E. Priebe, 2012. "A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1119-1128, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1119-1128
    DOI: 10.1080/01621459.2012.699795
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2012.699795
    Download Restriction: Access to full text is restricted to subscribers.

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

    Citations

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


    Cited by:

    1. A. Athreya & C. E. Priebe & M. Tang & V. Lyzinski & D. J. Marchette & D. L. Sussman, 2016. "A Limit Theorem for Scaled Eigenvectors of Random Dot Product Graphs," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 1-18, February.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:107:y:2012:i:499:p:1119-1128. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.