Issue No. 01 - Jan. (2014 vol. 36)
ISSN: 0162-8828
pp: 48-57
Daniel L. Sussman , Johns Hopkins Univ., Baltimore, MD, USA
Minh Tang , Johns Hopkins Univ., Baltimore, MD, USA
Carey E. Priebe , Johns Hopkins Univ., Baltimore, MD, USA
ABSTRACT
In this work, we show that using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the remaining vertices can be classified with error converging to Bayes optimal using the $(k)$-nearest-neighbors classification rule. We evaluate the proposed methods on simulated data and a graph derived from .
INDEX TERMS
Vectors, Stochastic processes, Estimation, Internet, Random variables, Pattern recognition, Encyclopedias,universal consistency, Random graph, $(k)$-nearest-neighbor, latent space model
CITATION
Daniel L. Sussman, Minh Tang, Carey E. Priebe, "Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 36, no. , pp. 48-57, Jan. 2014, doi:10.1109/TPAMI.2013.135
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