Issue No. 01 - Jan. (2014 vol. 36)
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
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 .
Vectors, Stochastic processes, Estimation, Internet, Random variables, Pattern recognition, Encyclopedias,universal consistency, Random graph, $(k)$-nearest-neighbor, latent space model
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