CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2014 vol.36 Issue No.01 - Jan.

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Issue No.01 - Jan. (2014 vol.36)

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. 1, pp. 48-57, Jan. 2014, doi:10.1109/TPAMI.2013.135REFERENCES