lapos {LLN}R Documentation

Use a binary sociomatrix to learn a latent space representation

Description

Learn a latent space from a binary sociomatrix associated to the studied network. The latent social network (hereafter LSN) model, introduced by Hoff, Raftery and Handcock (2002), relates the presence of a tie between nodes $i$ and $j$ to the distance between them in latent space, [ logit(P(Y_{ij}=1|theta))=α - | Z_{i}-Z_{j}|,] where $logit(P)=log(P/(1-P))$, $theta={α,Z}$ represents all model parameters, $Z={Z_{i}}_{i=1}^n$ are the $p$-dimensional latent coordinates associated to each node, where $p$ is unknown, and $α$ determines the prior probability of an existing link between two nodes. Nodes $i$ and $j$ have a high probability to be connected if $α$ is large or if they are close in the latent space, i.e., $| Z_{i}-Z_{j}|$ is close to $0$. The parameters are estimated using the maximum likelihood method via the simulated annealing optimizer in optim.

Usage

latpos(Y, p=2, alpha=0, method="SANN")

Arguments

Y The sociomatrix
p The latent space dimension
alpha An initial value for the intercept parameter in the logistic regression (optional, 0 by default)
method The optimization method used by optim to solve the ML estimation problem (optional)

Value

prms An LLN object
prms$alpha The value of the intercept parameter used for learning the latent position of new nodes
prms$Z The latent positions of the learning nodes
prms$Y A copy of the sociomatrix associated with the network
prms$flag A vector of length equal to the number of node, specifying whether each node was used to learn the network, or was a test node subsequently added to the network using "latproj" (1=learning node and 2=test node)
prms$bic The BIC value associated with the learned latent configuration
prms$optim The information returned by the optimization algorithm

Author(s)

Charles Bouveyron and Hugh Chipman <firstname.lastname@acadiau.ca>

References

Charles Bouveyron and Hugh Chipman, A supervised latent classifier for graph-structured data with application to social network analysis, Technical Report, Acadia University, 2007.

Peter D. Hoff, Adrian E. Raftery and Mark S. Handcock. Latent space approaches to social network analysis. Journal of the American Statistical Association, 97, 460, pp. 1090-1098, 2002.

See Also

latproj

Examples

# Type demo(LLN) for a complete demonstration
data(Monks)
pos <- latpos(Monks$Y,p=2)
plot(pos,cls=Monks$cls)

[Package LLN version 1.1 Index]