This function accounts for the fact that configurations in the latent space are invariant to rotations, reflections and translations.
invariant(z, zMAP)An n x d matrix of latent locations in the d dimensional space for each of n nodes.
The maximum a posteriori configuration of latent locations used as the template to which all sampled configurations are mapped.
The transformed version of the input configuration z that best matches zMAP.
Procrustean rotations, reflections and translations (note: NOT dilations) are employed to best match z to zMAP.
Isobel Claire Gormley and Thomas Brendan Murphy. (2010) A Mixture of Experts Latent Position Cluster Model for Social Network Data. Statistical Methodology, 7 (3), pp.385-405.