Extending the Rasch model to a multiclass parametric network model
Barnabas Szasz, Rita Fleiner and Andras Micsik
Abstract
The newly introduced $\alpha$-$\beta$-models~\cite{Chatterjee} and the
classical Rash model~\cite{Rasch} are united in a semiparametric
multiclass graph model. We give a classification of the nodes of an
observed network so that the generated subgraphs and bipartite graphs
of it obey these models, where their strongly connected parameters
give multiscale evaluation of the nodes. This is a heterogeneous
version of the stochastic block model, built via mixtures of loglinear
models, the parameters of which are estimated by collaborative
filtering~\cite{Ungar}. In the context of social networks, the
clusters can be identified with social groups and the parameters with
attitudes of people of one group towards people of the other, which
attitudes depend on the cluster memberships. The algorithm is applied
to randomly generated and real-word data.