A0395
Title: Clustering in multiway networks
Authors: Vladimir Batagelj - IMFM (Slovenia) [presenting]
Abstract: A weighted multiway network ${\bf N} = ({\bf V},{\bf L},w)$ is based on nodes from $k$ finite sets (ways or dimensions) ${\bf V} = ({\bf V}_1, {\bf V}_2, \ldots, {\bf V}_k) $, the set of links ${\bf L}$, and the weight $w : {\bf L} \to R$. The incidence function $I : {\bf L} \to {\bf V}_1\times {\bf V}_2\times \cdots\times {\bf V}_k$ assigns to each link $e \in {\bf L}$ a $k$-tuple of its nodes $I(e) = (e(1), e(2), \ldots, e(i), \ldots, e(k))$, $e(i) \in {\bf V}_i$. If for $i\ne j$, ${\bf V}_i = {\bf V}_j$, we say that ${\bf V}_i$ and ${\bf V}_j$ are of the same mode. In a general multiway network, different additional data can be known for nodes and/or links ${\bf N} = ({\bf V},{\bf L},{\bf P},{\bf W})$, where ${\bf P}$ is a set of node properties $p : {\bf V}_i \to S_p$, and ${\bf W}$ is a set of link weights $w : {\bf L} \to S_w$. An approach to clustering in multiway networks is discussed. Extending the projection approach from two-mode networks, some options are first explored to define the projection in a selected way. The obtained projection matrices can be transformed in the generalized Salton and Jaccard similarity measures that can be used for clustering ways using standard clustering procedures. The proposed approach is illustrated by analyzing selected data from ESS - European Social Survey 2023. The approach is supported by the R package MWnets.
