Abstract
In the present paper, we address the problem of extrapolating group proximities from member relations, which we refer to as the group proximity problem. We assume that a relational dataset consists of several groups and that pairwise relations of all members can be measured. Under these assumptions, the goal is to estimate group proximities from pairwise relations. In order to solve the group proximity problem, we present a method based on embedding and distribution mapping, in which all relational data, which consist of pairwise dissimilarities or dissimilarities between members, are transformed into vectorial data by embedding methods. After this process, the distributions of the groups are obtained. Group proximities are estimated as distances between distributions by distribution mapping methods, which generate a map of distributions. As an example, we apply the proposed method to document and bacterial flora datasets. Finally, we confirm the feasibility of using the proposed method to solve the group proximity problem.
