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.

In this paper we propose a novel classification method for the multiple k-nearest neighbor (MkNN) classifier and show its practical application to medical image processing. The proposed method performs fine classification when a pair of the spatial coordinate of the observation data in the observation space and its corresponding feature vector in the feature space is provided. The proposed MkNN classifier uses the continuity of the distribution of features of the same class not only in the feature space but also in the observation space. In order to validate the performance of the present method, it is applied to the tissue characterization problem of coronary plaque. The quantitative and qualitative validity of the proposed MkNN classifier have been confirmed by actual experiments.