Hierarchical, Granular Representation of Non-metric Proximity Data

Building granules in asymmetric relational data is still a challenging problem. In this paper, we present an approach that transcribes asymmetric property in a proximity matrix into a set of binary classifications constituted with respect to the directional proximity from each object. Indiscernibility of objects are then assessed based on the Jaccard coefficient that quantifies class commonality of object pairs in the binary classifications. Objects with high indiscernibility are more likely to be merged into single granule by coarsening the weak discrimination knowledge supported by the small number of binary classifications. According to this, we build a dendrogram based on indiscernibility and represent the hierarchy of granules. In experiments we evaluate the characteristics of our method by applying it to the brand switching data.