Hierarchical clustering of asymmetric proximity data based on the indiscernibility-level

In this paper, we present a method for clustering asymmetric proximity data. First, we calculate the indiscernibility level for each object pair, that quantifies the level of global agreement for regarding the two objects as indiscernible. Then, hierarchical linkage grouping is applied to unite objects according to the derived indiscernibility level. This scheme enables users to examine the hierarchy of data granularity and obtain the set of indiscernible objects that meets the given level of granularity. Additionally, since indiscernibility level is derived based on the binary classifications determined independently for each object, it can be applied to non-Euclidean, asymmetric relational data. Using a synthetic numerical data and a real-world data about inter-prefectural movement of university students, we demonstrate that the method could represent hierarchy of data granularity and could obtain interesting groups of objects from asymmetric proximity data.