Hierarchical Clustering of Asymmetric Networks
This work addresses clustering in asymmetric networks, offering theoretical insights but is incremental as it builds on existing hierarchical clustering frameworks.
The paper tackles the problem of hierarchical clustering for networks with directed dissimilarities by introducing admissible methods based on axioms of value and transformation, showing that reciprocal and nonreciprocal clustering provide bounds, and identifying a unique method when the axiom is modified to use minimum dissimilarities.
This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter. Our construction of hierarchical clustering methods is built around the concept of admissible methods, which are those that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less. Two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Furthermore, alternative clustering methodologies and axioms are considered. In particular, modifying the axiom of value such that clustering in two-node networks occurs at the minimum of the two dissimilarities entails the existence of a unique admissible clustering method.