Hierarchical Quasi-Clustering Methods for Asymmetric Networks
This provides a theoretical framework for clustering asymmetric data, which is incremental as it generalizes hierarchical clustering to asymmetric networks.
The paper tackles the problem of clustering asymmetric networks by introducing hierarchical quasi-clustering methods, which preserve asymmetry and are shown to be equivalent to finite quasi-ultrametric spaces, with a modified single linkage method proven as the only admissible approach and applied to U.S. internal migration data.
This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.