Versatile linkage: a family of space-conserving strategies for agglomerative hierarchical clustering
This work addresses the problem of developing more flexible and space-efficient clustering strategies for data analysis, though it appears incremental as it builds upon existing linkage methods.
The authors introduced versatile linkage, a new infinite family of agglomerative hierarchical clustering strategies based on generalized means, which includes existing methods like single and complete linkage and novel ones like geometric and harmonic linkage. They showed that this family is space-conserving, unlike the β-flexible system, and evaluated it using metrics such as cophenetic correlation and new measures like tree balance and space distortion.
Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite system of agglomerative hierarchical clustering strategies based on generalized means, which go from single linkage to complete linkage, passing through arithmetic average linkage and other clustering methods yet unexplored such as geometric linkage and harmonic linkage. We compare the different clustering strategies in terms of cophenetic correlation, mean absolute error, and also tree balance and space distortion, two new measures proposed to describe hierarchical trees. Unlike the $β$-flexible clustering system, we show that the versatile linkage family is space-conserving.