Order preserving hierarchical agglomerative clustering

Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains applications used to represent ordered relations between entities the domains. Examples task dependencies a project plan, transaction order distributed ledgers execution sequences of tasks computer programs, just mention few. We study problem preserving hierarchical clustering this kind data. That is, if we have $a < b$ original denote their respective clusters by $[a]$ $[b]$, then shall $[a] [b]$ produced clustering. The is similarity based uses standard linkage functions, such as single- complete linkage, an extension classical To achieve this, define output from running on strictly be partial dendrograms; sub-trees dendrograms with several connected components. construct embedding over set into family ultrametrics same set. An optimal defined dendrogram corresponding ultrametric closest dissimilarity measure, measured p-norm. Thus, method combination fitting. A reference implementation employed for experiments both synthetic random real world database machine parts. When compared existing methods, show our excels cluster quality preservation.