Ultrametric
adj, noun ·Rare ·Advanced level
Definitions
- 1 A metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z).
"This relation between hierarchical clusterings and ultrametrics is one-to-one; if, that is, we agree not to distinguish ultrametrics that are (strictly) monotonically related to each other. That is, there is one and only one ultrametric for each hierarchical tree structure. Thus there is an isomorphism between ultrametrics and hierarchical tree structures. In this sense the two can be identified."
- 1 Describing a metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z). not-comparable
- 2 Describing a phylogeny in which every tip is the same distance from the root. not-comparable
Example
More examples"This relation between hierarchical clusterings and ultrametrics is one-to-one; if, that is, we agree not to distinguish ultrametrics that are (strictly) monotonically related to each other. That is, there is one and only one ultrametric for each hierarchical tree structure. Thus there is an isomorphism between ultrametrics and hierarchical tree structures. In this sense the two can be identified."
Etymology
From ultra- + metric.
Related phrases
More for "ultrametric"
Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.