Word.ws English Dictionary

ultrametric

ultrametric adjective: describing a metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z).

Adjective

ultrametric (not comparable)

  1. Describing a metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z).
  2. Describing a phylogeny in which every tip is the same distance from the root.

Noun

ultrametric (plural ultrametrics)

  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...1973, Paul E. Green, Yoram Wind, Multiattribute Decisions in Marketing: A Measurement Approach, Dryden Press, →ISBN, page 366
    • Obviously, an absolute guarantee of optimality is not possible through this type of heuristic search, but the eventual stability achieved leads to an ultrametric that is usually very good (although not verifiably optimal). Throughout this discussion it is assumed that the subsets of objects for...1997, Lawrence Hubert, Phipps Arabie, Jacqueline Meulman, “Hierarchical clustering and the construction of (optimal) ultrametrics using Lₚ-norms”, in Yadolah Dodge, editor, L₁-Statistical Procedures...

Examples of ultrametric in a sentence

  • 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.1973, Paul E. Green, Yoram Wind, Multiattribute Decisions in Marketing: A Measurement Approach, Dryden Press, →ISBN, page 366:
  • The ultrametric defined by Theorem 10 is known as the maximal subdominant ultrametric for the dissimilarity d.2008, Dan A. Simovici, “Data Mining Algorithms I: Clustering”, in Amiya Nayak, Ivan Stojmenović, editors, Handbook of Applied Algorithms...

Forms of ultrametric

pluralultrametrics

Origin of ultrametric

From ultra- + metric.

Words formed from ultrametric

Phrases with ultrametric

Questions about ultrametric

What does ultrametric mean?
Ultrametric means describing a metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z).
How do you use ultrametric in a sentence?
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.
What part of speech is ultrametric?
Ultrametric can be an adjective or a noun.

Words near ultrametric in the dictionary

  1. ultrameric
  2. ultramers
  3. ultrametamorphic
  4. ultrametamorphism
  5. ultrametamorphosis
  6. ultrametric
  7. ultrametricised
  8. ultrametricity
  9. ultrametricization
  10. ultrametricize
  11. ultrametricized

Source and license

Adapted from Wiktionary: ultrametric (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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