Ultrametric

Quick meaning: Ultrametric is an adjective meaning (mathematics) Describing a metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z).

Meaning

(mathematics) Describing a metric whose triangle inequality has the stronger form d(x,z)< max d(x,y),d(y,z).

More Meanings

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

Example Sentences

The ultrametric defined by Theorem 10 is known as the maximal subdominant ultrametric for the dissimilarity d. The situation is not symmetric with respect to the infimum of a set of ultrametrics because, in general, the infimum of a set of ultrametrics is not necessarily an ultrametric.

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.

Word Forms

• ultrametrics

Related Words

Related dictionary entries include ultrameric, ultrametricized, ultrametricised, ultradifferential, ultrahyperbolic, trimaximal.

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