- from
seminorms on
vector spaces, and so it is
natural to call them "
semimetrics". This
conflicts with the use of the term in topology. Some
authors define...
-
distances between pairs of points. More abstractly, it is the
study of
semimetric spaces and the
isometric transformations between them. In this view, it...
-
seminormed space is a
pseudometric space.
Because of this analogy, the term
semimetric space (which has a
different meaning in topology) is
sometimes used as...
-
coefficient does not
satisfy the
triangle inequality, it can be
considered a
semimetric version of the
Jaccard index. The
function ranges between zero and one...
- of indiscernibles;
quasimetrics violate property (3), symmetry; and
semimetrics violate property (4), the
triangle inequality.
Statistical distances...
- and only if
every (k+3)×(k+3) prin****l
submatrix is. In
other words, a
semimetric on
finitely many
points is
embedabble isometrically in ℝk if and only...
- is
similarity search which takes place within metric spaces.
While the
semimetric properties are more or less
necessary for any kind of
search to be meaningful...
- Q)=0} for some P ≠ Q; this is
variously termed a "pseudometric" or a "
semimetric"
depending on the community. For instance,
using the
class F = { x ↦ 0...
-
Jesus M. F.; Montalvo,
Francisco (January 1990), "A
Counterexample in
Semimetric Spaces" (PDF),
Extracta Mathematicae, 5 (1): 38–40
Schaefer &
Wolff 1999...
- determinant,
which became known as Menger's Theorem. The
theorem states: A
semimetric ρ : A × A → R ≥ 0 {\displaystyle \rho :A\times A\rightarrow \mathbb {R}...
