Chebyshev distance (L-infinity metric)
E656653
Chebyshev distance (L-infinity metric) is a distance measure on a grid or in n-dimensional space defined as the maximum absolute difference along any coordinate axis between two points.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Chebyshev distance | 1 |
| Chebyshev distance (L-infinity metric) canonical | 1 |
| For x,y in R^n, d(x,y) = max_i |x_i - y_i| | 1 |
| Moore neighborhood (for same radius in 2D) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7337952 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chebyshev distance (L-infinity metric) Context triple: [Moore neighborhood, distanceMetric, Chebyshev distance (L-infinity metric)]
-
A.
Kolmogorov distance
Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
-
B.
Euclidean metric
The Euclidean metric is the standard distance function on Euclidean space, defined by the square root of the sum of squared coordinate differences between two points.
-
C.
Levenstein
Levenstein is a surname, often a variant of Löwenstein, borne by individuals of German or Ashkenazi Jewish origin.
-
D.
Bhattacharyya distance
Bhattacharyya distance is a statistical measure of similarity between two probability distributions, often used in pattern recognition and classification to quantify their overlap.
-
E.
Hausdorff metric
The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chebyshev distance (L-infinity metric) Target entity description: Chebyshev distance (L-infinity metric) is a distance measure on a grid or in n-dimensional space defined as the maximum absolute difference along any coordinate axis between two points.
-
A.
Kolmogorov distance
Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
-
B.
Euclidean metric
The Euclidean metric is the standard distance function on Euclidean space, defined by the square root of the sum of squared coordinate differences between two points.
-
C.
Levenstein
Levenstein is a surname, often a variant of Löwenstein, borne by individuals of German or Ashkenazi Jewish origin.
-
D.
Bhattacharyya distance
Bhattacharyya distance is a statistical measure of similarity between two probability distributions, often used in pattern recognition and classification to quantify their overlap.
-
E.
Hausdorff metric
The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
L-infinity metric
ⓘ
Minkowski distance ⓘ distance metric ⓘ mathematical concept ⓘ |
| alsoKnownAs |
L-infinity distance
ⓘ
L∞ metric ⓘ chessboard distance ⓘ maximum metric ⓘ |
| applicationDomain |
approximation theory
ⓘ
chess ⓘ clustering ⓘ computational geometry ⓘ grid-based pathfinding ⓘ image processing ⓘ operations research ⓘ pattern recognition ⓘ robot motion planning ⓘ |
| ballVolumeGrowth | proportional to radius^n in R^n ⓘ |
| coordinateDependence | depends on chosen coordinate axes ⓘ |
| definedOn |
grids
ⓘ
lattices ⓘ n-dimensional real vector space ⓘ |
| definition |
For x,y in R^n, d(x,y) = max_i |x_i - y_i|
ⓘ
linked to:
Chebyshev distance (L-infinity metric)
|
| field |
discrete geometry
ⓘ
functional analysis ⓘ metric geometry ⓘ |
| greaterOrEqualThan |
Euclidean distance on R^n
ⓘ
Manhattan distance on R^n is not always comparable ⓘ |
| inducedByNorm | L-infinity norm ⓘ |
| isLimitOf | Minkowski p-metrics as p -> infinity ⓘ |
| isMetric | true ⓘ |
| metricInequality |
d_1(x,y)/n <= d_infinity(x,y)
ⓘ
d_infinity(x,y) >= d_2(x,y)/sqrt(n) ⓘ |
| metricSpaceType | norm-induced metric ⓘ |
| MinkowskiParameter | p = infinity ⓘ |
| namedAfter | Pafnuty Chebyshev ⓘ |
| relationToChess | minimum number of king moves between squares ⓘ |
| satisfiesProperty |
identity of indiscernibles
ⓘ
non-negativity ⓘ symmetry ⓘ triangle inequality ⓘ |
| symmetryGroup | hypercube symmetry group ⓘ |
| topologyInduced |
same as L1 metric on R^n
ⓘ
same as L2 metric on R^n ⓘ |
| unitBallShape | hypercube ⓘ |
| unitBallShapeIn2D | square aligned with coordinate axes ⓘ |
| unitBallShapeIn3D | cube aligned with coordinate axes ⓘ |
| usedFor |
defining neighborhoods in grid-based images
ⓘ
estimating worst-case coordinate deviation ⓘ measuring distance on square grids ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Chebyshev distance (L-infinity metric) Description of subject: Chebyshev distance (L-infinity metric) is a distance measure on a grid or in n-dimensional space defined as the maximum absolute difference along any coordinate axis between two points.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Chebyshev distance (L-infinity metric)
linked to: Chebyshev distance (L-infinity metric)
subject linked to:
Chebyshev distance (L-infinity metric)
linked to: Chebyshev distance (L-infinity metric)