Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Metric
mathematical distance |
| gptkbp:alsoKnownAs |
Wasserstein distance
|
| gptkbp:closelyRelatedTo |
gptkb:Kantorovich–Rubinstein_metric
gptkb:Monge_problem gptkb:Hungarian_algorithm gptkb:Wasserstein_metric transportation theory |
| gptkbp:complexity |
polynomial time
O(n^3) for general case |
| gptkbp:definedIn |
continuous distributions
discrete distributions |
| gptkbp:firstDescribed |
1940s
|
| gptkbp:form |
gptkb:topology
non-negative symmetric satisfies triangle inequality zero iff distributions are identical |
| gptkbp:formedBy |
gptkb:Leonid_Kantorovich
|
| gptkbp:generalizes |
gptkb:Monge–Kantorovich_problem
|
| gptkbp:hasApplication |
natural language processing
pattern recognition document retrieval shape matching |
| gptkbp:hasApproximation |
Sinkhorn distance
entropic regularization |
| gptkbp:hasUnit |
cost per unit mass
|
| https://www.w3.org/2000/01/rdf-schema#label |
Earth mover's distance
|
| gptkbp:measures |
distance between probability distributions
distance between histograms |
| gptkbp:namedAfter |
the transportation problem
|
| gptkbp:parameter |
transport plan
cost matrix flow matrix ground distance supply and demand vectors |
| gptkbp:relatedTo |
optimal transport
|
| gptkbp:requires |
solving a linear programming problem
|
| gptkbp:usedFor |
Wasserstein GANs
comparing distributions with different supports domain adaptation in machine learning generative adversarial networks (GANs) measuring similarity between images measuring similarity between shapes measuring similarity between texts |
| gptkbp:usedIn |
gptkb:machine_learning
gptkb:probability_theory computer vision image retrieval |
| gptkbp:bfsParent |
gptkb:Kantorovich–Rubinstein_metric
|
| gptkbp:bfsLayer |
6
|