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- Lloyds_algorithm abstract "In computer science and electrical engineering, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces, and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition, and then re-partitions the input according to which of these centroids is closest. However, Lloyd's algorithm differs from k-means clustering in that its input is a continuous geometric region rather than a discrete set of points. Thus, when re-partitioning the input, Lloyd's algorithm uses Voronoi diagrams rather than simply determining the nearest center to each of a finite set of points as the k-means algorithm does.Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd's algorithm can be used to construct close approximations to centroidal Voronoi tessellations of the input, which can be used for quantization, dithering, and stippling. Other applications of Lloyd's algorithm include smoothing of triangle meshes in the finite element method.".
- Lloyds_algorithm thumbnail LloydsMethod1.svg?width=300.
- Lloyds_algorithm wikiPageID "20976757".
- Lloyds_algorithm wikiPageID "2607912".
- Lloyds_algorithm wikiPageLength "12234".
- Lloyds_algorithm wikiPageLength "55".
- Lloyds_algorithm wikiPageOutDegree "1".
- Lloyds_algorithm wikiPageOutDegree "33".
- Lloyds_algorithm wikiPageRedirects Lloyds_algorithm.
- Lloyds_algorithm wikiPageRevisionID "344653523".
- Lloyds_algorithm wikiPageRevisionID "686873503".
- Lloyds_algorithm wikiPageWikiLink Category:Geometric_algorithms.
- Lloyds_algorithm wikiPageWikiLink Category:Mathematical_optimization.
- Lloyds_algorithm wikiPageWikiLink Centroid.
- Lloyds_algorithm wikiPageWikiLink Centroidal_Voronoi_tessellation.
- Lloyds_algorithm wikiPageWikiLink Colors_of_noise.
- Lloyds_algorithm wikiPageWikiLink Computer_science.
- Lloyds_algorithm wikiPageWikiLink Data_compression.
- Lloyds_algorithm wikiPageWikiLink Dither.
- Lloyds_algorithm wikiPageWikiLink Electrical_engineering.
- Lloyds_algorithm wikiPageWikiLink Euclidean_space.
- Lloyds_algorithm wikiPageWikiLink Farthest-first_traversal.
- Lloyds_algorithm wikiPageWikiLink Finite_element_method.
- Lloyds_algorithm wikiPageWikiLink Information_theory.
- Lloyds_algorithm wikiPageWikiLink K-means_clustering.
- Lloyds_algorithm wikiPageWikiLink Laplacian_smoothing.
- Lloyds_algorithm wikiPageWikiLink Linde–Buzo–Gray_algorithm.
- Lloyds_algorithm wikiPageWikiLink Lloyds_algorithm.
- Lloyds_algorithm wikiPageWikiLink Mean_shift.
- Lloyds_algorithm wikiPageWikiLink Monte_Carlo_method.
- Lloyds_algorithm wikiPageWikiLink Mosaic.
- Lloyds_algorithm wikiPageWikiLink Non-Euclidean_geometry.
- Lloyds_algorithm wikiPageWikiLink Quantization_(signal_processing).
- Lloyds_algorithm wikiPageWikiLink Stippling.
- Lloyds_algorithm wikiPageWikiLink Taxicab_geometry.
- Lloyds_algorithm wikiPageWikiLink Triangle_mesh.
- Lloyds_algorithm wikiPageWikiLink Two-dimensional_space.
- Lloyds_algorithm wikiPageWikiLink Voronoi_diagram.
- Lloyds_algorithm wikiPageWikiLinkText "LGA".
- Lloyds_algorithm wikiPageWikiLinkText "Lloyd's Method I algorithm".
- Lloyds_algorithm wikiPageWikiLinkText "Lloyd's algorithm".
- Lloyds_algorithm wikiPageWikiLinkText "Lloyd’s".
- Lloyds_algorithm wikiPageWikiLinkText "Voronoi iteration".
- Lloyds_algorithm align "right".
- Lloyds_algorithm alt "Lloyd's method, iteration 1".
- Lloyds_algorithm alt "Lloyd's method, iteration 15".
- Lloyds_algorithm alt "Lloyd's method, iteration 2".
- Lloyds_algorithm alt "Lloyd's method, iteration 3".
- Lloyds_algorithm caption "Fifteenth iteration".
- Lloyds_algorithm caption "First iteration".
- Lloyds_algorithm caption "Second iteration".
- Lloyds_algorithm caption "Third iteration".
- Lloyds_algorithm direction "vertical".
- Lloyds_algorithm footer "In the last image, the points are very near the centroids of the Voronoi cells. A centroidal Voronoi tessellation has been found.".
- Lloyds_algorithm footerAlign "center".
- Lloyds_algorithm header "Example of Lloyd's algorithm. The Voronoi diagram of the current points at each iteration is shown. The plus signs denote the centroids of the Voronoi cells.".
- Lloyds_algorithm headerAlign "center".
- Lloyds_algorithm image "LloydsMethod1.svg".
- Lloyds_algorithm image "LloydsMethod15.svg".
- Lloyds_algorithm image "LloydsMethod2.svg".
- Lloyds_algorithm image "LloydsMethod3.svg".
- Lloyds_algorithm width "200".
- Lloyds_algorithm wikiPageUsesTemplate Template:Harvtxt.
- Lloyds_algorithm wikiPageUsesTemplate Template:Multiple_image.
- Lloyds_algorithm wikiPageUsesTemplate Template:R_from_modification.
- Lloyds_algorithm wikiPageUsesTemplate Template:Reflist.
- Lloyds_algorithm subject Category:Geometric_algorithms.
- Lloyds_algorithm subject Category:Mathematical_optimization.
- Lloyds_algorithm hypernym Algorithm.
- Lloyds_algorithm type Area.
- Lloyds_algorithm type Software.
- Lloyds_algorithm type Algorithm.
- Lloyds_algorithm type Area.
- Lloyds_algorithm type Datum.
- Lloyds_algorithm type Redirect.
- Lloyds_algorithm comment "In computer science and electrical engineering, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces, and partitions of these subsets into well-shaped and uniformly sized convex cells.".
- Lloyds_algorithm label "Lloyd's algorithm".
- Lloyds_algorithm label "Lloyds algorithm".
- Lloyds_algorithm sameAs Q2835805.
- Lloyds_algorithm sameAs Algorithme_de_Lloyd-Max.
- Lloyds_algorithm sameAs m.07rd1w.
- Lloyds_algorithm sameAs Алгоритм_Ллойда.
- Lloyds_algorithm sameAs لائیڈ_الخوارزم.
- Lloyds_algorithm sameAs Q2835805.
- Lloyds_algorithm wasDerivedFrom Lloyds_algorithm?oldid=344653523.
- Lloyds_algorithm wasDerivedFrom Lloyds_algorithm?oldid=686873503.
- Lloyds_algorithm depiction LloydsMethod1.svg.
- Lloyds_algorithm isPrimaryTopicOf Lloyds_algorithm.