Lloyd's Method I algorithm, originally described in 1957, can be generalized in a straighforward way for application to vector data.

The most common form of the algorithm uses an iterative refinement heuristic known as Lloyd's algorithm.

Lloyd's algorithm starts by partitioning the input points into k initial sets, either at random or using some heuristic data.

Lloyd's algorithm and k-means are often used synonymously, but in reality Lloyd's algorithm is a heuristic for solving the k-means problem, as with certain combinations of starting points and centroids, Lloyd's algorithm can in fact converge to the wrong answer.

Other variations exist, but Lloyd's algorithm has remained popular, because it converges extremely quickly in practice.

* The original paper describing the algorithm, as an extension to Lloyd's algorithm:

In computer science and electrical engineering, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm for grouping data points into a given number of categories, used for k-means clustering.

Lloyd's algorithm is usually used in a Euclidean space, so the distance function serves as a measure of similarity between points, and averaging of each dimension for the averaging, but this need not be the case.

Lloyd's algorithm starts by partitioning the input points into k initial sets, either at random or using some heuristic.

Since the algorithm converges slowly, and, due to limitations in numerical precision the algorithm will often not converge, real-world applications of Lloyd's algorithm stop once the distribution is " good enough.

Lloyd's algorithm is also used to generate dot drawings in the style of stippling.

Antoon's 1990 production at the New York Shakespeare Festival, starring Morgan Freeman and Tracey Ullman, which was set in the old west ; Bill Alexander's 1992 RSC production at the Barbican, starring Anton Lesser and Amanda Harris, in which the Induction was rewritten in modern language, and the play-within-the-play featured actors carrying scripts and continually forgetting lines ; Delia Taylor's 1999 production at the Clark Street Playhouse, which featured an all female cast, with Diane Manning as Petruchio and Elizabeth Perotti as Katherina ; Phyllida Lloyd's 2003 production at the Globe, again with an all female cast, starring Janet McTeer as Petruchio and Kathryn Hunter as Katherina ; Gregory Doran's 2003 RSC production at the Royal Shakespeare Theatre, where the play was presented with Fletcher's The Tamer Tamed as a two-part piece, with Jasper Britton and Alexandra Gilbreath ( playing both Katherina in The Shrew and Maria ( Petruchio's second wife ) in The Tamer Tamed ); Edward Hall's 2006 Propeller Company production at the Courtyard Theatre as part of the RSC's presentation of the Complete Works, featuring an all-male cast, with Dugald Bruce Lockhart as Petruchio and Simon Scardifield as Katherina ; and Conall Morrison's 2008 RSC production at the Royal Shakespeare Theatre, starring Stephen Boxer and Michelle Gomez.

The site, which will be occupied from 2014, will house, amongst others, the Group Technology Centre of Lloyd's Register who have announced a strategic alliance with the University and the University Maritime Institute.

She has appeared on backing vocals on various albums such as Crowded House and Alex Lloyd's Watching Angels Mend She also features prominently on the new 7 Worlds Collide project, co-writing ( and sharing lead vocal ) the track ' Little By Little ' with her husband and sings on the track ' Isolation ' on the new Crowded House album, Intriguer.

When the city pressured local insurance companies to stop insuring cars used in the carpools, the boycott leaders arranged policies with Lloyd's of London.

Arising simultaneously with these developments were wider issues: firstly, in the United States, an ever-widening interpretation by the Courts of insurance coverage in relation to workers ' compensation in relation to asbestos-related losses, which had the effect of creating a huge, and initially not recognised and then not acknowledged hole in Lloyd's reserves.

* Enforcement officials in 11 U. S. states charged Lloyd's and some of its associates with various wrongs such as fraud and selling unregistered securities ;

* Ian Posgate, one of Lloyd's leading underwriters, was charged with skimming money from investors and secretly trying to buy a Swiss bank ; he was later acquitted.

For most of Lloyd's history, rich individuals ( Names ) backed policies written at Lloyd's with all of their personal wealth ( unlimited liability ).

Since 1994, Lloyd's has allowed corporate members into the market, with limited liability.

Today, individual Names provide only 14 % of capacity at Lloyd's, with UK-listed and other corporate members providing 31 % and the remainder via the international insurance industry.

Outsiders, whether individuals or other insurance companies, cannot do business directly with Lloyd's syndicates.

Lloyd's finance director Luke Savage explained, “ There are a lot of banks who, because of the uncertainty around Europe, the market has stopped using to place deposits with.

In the case of Lloyd's this resulted in the bankruptcy of thousands of individual investors who indemnified ( via RITC ) general liability insurance written from the 1940s to the mid 1970s for companies with exposure to asbestosis claims.

Lloyd's is in talks with Virgin Galactic to insure spaceflights.

Illustrated with black-and-white photographic plates, which include the Twin Towers in New York, with a colour frontispiece of ' The Room ' at Lloyd's ( Originally supplied in cardboard box ).

Heinlein may have come up with the term himself, but there are earlier citations: a piece in Lippincott's Monthly Magazine in 1889, used the term in reference to Edward Bellamy's Looking Backward: 2000 – 1887 and other works ; and one in the May, 1900 issue of The Bookman said that John Uri Lloyd's Etidorhpa, The End of the Earth had " created a great deal of discussion among people interested in speculative fiction ".

Released a few weeks before the start of the Great Depression, Welcome Danger was a huge financial success, with audiences eager to hear Lloyd's voice on film.

The films released during this period were: Feet First, with a similar scenario to Safety Last which found him clinging to a skyscraper at the climax ; Movie Crazy with Constance Cummings ; The Cat's-Paw, which was a dark political comedy and a big departure for Lloyd ; and The Milky Way, which was Lloyd's only attempt at the fashionable genre of the screwball comedy film.

His initial career was as a member of Harold Lloyd's writing staff.

Lloyd's method is used in computer graphics because the resulting distribution has blue noise characteristics ( see also Colors of noise ), meaning there are few low-frequency components that could be interpreted as artifacts.

We had a couple of schools in this country, the principal one being on the Marshall Field estate out in Lloyd's Neck.

Lloyd's of London, pictured in 1991, is one of the world's leading and most famous insurance markets

Referring to the same, one of the entries in Douglas Adams & John Lloyd's The Meaning of Liff reads " WATH ( n .): The rage of Roy Jenkins.

Due to the focus on marine business, during the formative years of Lloyd's ( between 1688 and 1807 ), one of the sources of Lloyd's business was the insurance of ships engaged in slave trading, as Britain rapidly established itself as the chief trading power in the Atlantic.

An individual " joined " for one calendar year only – known as the Lloyd's annual venture.

) and strongly hinted that one of Lloyd's main witnesses, Murray Lawrence, a previous Chairman, had lied in his testimony ( 405 of the judgment: We have serious reservations about the veracity of Mr. Lawrence's evidence [...].

Lloyd's rate of film releases, which had been one or two a year in the 1920s, slowed to about one every two years until 1938.

Returning to England, he worked for two years at Lloyd's of London for no pay, then for another year at one pound a week.

Reporter Chad Garrison spoke with George Gaines, a nephew of Lloyd's who was one of only two surviving family members who had been alive when Lloyd disappeared, although he had only been an infant at the time, and other, younger descendants.

In her teens, the younger Matilda Wood adopted the name Marie Lloyd, the surname taken from Lloyd's Weekly Newspaper, and quickly became one of the most famous of English music hall singers and comediennes.

Cooper had become a ' name ' at Lloyd's of London, a supposedly ' blue chip ' investment, but in the 1990s he was reportedly one of those who suffered enormous personal losses because of the unlimited liability which a ' name ' was then responsible for, and he was forced to sell his hard won Lonsdale belts.

In 1978, again due to the prospect of overcrowding, Lloyd's commissioned Richard Rogers to redevelop the site and the original 1928 building was demolished to make way for the present one which was opened by Queen Elizabeth II in 1986.

* Christopher Lloyd's character of Doctor Emmett Brown, one of the two main fictional characters of the Back To The Future film series, attributed the origins of his lifelong devotion to science to having read as a child the works of Jules Verne in general, and Journey to the Centre of the Earth in particular.

Ships are inspected on a regular basis by a team of Lloyd's Register surveyors, one of the most important inspections being a ship's annual Load Line Survey.

A Lloyd's Coverholder is one such example in which a Lloyd's Syndicate ( an insurer who is a member of Lloyd's of London ) delegates its underwriting authority to, hence allowing that syndicate to operate in a region or country as if it is a local insurer.

The African-American abolitionist Frederick Douglass, who had grown up as a slave on one of Lloyd's plantations, discussed Lloyd in his 1845 autobiography The Narrative of Frederick Douglass.

Rude collected on a Lloyd's of London insurance policy and did not appear in wrestling again until 1996, when he joined Extreme Championship Wrestling ( ECW ) as a masked man who harassed Shane Douglas, at one point spanking Francine.

An example is Alan Moore and David Lloyd's V for Vendetta, wherein during one chapter, a monologue expressed in captions serves not only to express the thoughts of a character but also the mood, status and actions of three others.

Lloyd's Monks Orchard House was one of the most substantial mansions in the Croydon area.