title: Women's rights

text: 27. In giving effect to recognition of the family in the context of article 23, it is important to accept the concept of the various forms of family, including unmarried couples and their children and single parents and their children and to ensure the equal treatment of women in these contexts (General Comment 19 paragraph 2 last sentence). Single parent families frequently consist of a single woman caring for one or more children, and States parties should describe what measures of support are in place to enable her to discharge her parental functions on the basis of equality with a man in a similar position.


title: Women's rights

text: The Vienna Declaration and Programme of Action (VDPA) is a human rights declaration adopted by consensus at the World Conference on Human Rights on 25 June 1993 in Vienna, Austria. This declaration recognizes women's rights as being protected human rights. Paragraph 18 reads:


title: Women's rights

text: The human rights of women and of the girl-child are an inalienable, integral and indivisible part of universal human rights. The full and equal participation of women in political, civil, economic, social and cultural life, at the national, regional and international levels, and the eradication of all forms of discrimination on grounds of sex are priority objectives of the international community.


title: Women's rights

text: On 31 October 2000, the United Nations Security Council unanimously adopted United Nations Security Council Resolution 1325, the first formal and legal document from the United Nations Security Council that requires all states to fully respect international humanitarian law and international human rights law applicable to the rights and protection of women and girls during and after the armed conflicts.


title: Women's rights

text: The Inter-American Convention on the Prevention, Punishment, and Eradication of Violence against Women, better known as the Belém do Pará Convention, was adopted by the Organization of American States on 9 June 1994. As of March 2020, 32 of the 34 or 35 member states of the Organization of American States have either signed and ratified or acceded to the Belém do Pará Convention; only Canada, Cuba and the United States have not.


title: Women's rights

text: The Protocol to the African Charter on Human and Peoples' Rights on the Rights of Women in Africa, better known as the Maputo Protocol, was adopted by the African Union on 11 July 2003 at its second summit in Maputo, Mozambique. On 25 November 2005, having been ratified by the required 15 member nations of the African Union, the protocol entered into force. The protocol guarantees comprehensive rights to women including the right to take part in the political process, to social and political equality with men, and to control of their reproductive health, and an end to female genital mutilation.


title: Women's rights

text: The Convention on preventing and combating violence against women and domestic violence, better known as the Istanbul Convention, was adopted by the Council of Europe on 11 May 2011. As of June 2020, the treaty has been signed by 45/47 Council of Europe member states and the European Union; 34 of the signatories have also ratified the convention.


title: Women's rights

text: The Declaration on the Elimination of Violence Against Women was adopted by the United Nations in 1993. It defines violence against women as "any act of gender-based violence that results in, or is likely to result in, physical, sexual or psychological harm or suffering to women, including threats of such acts, coercion or arbitrary deprivation of liberty, whether occurring in public or in private life." This resolution established that women have a right to be free from violence. As a consequence of the resolution, in 1999, the General Assembly declared the day of 25 November to be the International Day for the Elimination of Violence against Women.


title: Women's rights

text: Article 2 of The Declaration on the Elimination of Violence Against Women outlines several forms of violence against women:


title: Women's rights

text: The Council of Europe Convention on preventing and combating violence against women and domestic violence, also known as the Istanbul Convention, is the first legally binding instrument in Europe in the field of domestic violence and violence against women, and came into force in 2014.


title: Women's rights

text: Countries which ratify it must ensure that the forms of violence defined in its text are outlawed. In its Preamble, the Convention states that "the realisation of "de jure" and "de facto" equality between women and men is a key element in the prevention of violence against women". The convention also provides a definition of domestic violence as "all acts of physical, sexual, psychological or economic violence that occur within the family or domestic unit or between former or current spouses or partners, whether or not the perpetrator shares or has shared the same residence with the victim". Although it is a Convention of the Council of Europe, it is open to accession by any country.


title: Women's rights

text: Rape, sometimes called sexual assault, is an assault by a person involving sexual intercourse with or sexual penetration of another person without that person's consent. Rape is generally considered a serious sex crime as well as a civil assault. When part of a widespread and systematic practice, rape and sexual slavery are now recognised as a crime against humanity as well as a war crime. Rape is also now recognised as a form of genocide when committed with the intent to destroy, in whole or in part, a targeted group.


title: Women's rights

text: In 1998, the International Criminal Tribunal for Rwanda established by the United Nations made landmark decisions that rape is a crime of genocide under international law. The trial of Jean-Paul Akayesu, the mayor of Taba Commune in Rwanda, established precedents that rape is an element of the crime of genocide. The Akayesu judgement includes the first interpretation and application by an international court of the 1948 Convention on the Prevention and Punishment of the Crime of Genocide. The Trial Chamber held that rape, which it defined as "a physical invasion of a sexual nature committed on a person under circumstances which are coercive", and sexual assault constitute acts of genocide insofar as they were committed with the intent to destroy, in whole or in part, a targeted group. It found that sexual assault formed an integral part of the process of destroying the Tutsi ethnic group and that the rape was systematic and had been perpetrated against Tutsi women only, manifesting the specific intent required for those acts to constitute genocide.


title: Women's rights

text: Judge Navanethem Pillay said in a statement after the verdict: "From time immemorial, rape has been regarded as one of the spoils of war. Now it will be considered a war crime. We want to send out a strong message that rape is no longer a trophy of war." An estimated 500,000 women were raped during the 1994 Rwandan Genocide.


title: Women's rights

text: The Rome Statute Explanatory Memorandum, which defines the jurisdiction of the International Criminal Court, recognises rape, sexual slavery, enforced prostitution, forced pregnancy, enforced sterilization, "or any other form of sexual violence of comparable gravity" as a crime against humanity if the action is part of a widespread or systematic practice. The Vienna Declaration and Programme of Action also condemn systematic rape as well as murder, sexual slavery, and forced pregnancy, as the "violations of the fundamental principles of international human rights and humanitarian law." and require a particularly effective response.


title: Women's rights

text: Rape was first recognised as a crime against humanity when the International Criminal Tribunal for the former Yugoslavia issued arrest warrants based on the Geneva Conventions and Violations of the Laws or Customs of War. Specifically, it was recognised that Muslim women in Foca (southeastern Bosnia and Herzegovina) were subjected to systematic and widespread gang rape, torture, and sexual enslavement by Bosnian Serb soldiers, policemen, and members of paramilitary groups after the takeover of the city in April 1992. The indictment was of major legal significance and was the first time that sexual assaults were investigated for the purpose of prosecution under the rubric of torture and enslavement as a crime against humanity. The indictment was confirmed by a 2001 verdict by the International Criminal Tribunal for the former Yugoslavia that rape and sexual enslavement are crimes against humanity. This ruling challenged the widespread acceptance of rape and sexual enslavement of women as intrinsic part of war. The International Criminal Tribunal for the former Yugoslavia found three Bosnian Serb men guilty of rape of Bosniak (Bosnian Muslim) women and girls (some as young as 12 and 15 years of age), in Foca, eastern Bosnia and Herzegovina. Furthermore, two of the men were found guilty of the crime against humanity of sexual enslavement for holding women and girls captive in a number of de facto detention centres. Many of the women subsequently disappeared.


title: Women's rights

text: According to a report by the UN Human Rights Office, published on 28 July 2020, the women who traveled abroad were forcibly returned to North Korea and were subjected to abuse, torture, sexual violence and other violations. North Korea bans citizens from traveling abroad. Those women who were detained for doing so were regularly beaten, tortured, and subjected to forced nudity and invasive body searches. Women have also reported that in case of pregnancy, the prison officials aborted many children by either beating the women or making them do hard labor.


title: Women's rights

text: The 1956 Supplementary Convention on the Abolition of Slavery, the Slave Trade, and Institutions and Practices Similar to Slavery defines "institutions and practices similar to slavery" to include:


title: Women's rights

text: The Istanbul Convention requires countries which ratify it to prohibit forced marriage (Article 37) and to ensure that forced marriages can be easily voided without further victimization (Article 32).


title: Women's rights

text: The Protocol to Prevent, Suppress and Punish Trafficking in Persons, especially Women and Children (also referred to as the "Trafficking Protocol" or "UN TIP Protocol") is a protocol to the Convention against Transnational Organised Crime. It is one of the three Palermo protocols. Its purpose is defined in "Article 2. Statement of purpose" as: "(a) To prevent and combat trafficking in persons, paying particular attention to women and children; (b) To protect and assist the victims of such trafficking, with full respect for their human rights; and (c) To promote cooperation among States Parties in order to meet those objectives."


title: Pembroke Welsh Corgi

text: The Pembroke Welsh Corgi (; Welsh for "dwarf dog") is a cattle herding dog breed that originated in Pembrokeshire, Wales. It is one of two breeds known as a Welsh Corgi. Pembroke Welsh Corgis descended from the Spitz family of dogs. The other is the Cardigan Welsh Corgi, which descend from the Teckel family of dogs, which also produced the Dachshund.


title: Pembroke Welsh Corgi

text: Pembroke Welsh Corgis are famous as the preferred breed of Queen Elizabeth II, who owned more than 30 Royal corgis during her reign. Although these dogs have been favoured by British royalty for more than seventy years, among the British public they have recently fallen into decline in terms of popularity and demand. However, they remain very popular in the United States. Cities such as New York, Boston, Los Angeles, and San Francisco hold annual "Corgi Meetups" in which hundreds of dogs and their owners congregate to spend the day.


title: Pembroke Welsh Corgi

text: The Pembroke Welsh Corgi has been ranked 11th in Stanley Coren's "The Intelligence of Dogs", which states that the breed is considered an excellent working dog. Pembroke Welsh Corgis were ranked 11th most popular breed of dog in 2020 according to the American Kennel Club.


title: Pembroke Welsh Corgi

text: The Pembroke Welsh Corgi has erect ears that are in proportion to the equilateral triangle of the head. The breed standard indicates that the ears should be firm, medium in size, and tapered slightly to a rounded point. The head should be "fox-like" in shape and appearance. Pembroke Welsh Corgis differ from the Cardigan Welsh Corgi by being shorter in length, having smaller ears, and being slightly straighter of leg. The Pembroke Welsh Corgi has somewhat lighter markings on each side of the withers caused by changes in the thickness, length, and direction of hair growth.


title: Pembroke Welsh Corgi

text: Being a double-coated dog, the Pembroke Welsh Corgi sheds heavily all year around, with peaks in the spring and autumn. With regular brushing, their coat is fairly easy to maintain, as well as naturally water- and dirt repellent (at the exception of "fluffies"). Intact females are also known to shed during heat.


title: Pembroke Welsh Corgi

text: Breed faults exist and should not be bred on purpose; such as corgis with a very long and thinner coat coming from a recessive gene and red coats present with a bluish cast which have a diluted colour.


title: Pembroke Welsh Corgi

text: While some outlying Pembroke Welsh Corgis are born with their tail naturally short, the majority often have their tails docked between 2–5 days old due to historical tradition or to conform to the Breed Standard. Artificial docking was not needed for the dog to do its job as a herding dog in the United Kingdom as many claim (since Cardigan Welsh corgis were also herding dogs but never docked) but rather because a non-herding dog was considered a luxury under tax law and attracted a tax, so to demonstrate that their dogs were herding dogs, owners had to ensure the dogs had docked tails. The Kennel Club, the United Kennel Club, and the FCI allow intact tails in Conformation shows. The AKC Standard states tails should be docked no longer than . In many countries including the United Kingdom, docking has been deemed illegal.


title: Pembroke Welsh Corgi

text: Pembroke Welsh Corgis love to be involved in the family, and tend to follow wherever their owners go. They have a great desire to please their owners, thus making them eager to learn and train. The dogs can also be challenging to train due to their working background, stubbornness and intelligence - they were ranked as the eleventh most intelligent dog in Stanley Coren's "The Intelligence of Dogs". Besides herding, they also function as watchdogs due to their alertness and tendency to bark, which can be aggravated if they are not stimulated adequately. Most Pembrokes will seek the attention of everyone they meet and behave well around children and other pets. It is important to socialize this breed with other animals, adults, and children when they are very young to avoid any anti-social behaviour or aggression later in life. Due to their herding and - for some - prey instinct, they love to chase anything that moves, so it is best to keep them inside fenced areas. The herding instinct will also cause some younger Pembrokes to nip at their owners' ankles as this is what they were bred to do with cattle.


title: Pembroke Welsh Corgi

text: Pembroke Welsh Corgis are achondroplastic, meaning they are a "true dwarf" breed. As such, their stature and build can lead to certain non-inherited health conditions, but genetic issues should also be considered. Commonly, Pembrokes can suffer from monorchidism, Von Willebrand's disease, hip dysplasia, degenerative myelopathy (DM), and inherited eye problems such as progressive retinal atrophy. Genetic testing is available for Pembroke Welsh Corgis to avoid these issues and enhance the genetic health pool.


title: Pembroke Welsh Corgi

text: The Pembroke Welsh Corgi lineage has been traced back as far as 1107 AD. It is said that Flemish weavers brought the dogs with them as they traveled to reside in Wales. Some popular stories give Corgis a creation myth connected to fairies. One story states that two children were running through a forest and stumbled upon the funeral of a fairy. The mourning fairies gave the two children two small corgi puppies and the children took them home, thus giving the breed popularity. Stories also state that Corgis played the role of war horses for fairies before they became herding dogs for humans. At the base of the haunches of Corgis, there is a line of slightly rougher fur called the fairy saddle. Rather than Welsh lore, this may be a modern myth sparked by corgi breeders of the 1940s.


title: Pembroke Welsh Corgi

text: Pembrokes and Cardigans first appeared together in 1925 when they were shown under the rules of The Kennel Club in Britain. The Corgi Club was founded in December 1925 in Carmarthen, Carmarthenshire. It is reported that the local members favored the Pembroke breed, so a club for Cardigan enthusiasts was founded a year or so later. Both groups have worked hard to ensure the appearance and type of breed are standardized through careful selective breeding. Pembrokes and Cardigans were officially recognized by the Kennel Club in 1928 and were initially categorized together under the single heading of Welsh Corgis before the two breeds were recognized as separate and distinct in 1934.


title: Pembroke Welsh Corgi

text: Pembroke Welsh Corgis are becoming more popular in the United States and rank 20th (24th) in American Kennel Club registrations, as of 2015 (2012). However, corgis are now listed as a "vulnerable" breed in the United Kingdom; the decline has been said to be due to a 2007 ban on tail-docking (the practice of cutting off the animal's tail) in the U.K., as well as the lack of breeders in the U.K. In 2009, the corgi was added to The Kennel Club's "At Watch" list of British breeds when annual registrations numbered between 300 and 450. In 2014, the breed was put on the Club's "Vulnerable Native Breeds" list when registrations dropped under 300. In 2018, the breed came off the "At-Risk" list with 456 puppies registered in December 2017. The Kennel Club has credited the renewed interest in the breed to the popular Netflix television series, "The Crown", and others. The Pembroke Welsh Corgi has also appeared in the American television "Brooklyn Nine-Nine" as the pet dog of Captain Raymond Holt and Kevin M. Cozner and is shown to be extremely loyal. Ein, a Corgi with human-level intelligence, is one of the 5 main characters in the TV show "Cowboy Bebop".


title: Pembroke Welsh Corgi

text: Pembroke Welsh Corgis can compete in dog agility trials, obedience, showmanship, flyball, tracking, and herding events. Herding instincts and trainability can be measured at noncompetitive herding tests. Corgis, despite their dwarfism giving the illusion of small slow legs, can reach up to 25 mph if they are healthy and fit. This is because Corgis tend to use more upper body strength to run than most dogs, giving them enhanced abilities with such activities as agility and herding and racing.


title: Pembroke Welsh Corgi

text: At a young age, the Queen's passion for this breed started when her father, King George VI, brought home their first royal corgi who was later named Dookie. The Queen ceased breeding corgis around 2012 so as not to leave any behind after she died; her last corgi, Willow, died in April 2018. She was gifted two new corgi pups by her family in 2021.


title: Steven Crowder

text: Steven Blake Crowder ( ; born July 7, 1987) is an American-Canadian conservative political commentator and media host.


title: Steven Crowder

text: Early in his career, Crowder worked for Fox News and posted satirical videos on conservative media platforms. He then began hosting "Louder with Crowder", a daily political podcast and YouTube channel with conservative commentary and comedic content. It includes a recurring segment called "Change My Mind", in which Crowder invites passers-by to converse.


title: Steven Crowder

text: In December 2012, Crowder and members of Americans for Prosperity were involved in an altercation at a demonstration in Michigan concerning the state's recently passed right-to-work law. Crowder's YouTube channel has been demonetized twice, first in 2019 after repeated use of racist and homophobic slurs. His channel was re-monetized after YouTube said Crowder addressed his behavior and content, and it was demonetized again in March 2021, with uploads suspended for a week, after violating YouTube's presidential election integrity policy for advancing false claims about the election's integrity. YouTube suspended the channel again for two weeks in October 2022 for violating its harassment, threats and cyberbullying policy. The channel had 5.91 million subscribers as of 2022.


title: Steven Crowder

text: Crowder was born on July 7, 1987, in Detroit, Michigan. His mother was French Canadian, and at the age of three, his family moved to the Montreal suburb of Greenfield Park, Quebec, Canada where he would live for the rest of his childhood. Crowder attended Centennial Regional High School, and at the age of 18, he moved back to the United States. Crowder attended two semesters at Champlain College in Burlington, Vermont.


title: Steven Crowder

text: At age 12, he worked as a voice actor for the character Alan "The Brain" Powers on the children's television series "Arthur". He began performing stand-up comedy at age 17. He then acted in a number of films, including the role of Doug Moore in the 2009 movie "To Save a Life". From 2009 to 2012, Crowder worked for Fox News.


title: Steven Crowder

text: By 2009, Crowder regularly posted satirical videos on politically conservative media, including Pajamas Media and later at Andrew Breitbart's Big Hollywood. Crowder served as the master of ceremonies at the 2011 Conservative Political Action Conference (CPAC), and generated some controversy with a rap video he premiered at CPAC 2012.


title: Steven Crowder

text: In December 2012, Crowder and members of Americans for Prosperity were involved in an altercation at a demonstration in Michigan concerning the state's recently passed right-to-work law. The incident began with an attempt by union activists to tear down the Americans for Prosperity tent, which was eventually successful. During the altercation, Crowder was punched several times by a union activist. Crowder posted an edited video of the incident to his YouTube channel that cut footage of the alleged assailant being pushed to the ground and getting back up, right before throwing the punches at Crowder. However, Fox News' broadcasts of the incident included footage of the man being pushed. "The New York Times" stated, "The same footage also shows that Mr. Crowder had his hand on that man's shoulder just before he tumbled to the ground, but, while the camera does not capture the whole sequence of events, it seems likely that the man was knocked to the ground as members of the two sides pushed against one other, not shoved down by Mr. Crowder." Crowder later released an unedited copy of the video.


title: Steven Crowder

text: An AFL–CIO spokesman, Eddie Vale, stated that the organization did not condone the tearing down of the Americans for Prosperity tent or the violence against Crowder and his group.


title: Steven Crowder

text: In March 2013, Ingham County Prosecutor Stuart Dunnings III declined to press charges against anyone involved in the December 2012 altercation. According to Dunnings, his office was originally sent an edited version of the video of Crowder's altercation. However, upon reviewing the unedited version, the prosecutor's office decided not to pursue the case because the union member had acted in self-defense.


title: Steven Crowder

text: In October 2013, Fox News ended its relationship with Crowder. This was announced shortly after Crowder made negative statements about Fox News host Sean Hannity and about Fox News. In 2017, the "Louder with Crowder" program, featuring mainly comedic content and political commentary, became a daily program featured on "Conservative Review"s new streaming service, CRTV. On December 3, 2018, CRTV merged with Glenn Beck's "TheBlaze", where Crowder continues to be hosted, alongside his YouTube channel, which has existed since 2009.


title: Steven Crowder

text: "Change My Mind" is a regular segment conducted by Crowder in which he sits at a table with a sign including the phrase "Change My Mind" and invites people walking by, often students at a university campus, to change his mind on a controversial subject. A photograph of Crowder seated behind a sign in February 2018 reading "Male Privilege is a Myth | Change My Mind" outside the Texas Christian University campus became an Internet meme. Variations of the meme often feature humorously controversial statements in place of "Male Privilege is a Myth", such as "Pineapple goes on pizza | Change My Mind".


title: Steven Crowder

text: Francesca Tripodi, a sociologist at the University of North Carolina at Chapel Hill, said that Crowder is "very popular, especially among young, conservative voters". Stanford extremism researcher Becca Lewis told Bloomberg News that while Crowder does not directly express white nationalist views, his channel "has some of the most overt racism of any of the shows I've looked at". Crowder's channel faced similar criticism after he described CBS reporter Betty Yu's face as "aggressively Asian", with CBS and KPIX 5 condemning what they described as the "horrific, racist comments" and "demeaning Asian stereotypes" on his show.


title: Steven Crowder

text: Crowder's show has also seen success on Apple's podcast list, having remained on the top 100 list over the course of 2020. On YouTube, the Louder with Crowder podcast has 5.57 million subscribers and his secondary channel CrowderBits has approximately 1.09 million subscribers.


title: Steven Crowder

text: In June 2019, YouTube investigated Crowder for using racist and homophobic slurs targeting Carlos Maza in multiple videos reacting to the Vox series "Strikethrough", which Maza hosts. Crowder referred to Maza as "Mr. Lispy queer", an "angry little queer", and a "gay Mexican". Crowder mocked Maza using a stereotypical gay voice, sometimes while wearing a t-shirt with Che Guevara on it that said "Socialism is for f*gs ["sic"]". In addition, Maza said that Crowder's fans have doxxed and harassed him. Maza said Crowder's videos about him are "dehumanizing, and it's something I thought YouTube would be more protective about because it brands itself as being a queer space". According to an analysis by Vox Media's "The Verge", Crowder's videos "routinely contain egregious violations of YouTube's policies against cyberbullying". Crowder responded with a video where he said his use of slurs was "playful ribbing" and that "it's funny, it's a comedy show". He said that the investigation was "an example of a giant, multinational media conglomeration... attempting to squash a competitor". He also stated that he is opposed to doxxing and harassment.


title: Steven Crowder

text: YouTube concluded that the language used by Crowder "was clearly hurtful", but "the videos as posted don't violate our policies". It determined that Crowder had not encouraged his viewers to harass or dox Maza either on YouTube or other platforms and that the main point of his video was to respond to opinion. The decision to not suspend the channel drew considerable criticism. The next day, YouTube suspended the channel's monetization, because "a pattern of egregious actions harmed the broader community". Republican Senator Ted Cruz, who had previously appeared on Crowder's show, criticized YouTube's demonetization of Crowder's account, and Crowder stated on his Twitter account that, "Vox is still going to be pissed" because he was not removed from the platform. In August 2020, YouTube re-monetized some of Crowder's content on the site, stating that Crowder had satisfactorily addressed the issues with his behavior and content.


title: Steven Crowder

text: Crowder announced in February 2021 that he filed a lawsuit against Facebook, alleging he was unfairly censored by the platform. The next month, YouTube suspended Crowder's channel for one week for violating its presidential election integrity policy by advancing false claims about the 2020 United States presidential election in Nevada and again indefinitely demonetized his account. His account was then given a second strike on the platform for "reveling in or mocking" the killing of Ma'Khia Bryant in a video he posted, and Crowder responded by announcing that he had filed a lawsuit against YouTube seeking an injunction.


title: Steven Crowder

text: YouTube suspended his channel on October 27, 2022, for two weeks for violating its policy on harassment, threats and cyberbullying. Crowder alleged that the suspension was election interference because it lasted through the November 8, 2022, midterm election day.


title: Steven Crowder

text: Crowder is a self-described Christian. He married his wife Hilary in August 2012 and wrote about the benefits of remaining abstinent before his marriage.


title: Steven Crowder

text: In July 2021, Crowder underwent a surgical operation in which titanium bars were inserted into his chest in order to counteract his congenital condition of pectus excavatum (sunken chest). The surgery caused fluid to accumulate in his lungs, which he called "excruciatingly painful". Several weeks later, he was rushed to the hospital due to a collapsed lung. In August 2021, as Crowder was still recovering from both treatments, his wife gave birth to twins—a son, Magnus, and a daughter, Charlotte.


title: Leslie Cheung

text: Leslie Cheung Kwok-wing (12 September 1956 – 1 April 2003) was a Hong Kong singer and actor. Throughout a 26-year career from 1977 until his death, Cheung released over 40 music albums and acted in 56 films. He was one of the most prominent pioneers that shaped the identity of Cantopop during the 1980s and became known for his flamboyant, often outrageous stage appearance. His venture into acting in the 1990s was recognised for his portrayal of queer characters in a then-conservative film industry. His career was marked with both praise and criticism, with numerous public discussions focusing on his sexual orientation and androgynous persona.


title: Leslie Cheung

text: Born Cheung Fat-chung in Kowloon, British Hong Kong, Cheung studied in England from the age of 12 until returning to Hong Kong in 1976 to pursue a career in show business. He achieved wide popularity with his 1984 self-titled album and its single "Monica", whose upbeat dance production introduced a new popular trend to Cantopop in addition to the contemporary pool of sentimental ballads. Cheung's continued success with a string of hit albums in the mid- and late-1980s, most notably 1987 best-seller "Summer Romance", won him numerous awards, including Most Popular Male Artist at the 1988 and 1989 Jade Solid Gold Best Ten Music Awards. In addition to music, Cheung had breakthrough film roles as a disillusioned teenager in "Nomad" (1982) and as a police officer torn between justice and brotherhood in "A Better Tomorrow" (1986). He announced his "retirement" from music and emigrated to Canada in 1989, but remained active in his burgeoning acting career.


title: Leslie Cheung

text: Cheung achieved widespread recognition as an actor in the 1990s. He played a womaniser longing for the return of his estranged mother in "Days of Being Wild" (1990), which won him Best Actor at the 1991 Hong Kong Film Awards. His role as a homosexual Peking opera actor in "Farewell My Concubine" (1993) catapulted him to prominence in the western world. Cheung's reputation as a queer celebrity consolidated with his role in the 1997 drama "Happy Together", a film explicitly depicting a homosexual male relationship. His comeback as a recording artist in the late 1990s, particularly with his 1996 album "Red", was noted for sonic experimentation and extravagant, graphic imagery. He was awarded the Golden Needle Award, the highest distinction of the RTHK Top 10 Gold Songs Awards, in 1999. In 2000, he was honoured as "Asia's Biggest Superstar" at the CCTV/MTV Music Honours in mainland China. Cheung died by suicide by jumping off the 24th floor of the hotel Mandarin Oriental on 1 April 2003, having been diagnosed with severe clinical depression.


title: Leslie Cheung

text: Cheung was born Cheung Fat-chung in Kowloon, British Hong Kong, the youngest of 10 children in a middle-class Hakka family. His father, Cheung Wut-hoi, was a well-known tailor specialised in suits whose customers included Western celebrities such as film director Alfred Hitchcock and actors Marlon Brando and Cary Grant. Despite his father's reputation in the fashion industry, Cheung was uninspired by the profession. Cheung told many interviewers that he had an unhappy childhood, feeling emotionally estranged from his father and siblings, and frequently witnessing arguments and fights in the household. He felt "depressed sometimes" and longed for affection from his parents who were absent from home most of the time in his childhood. His father's abusive treatment of his mother had a lasting effect on Cheung's perspectives on marriage. When Cheung's father married another woman, his emotional life further deteriorated. He was brought up by his grandmother, whom he was very close with. Cheung summed up his upbringing as a "silent resentment" with "nothing worth remembering", except for the death of his grandmother when he was in primary school, which was the "one thing that I do remember about my childhood."


title: Leslie Cheung

text: Cheung attended Rosaryhill School for secondary education in Hong Kong and, at age 12, enrolled at an independent boys boarding school Eccles Hall School Quideham near Norwich in England. During his time at Rosaryhill, Cheung was academically poor but excelled in the English language. He discovered a newfound interest in Western films and immersed himself in music, studying the original soundtrack of "Romeo and Juliet". When in England, he recalled that there were "racial problems", but managed to make friends. During weekends, he worked as a bartender and would sometimes do amateur singing at his relatives' restaurant in Southend-on-Sea. He came across the film "Gone with the Wind" and chose Leslie as his English name inspired by the actor Leslie Howard, feeling that "The name can be a man's or woman's, it's very unisex." Cheung attended the University of Leeds, where he studied textile management. After one year of study, in 1976, he returned to Hong Kong when his father became paralysed on one side of the body after a stroke. As the father wanted all of his children to be at home, Cheung abandoned his study and became a salesman for Levi's for a living. Cheung recalled that during this time, "I had no plans; there I was, feeling like I was hanging in the middle of nowhere."


title: Leslie Cheung

text: Upon returning to Hong Kong, Cheung went back to high school as a mature student and formed a band, where he was the lead singer, with his classmates. In May 1977, the band members signed up individually for Rediffusion Television (RTV)'s Asian Singing Contest. Only Cheung remained until the final round of the Hong Kong division, where he finished as the first runner-up with a rendition of "American Pie". He proceeded to the pan-Asian division, finishing fifth. Soon after the competition, RTV offered Cheung a three-year contract as a second-rate actor for RTV. He also signed with Polydor Records with hopes of releasing music albums.


title: Leslie Cheung

text: Cheung's career in show business did not take off immediately. His first film role was in "Erotic Dream of the Red Chamber" (, 1978), a softcore porn production that features his bare buttocks. His first two albums were solely recorded in English, and his third album, "Lover's Arrow" (, 1979) was recorded in Cantonese. The albums failed commercially, and critics lambasted Cheung's voice as "chicken-like". Cheung's first public performance at the 1977 Hong Kong Pop Folk Music Festival was booed off the stage by the audience. He described his early days into show business as "full of uncertainty ... I remember well that my singing career at the early stage was like 'a person running into a rock', full of despair and obstacles." Seeing little potential in Cheung, Polydor allowed him to depart on his own terms.


title: Leslie Cheung

text: Cheung signed with Capital Artists, a record label closely associated with the then-dominant television network TVB, in 1982. His first hit single, "The Wind Blows On" (; 1982), is a cover version of Momoe Yamaguchi's Japanese single "The Other Side of Goodbye" . The song was successful on charts, revitalising Cheung's image as a Cantopop singer. The titular album was Cheung's first to be certified gold by the International Federation of the Phonographic Industry (IFPI) Hong Kong. His second album with Capital, "Craziness" (, 1983), is a compilation of songs he recorded for TVB dramas. The album was also a success, receiving a gold certification from the IFPI Hong Kong. He continued his movie crossover with roles mostly in teenage films, and earned his first major recognition for starring in "Nomad" (1982). While Cheung had already been a well-known actor with likeable personae in TVB productions, his role as a disillusioned teenager in "Nomad" foresaw his future reputation as an icon of rebel. The role garnered Cheung a nomination for Best Actor at the 1983 Hong Kong Film Awards.


title: Leslie Cheung

text: The year 1984 was when Cheung achieved mass stardom. He released the hit single "Monica", a cover of the single by Japanese singer Kōji Kikkawa. The song topped charts in Hong Kong and was one of the 10 gold-certified songs honoured at TVB's 1984 Jade Solid Gold Best Ten Music Awards and the 1984 RTHK Top 10 Gold Songs Awards. The song's upbeat dance production introduced a new musical trend to Cantopop, in addition to the traditional sentimental ballads that had dominated the scene. Cheung's 1984 self-titled album, which included "Monica", was his first to be certified platinum by the IFPI Hong Kong and sold over 200,000 copies. He starred in the TVB drama "Once Upon an Ordinary Girl" () and the film "Behind the Yellow Line". In the latter, he co-starred with actress Maggie Cheung and singer-actress Anita Mui. Both productions were commercially successful and put Cheung into the limelight as a prominent entertainer. As Cheung's fame expanded, the media began to pit him against fellow singer-actor Alan Tam, as the two were the most successful male Cantopop singers at the moment. The publicised so-called rivalry contributed to Cantopop's booming sales and lasted until the end of the 1980s.


title: Leslie Cheung

text: Cheung's next albums with Capital were met with similar success. "For Your Heart Only" (, 1985) yielded the hit single "Wild Wind" (), which was among the 10 gold-certified songs honoured at both TVB's Jade Solid Gold and RTHK Top 10 awards. The album also included songs Cheung recorded for TVB dramas, propelling his image as a romantic male lead. His 1986 single "Who Feels the Same?" () won the Gold Song Gold Award, the distinction for the most popular song of the year, at TVB's Jade Solid Gold Awards. With this achievement, Cheung became an arguably undisputed royalty of Cantopop. After the release of "Who Feels the Same?", he left Capital and joined Cinepoly Records. A turning point in his burgeoning acting career was in the John Woo-directed 1986 crime-action "A Better Tomorrow", in which he co-starred with Ti Lung and Chow Yun-fat. He played a youthful and impulsive police officer torn between justice and his criminal brother.


title: Leslie Cheung

text: Cheung's career ascended to a new peak in 1987, when he released his first album under Cinepoly, "Summer Romance". The album was the best-selling Cantopop release of the year, earning seven times platinum certification from the IFPI Hong Kong and sold over 350,000 copies. Its lead single, "Sleepless Night" (), won the Gold Song Gold Award at the 1987 Jade Solid Gold Awards. The next two albums, "Virgin Snow" and "Hot Summer", both were released in 1988 and sold well, receiving gold and platinum certifications from the IFPI Hong Kong. He also had starring roles in the films "A Chinese Ghost Story" and "Rouge". The performance of Cheung and his co-star Anita Mui in "Rouge" consolidated the pair's reputation as the top Hong Kong entertainers. Yiu-wai Chu, author of the book "Hong Kong Cantopop: A Concise History" (2017), noted that Cheung and Mui formed an "unprecedented" chemistry showcasing "mystic power of charisma", not only in films but also on stage performances together. The two were also close friends in real life.


title: Leslie Cheung

text: Cheung embarked on a 23-date tour at the Hong Kong Coliseum in mid-1988, sponsored by Pepsi. The tour was a sold-out and accumulated over 250,000 spectators. He also held several shows catering to the Chinese community in North America, visiting Atlantic City, Calgary, Toronto, and Vancouver. In the wake of the intense political atmosphere in mainland China in the late 1980s, which would culminate in the 1989 Tiananmen Square protests, successful Cantopop singers announced public withdrawal from the music industry and emigrated to western countries. Cheung followed suit, announcing his "retirement" from Cantopop and emigrating to Vancouver, Canada in 1989. Prior to his retirement, Cheung released three further albums under Cinepoly—"Leslie '89", "Salute", "Final Encounter"—all of which received platinum certifications from the IFPI Hong Kong. He won Most Popular Male Artist twice, at the 1988 and 1989 Jade Solid Gold Best Ten Music Awards. His "farewell concert tour", in support of the album "Final Encounter", ran for 33 consecutive sold-out shows at the Hong Kong Coliseum. Cheung donated profits of his 1989 album "Salute" to the Hong Kong Academy for Performing Arts, which was named the Leslie Cheung Memorial Scholarship after his death.


title: Leslie Cheung

text: In addition to music, Cheung had his breakthrough movie role in the crime-action "A Better Tomorrow" (1986), which would pave the way for his upcoming career in cinema. Cheung announced his "retirement" and emigrated to Canada in 1989, in the aftermath of the handover of Hong Kong, but subsequently returned to show business in 1990.


title: Leslie Cheung

text: He also won Best Actor at the 1994 Hong Kong Film Critics Society Awards in the comedy-drama "Ashes of Time" (1994).


title: Leslie Cheung

text: The turning point in Cheung's acting career came in 1986 with his starring role in John Woo's () "A Better Tomorrow", which broke Hong Kong's box office record. In the following years Cheung was praised for his performances in films which found popularity with audiences worldwide, including "A Chinese Ghost Story" (1987), "Rouge" (1987), Wong Kar-Wai's "Days of Being Wild" (1991) and "Farewell My Concubine" (1993).


title: Leslie Cheung

text: Although Cheung quit his career as a pop singer from 1989 to 1995, he continued his music career as a songwriter. He composed more than ten songs during that time. In 1993, he won "Best Original Movie Song Award" from Golden Horse Film Festival for the theme song "Red Cheek, White Hair" to the film "The Bride with White Hair" (as a film score composer). In 1995, he wrote all three theme songs for the film "The Phantom Lover". As for songwriting, Cheung won four nominations for "Best Original Movie Song Award" at the Golden Horse Film Festival and Awards and two nominations for "Best Original Film Song" at the Hong Kong Film Awards. In 1998, he was a member of the jury at the 48th Berlin International Film Festival.


title: Leslie Cheung

text: In 1995 Cheung signed a contract with Rock Records, returning to music as a singer. At the same year, he released his first post-"retirement" album, "Beloved". "Beloved" achieved large market success with the award of "IFPI Best Selling Album".


title: Leslie Cheung

text: In 2001 Cheung collaborated with William Chang, the art director of Wong Kar-Wai's "Days of Being Wild" (1991), to make his music video "Bewildered", about the intimacy between two gay men. Japanese ballet dancer Nishijima Kazuhiro played Cheung's lover in the video. The music video was demonised for advocating homosexuality and was banned by TVB, but Cheung refused to edit the scenes and censor himself.


title: Leslie Cheung

text: Cheung's last concert tour was the "Passion Tour", which took place in Hong Kong and overseas from 2000 to 2001. Cheung collaborated with fashion designer Jean Paul Gaultier, transforming Cheung "From Angel to Devil" in four costumes: the Angel, the Pretty Boy, the Latin Lover, and the Devil – denoting cross-cultural drag and focusing on Cheung's androgyny and bisexuality. Although "Passion Tour" was acclaimed in Japan, Korea, and Canada for Cheung's glamour and dignity in using drag performance through Gaultier's costume designs, in Hong Kong it was received with disapproval. His final concert tour, the Passion Tour (2000–01), visited Asia, the United Kingdom, and the United States. The tour broke attendance records throughout Asia, including a record for the first foreign artist to hold 16 concerts in Japan.


title: Leslie Cheung

text: While Cheung could sell well over 200,000 copies for an album in his 1980s heyday, his later albums struggled to match the same success, only 50,000 copies each.


title: Leslie Cheung

text: In 2011, CCTV commented the "Passion Tour" that from performance form, art concept, costume props and audience response, all represent the highest standard of Chinese concerts, no one has ever surpassed.


title: Leslie Cheung

text: In 1977, during the filming of the RTV television series "Love Story", the then 20-year-old Cheung met and fell in love with his 17-year-old co-star, Teresa Mo (毛舜筠), and they got together after they finished the series. In 1979, Cheung proposed to Mo with flowers, but his sudden proposal startled her and she began to distance herself from him. Although Cheung and Teresa Mo eventually broke up after the proposal and briefly lost contact, they remained close friends after they had reunited for the 1992 film "All's Well, Ends Well".


title: Leslie Cheung

text: Cheung later went into a brief relationship with an actress , the younger sister of Michelle Yim, but they broke up in 1980, due to their incompatibility for each other's lifestyles.


title: Leslie Cheung

text: Cheung and Ngai Sze-pui (), a Hong Kong model and actress whom he met on the set of ATV television series "Agency 24", were in a relationship for two years from 1981 to 1983.


title: Leslie Cheung

text: In 1984, at the house of Albert Yeung, Cheung met Cindy Yeung (楊諾詩), the youngest daughter of Albert Yeung who had recently returned from Boston. Cindy Yeung was also a fan of Cheung and was seven years younger than him. Cheung and Yeung went out on several dates until the latter returned to Boston. They continued their relationship through phone calls and letters, but would part ways in the following year, still remaining good friends. Cheung felt that if he had not been in the showbusiness, he could have already been married with children, like most of his friends.


title: Leslie Cheung

text: In an interview in 1992, Cheung stated that "My mind is bisexual. It's easy for me to love a woman. It's also easy for me to love a man, too" and "I believe that a good actor would be androgynous, and ever changing."


title: Leslie Cheung

text: He announced his same-sex relationship with his childhood friend Daffy Tong Hok-tak (唐鶴德) during a concert in 1997. He dedicated a love song to the two "lovers of his life", his mother and his boyfriend Daffy Tong at that concert, which is seen as the moment he came out of the closet. This action earned him prestige in LGBT communities in China, Japan, Taiwan, and Hong Kong. His relationship with Daffy lasted until his death in 2003.


title: Leslie Cheung

text: Cheung responded to questions regarding his love life: "In terms of lovers, I think I can be a better friend than a lover. Because I am a workaholic. To share my romance, that person has to compromise something." This statement was out during the interview following the release of the film "Okinawa Rendez-vous" in 2000.


title: Leslie Cheung

text: In a 2001 interview with "Time" magazine, Cheung said: "It's more appropriate to say I'm bisexual. I've had girlfriends. When I was 22 or so, I asked my girlfriend Teresa Mo to marry me."


title: Leslie Cheung

text: Cheung was a supporter of several charities concerning children's welfare. He was a patron of the Children's Cancer Foundation, a charity that cares for young children with cancer and their families. Cheung donated HK$1 million (US$128,000) in 1996 and launched five sets of RED cards to help raise funds for the Children's Cancer Foundation.


title: Leslie Cheung

text: He was the first Cantopop star to launch a charity fundraising at a concert. In 1996, although he rarely sang in public at that time, he sang three theme songs from his films to raise money for the elderly.


title: Leslie Cheung

text: For his 1997 concert at the HK Coliseum, Cheung set up a collection booth for the RED Card charity. Donations of HK$100 or above could obtain a set of cards. Cheung said, "I will lead the way, so I donated HK$1,000,000 to Hong Kong children's cancer fund in my own name." The concert raised more than HK$800,000, to which Cheung and his friends added more than HK$100,000, and made up a million Hong Kong dollars to donate to the cancer fund.


title: Leslie Cheung

text: He was also a patron of the End Child Sexual Abuse Foundation (ECSAF) (護苗基金), founded by veteran actress Josephine Siao ().


title: Leslie Cheung

text: In 1999, at a party to raise relief funds in the aftermath of the Taiwan earthquake, Cheung participated in a fried rice tasting event. He donated HK$250,000 for a bowl of rice; this was matched by fan donations, bringing the total to HK$500,000.


title: Leslie Cheung

text: In 2000, Sun Entertainment opened the "Star Second-hand Shop", where second-hand goods donated by celebrities were auctioned to raise money for the "Sun Love Fund". Leslie Cheung was known for his very good fashion sense and he was the first to donate three well-loved, carefully selected pieces to the auction. Leslie also donated his beloved badminton racket to IDclub Taiwan, to be auctioned to raise money for the children's cancer fund.


title: Leslie Cheung

text: In 1999 and 2000, he appeared in TVB charity shows to help raise funds for ECSAF, in which he was appointed a goodwill ambassador in 2002.


title: Leslie Cheung

text: In 2003, Cheung donated HK$100,000 to the Seedling protection fund, who were holding a large-scale charity night on the 12th of March. He told his party guests to give him cash instead of presents, then he donated all of the money that he received to the fund.


title: Leslie Cheung

text: Cheung died by suicide on 1 April 2003 at 6:43 pm (HKT). He leapt from the 24th floor of the Mandarin Oriental hotel, located in the Central district of Hong Kong Island. He left a suicide note saying that he had been suffering from depression.


title: Leslie Cheung

text: As one of the most popular performers in Asia, Cheung's death broke the hearts of millions of his fans across Asia and shocked the Asian entertainment industry and Chinese community worldwide. The day after Cheung's death, his partner Daffy Tong confirmed that Cheung suffered from clinical depression and had been seeing Professor Felice Lieh Mak, a famous therapist, for treatment for almost a year. He also revealed that Cheung had previously attempted suicide in November 2002. Later at his funeral, Cheung's niece disclosed that her uncle had severe clinical depression and suffered much over the past year. He was buried in Po Fook Hill, Shatin.


title: Leslie Cheung

text: Despite the risk of infection from SARS and the WHO's warning on traveling to Hong Kong, tens of thousands attended Cheung's memorial service, which was held for the public, on 7 April 2003, including celebrities and other fans, many from other parts of the world such as mainland China, Taiwan, Korea, Japan, Southeast Asia, the United States, and Canada. Cheung's funeral was held on 8 April 2003. For almost a month, Cheung's death dominated newspaper headlines in Hong Kong and his songs were constantly on the air. His final album, "Everything Follows the Wind" (), was released three months after his death.


title: Leslie Cheung

text: In a 2012 interview, Cheung's eldest sister, Ophelia, stated Cheung was diagnosed with clinical depression caused by a chemical imbalance in the brain. She said that reporters were frequently found outside of her brother's home which hampered his ability to get to his doctor's facility. Thus, he would come over to her house to consult with his doctor. He would ask his sister, "Why am I depressed? I have money and so many people love me." He was reluctant to take medication for his depression.


title: Leslie Cheung

text: In 2013, Cheung's former music agent Florence Chan organised two memorial concerts entitled "Miss You Much Leslie" on 31 March and 1 April for the 10th anniversary of Cheung's death. Big names of the Hong Kong entertainment industry performed at the concert at Hong Kong Coliseum. In addition, in 2013, Cheung's fans from around the world made two million orizuru cranes for the "Guinness World Record" as a tribute to the anniversary.


title: Leslie Cheung

text: On 12 September 2016, on what would have been Cheung's 60th birthday, over one thousand fans joined Florence Chan in the morning at Po Fook Hill Ancestral Hall (寶福山) for prayers. At night, Cheung's fans club, Red Mission organised "Leslie Cheung 60th Red Hot Birthday Party" to commemorate Cheung. It was an outdoor birthday party at Central Harbourfront Event Space with a big LED screen projecting Cheung's past video clips, concerts, songs and pictures. Eason Chan () as a member of Red Mission joined the party singing Cheung's song "4 season" (春夏秋冬) as a tribute to Cheung. In the same month, another fans club, United Leslie also celebrated the big day of this renowned star. United Leslie organised an exhibition and movie screening of Cheung's two selected movies in PMQ, Central of Hong Kong.


title: Leslie Cheung

text: On 1 April 2022, 8pm, Leslie Cheung's Passion Tour concert remastered in 4K was released online to mark the 19th anniversary of the Canto-pop star's death. The remastered concert was live streamed on Tencent Video and WeChat platforms with enhanced visual image thanks to AI technology performed by Tencent Media Lab.


title: Leslie Cheung

text: Cheung is well known for his prominent roles portraying queer characters in "Happy Together" and "Farewell My Concubine". A pair of red high heels Cheung wore during a performance of his song "Red" were described as "a top draw" at an exhibit on androgynous fashion in Hong Kong. Many media outlets focused primarily on arguing about his queer identity instead of on his artistic achievement in film and music. Before his death, Cheung mentioned in interviews that he had become depressed because of negative comments about gender-crossing in his "Passion Tour" concert. He had planned to retire from stage performance because of the strain of being a bisexual artist in Hong Kong, facing stigmatisation, surveillance, and marginalisation.


title: Leslie Cheung

text: In 2018, 55383 Cheungkwokwing was named in memory of Leslie Cheung. The main-belt asteroid was discovered by Bill Yeung at the Desert Eagle Observatory in 2003.


title: Godwin's law

text: Godwin's law, short for Godwin's law (or rule) of Nazi analogies, is an Internet adage asserting that as an online discussion grows longer (regardless of topic or scope), the probability of a comparison to Nazis or Adolf Hitler approaches 1.


title: Godwin's law

text: Promulgated by the American attorney and author Mike Godwin in 1990, Godwin's law originally referred specifically to Usenet newsgroup discussions. He stated that he introduced Godwin's law in 1990 as an experiment in memetics. Later it was applied to any threaded online discussion, such as Internet forums, chat rooms, and comment threads, as well as to speeches, articles, and other rhetoric where "reductio ad Hitlerum" occurs.


title: Godwin's law

text: In 2012, "Godwin's law" became an entry in the third edition of the "Oxford English Dictionary". In 2021, Harvard researchers published an article showing the phenomenon does not occur with statistically meaningful frequency in Reddit discussions.


title: Godwin's law

text: There are many corollaries to Godwin's law, some considered more canonical (by being adopted by Godwin himself) than others. For example, there is a tradition in many newsgroups and other Internet discussion forums that, when a Hitler comparison is made, the thread is finished and whoever made the comparison loses whatever debate is in progress. This principle is itself frequently referred to as Godwin's law.


title: Godwin's law

text: Godwin's law itself can be applied mistakenly or abused as a distraction, diversion or even as censorship, when fallaciously miscasting an opponent's argument as hyperbole when the comparison made by the argument is appropriate. Godwin himself has also criticized the overapplication of the law, claiming that it does not articulate a fallacy, but rather is intended to reduce the frequency of inappropriate and hyperbolic comparisons. Godwin wrote that "Although deliberately framed as if it were a law of nature or of mathematics, its purpose has always been rhetorical and pedagogical: I wanted folks who glibly compared someone else to Hitler to think a bit harder about the Holocaust."


title: Godwin's law

text: In December 2015, Godwin commented on comparisons to Nazism and fascism being made by several articles between Republican presidential candidate Donald Trump, saying: "If you're thoughtful about it and show some real awareness of history, go ahead and refer to Hitler when you talk about Trump, or any other politician." In August 2017, Godwin made similar remarks on social media with respect to the two previous days' Unite the Right rally in Charlottesville, Virginia, endorsing and encouraging comparisons of its alt-right organizers to Nazis.


title: Godwin's law

text: In June 2018, Godwin wrote an opinion piece in the "Los Angeles Times" denying the need to update or amend the rule. He rejected the idea that whoever invokes Godwin's law has lost the argument, and argued that, applied appropriately, the rule "should function less as a conversation ender and more as a conversation starter."


title: Multivariate normal distribution

text: In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be "k"-variate normally distributed if every linear combination of its "k" components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value.


title: Multivariate normal distribution

text: The multivariate normal distribution of a "k"-dimensional random vector formula_4 can be written in the following notation:


title: Multivariate normal distribution

text: such that formula_10 and formula_11. The inverse of the covariance matrix is called the precision matrix, denoted by formula_12.


title: Multivariate normal distribution

text: A real random vector formula_4 is called a standard normal random vector if all of its components formula_14 are independent and each is a zero-mean unit-variance normally distributed random variable, i.e. if formula_15 for all formula_16.


title: Multivariate normal distribution

text: A real random vector formula_4 is called a centered normal random vector if there exists a deterministic formula_18 matrix formula_19 such that formula_20 has the same distribution as formula_21 where formula_22 is a standard normal random vector with formula_23 components.


title: Multivariate normal distribution

text: A real random vector formula_4 is called a normal random vector if there exists a random formula_23-vector formula_22, which is a standard normal random vector, a formula_27-vector formula_28, and a formula_18 matrix formula_19, such that formula_31.


title: Multivariate normal distribution

text: In the degenerate case where the covariance matrix is singular, the corresponding distribution has no density; see the section below for details. This case arises frequently in statistics; for example, in the distribution of the vector of residuals in the ordinary least squares regression. The formula_14 are in general "not" independent; they can be seen as the result of applying the matrix formula_19 to a collection of independent Gaussian variables formula_22.


title: Multivariate normal distribution

text: The following definitions are equivalent to the definition given above. A random vector formula_36 has a multivariate normal distribution if it satisfies one of the following equivalent conditions.


title: Multivariate normal distribution

text: The spherical normal distribution can be characterised as the unique distribution where components are independent in any orthogonal coordinate system.


title: Multivariate normal distribution

text: The multivariate normal distribution is said to be "non-degenerate" when the symmetric covariance matrix formula_42 is positive definite. In this case the distribution has density


title: Multivariate normal distribution

text: where formula_46 is a real "k"-dimensional column vector and formula_47 is the determinant of formula_42, also known as the generalized variance. The equation above reduces to that of the univariate normal distribution if formula_42 is a formula_50 matrix (i.e. a single real number).


title: Multivariate normal distribution

text: Each iso-density locus — the locus of points in "k"-dimensional space each of which gives the same particular value of the density — is an ellipse or its higher-dimensional generalization; hence the multivariate normal is a special case of the elliptical distributions.


title: Multivariate normal distribution

text: The quantity formula_51 is known as the Mahalanobis distance, which represents the distance of the test point formula_46 from the mean formula_53. Note that in the case when formula_54, the distribution reduces to a univariate normal distribution and the Mahalanobis distance reduces to the absolute value of the standard score. See also Interval below.


title: Multivariate normal distribution

text: In the 2-dimensional nonsingular case (formula_55), the probability density function of a vector formula_56 is:


title: Multivariate normal distribution

text: In the bivariate case, the first equivalent condition for multivariate reconstruction of normality can be made less restrictive as it is sufficient to verify that countably many distinct linear combinations of formula_59 and formula_60 are normal in order to conclude that the vector of formula_56 is bivariate normal.


title: Multivariate normal distribution

text: The bivariate iso-density loci plotted in the formula_67-plane are ellipses, whose principal axes are defined by the eigenvectors of the covariance matrix formula_42 (the major and minor semidiameters of the ellipse equal the square-root of the ordered eigenvalues).


title: Multivariate normal distribution

text: As the absolute value of the correlation parameter formula_58 increases, these loci are squeezed toward the following line :


title: Multivariate normal distribution

text: This is because this expression, with formula_71 (where sgn is the Sign function) replaced by formula_58, is the best linear unbiased prediction of formula_60 given a value of formula_59.


title: Multivariate normal distribution

text: If the covariance matrix formula_42 is not full rank, then the multivariate normal distribution is degenerate and does not have a density. More precisely, it does not have a density with respect to "k"-dimensional Lebesgue measure (which is the usual measure assumed in calculus-level probability courses). Only random vectors whose distributions are absolutely continuous with respect to a measure are said to have densities (with respect to that measure). To talk about densities but avoid dealing with measure-theoretic complications it can be simpler to restrict attention to a subset of formula_76 of the coordinates of formula_77 such that the covariance matrix for this subset is positive definite; then the other coordinates may be thought of as an affine function of these selected coordinates.


title: Multivariate normal distribution

text: To talk about densities meaningfully in singular cases, then, we must select a different base measure. Using the disintegration theorem we can define a restriction of Lebesgue measure to the formula_76-dimensional affine subspace of formula_79 where the Gaussian distribution is supported, i.e. formula_80. With respect to this measure the distribution has the density of the following motif:


title: Multivariate normal distribution

text: where formula_82 is the generalized inverse, formula_27 is the rank of formula_42 and formula_85 is the pseudo-determinant.


title: Multivariate normal distribution

text: The notion of cumulative distribution function (cdf) in dimension 1 can be extended in two ways to the multidimensional case, based on rectangular and ellipsoidal regions.


title: Multivariate normal distribution

text: The first way is to define the cdf formula_86 of a random vector formula_21 as the probability that all components of formula_21 are less than or equal to the corresponding values in the vector formula_77:


title: Multivariate normal distribution

text: Though there is no closed form for formula_86, there are a number of algorithms that estimate it numerically.


title: Multivariate normal distribution

text: Another way is to define the cdf formula_92 as the probability that a sample lies inside the ellipsoid determined by its Mahalanobis distance formula_93 from the Gaussian, a direct generalization of the standard deviation.


title: Multivariate normal distribution

text: The interval for the multivariate normal distribution yields a region consisting of those vectors x satisfying


title: Multivariate normal distribution

text: Here formula_46 is a formula_27-dimensional vector, formula_53 is the known formula_27-dimensional mean vector, formula_42 is the known covariance matrix and formula_100 is the quantile function for probability formula_101 of the chi-squared distribution with formula_27 degrees of freedom.


title: Multivariate normal distribution

text: When formula_103 the expression defines the interior of an ellipse and the chi-squared distribution simplifies to an exponential distribution with mean equal to two (rate equal to half).


title: Multivariate normal distribution

text: While no simple closed formula exists for computing the ccdf, the maximum of dependent Gaussian variables can


title: Multivariate normal distribution

text: The probability content of the multivariate normal in a quadratic domain defined by formula_107 (where formula_108 is a matrix, formula_109 is a vector, and formula_110 is a scalar), which is relevant for Bayesian classification/decision theory using Gaussian discriminant analysis, is given by the generalized chi-squared distribution.


title: Multivariate normal distribution

text: The probability content within any general domain defined by formula_111 (where formula_112 is a general function) can be computed using the numerical method of ray-tracing (Matlab code).


title: Multivariate normal distribution

text: where the sum is taken over all allocations of the set formula_114 into "λ" (unordered) pairs. That is, for a "k"th central moment, one sums the products of covariances (the expected value μ is taken to be 0 in the interests of parsimony):


title: Multivariate normal distribution

text: This yields formula_116 terms in the sum (15 in the above case), each being the product of "λ" (in this case 3) covariances. For fourth order moments (four variables) there are three terms. For sixth-order moments there are terms, and for eighth-order moments there are terms.


title: Multivariate normal distribution

text: The covariances are then determined by replacing the terms of the list formula_117 by the corresponding terms of the list consisting of "r" ones, then "r" twos, etc.. To illustrate this, examine the following 4th-order central moment case:


title: Multivariate normal distribution

text: where formula_119 is the covariance of "X" and "X". With the above method one first finds the general case for a "k"th moment with "k" different "X" variables, formula_120, and then one simplifies this accordingly. For example, for formula_121, one lets and one uses the fact that formula_122.


title: Multivariate normal distribution

text: A quadratic form of a normal vector formula_123, formula_124 (where formula_108 is a matrix, formula_109 is a vector, and formula_110 is a scalar), is a generalized chi-squared variable.


title: Multivariate normal distribution

text: If formula_112 is a general scalar-valued function of a normal vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can be computed with the numerical method of ray-tracing (Matlab code).


title: Multivariate normal distribution

text: If the mean and covariance matrix are known, the log likelihood of an observed vector formula_123 is simply the log of the probability density function:


title: Multivariate normal distribution

text: The circularly symmetric version of the noncentral complex case, where formula_131 is a vector of complex numbers, would be


title: Multivariate normal distribution

text: i.e. with the conjugate transpose (indicated by formula_133) replacing the normal transpose (indicated by formula_134). This is slightly different than in the real case, because the circularly symmetric version of the complex normal distribution has a slightly different form for the normalization constant.


title: Multivariate normal distribution

text: Since the log likelihood of a normal vector is a quadratic form of the normal vector, it is distributed as a generalized chi-squared variable.


title: Multivariate normal distribution

text: The Kullback–Leibler divergence from formula_136 to formula_137, for non-singular matrices Σ and Σ, is:


title: Multivariate normal distribution

text: The logarithm must be taken to base "e" since the two terms following the logarithm are themselves base-"e" logarithms of expressions that are either factors of the density function or otherwise arise naturally. The equation therefore gives a result measured in nats. Dividing the entire expression above by log 2 yields the divergence in bits.


title: Multivariate normal distribution

text: The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which formula_142 is the full multivariate distribution and formula_143 is the product of the 1-dimensional marginal distributions. In the notation of the Kullback–Leibler divergence section of this article, formula_144 is a diagonal matrix with the diagonal entries of formula_145, and formula_140. The resulting formula for mutual information is:


title: Multivariate normal distribution

text: If formula_59 and formula_60 are normally distributed and independent, this implies they are "jointly normally distributed", i.e., the pair formula_153 must have multivariate normal distribution. However, a pair of jointly normally distributed variables need not be independent (would only be so if uncorrelated, formula_154 ).


title: Multivariate normal distribution

text: The fact that two random variables formula_59 and formula_60 both have a normal distribution does not imply that the pair formula_153 has a joint normal distribution. A simple example is one in which X has a normal distribution with expected value 0 and variance 1, and formula_158 if formula_159 and formula_160 if formula_161, where formula_162. There are similar counterexamples for more than two random variables. In general, they sum to a mixture model.


title: Multivariate normal distribution

text: In general, random variables may be uncorrelated but statistically dependent. But if a random vector has a multivariate normal distribution then any two or more of its components that are uncorrelated are independent. This implies that any two or more of its components that are pairwise independent are independent. But, as pointed out just above, it is "not" true that two random variables that are ("separately", marginally) normally distributed and uncorrelated are independent.


title: Multivariate normal distribution

text: Here formula_168 is the generalized inverse of formula_169. The matrix formula_170 is the Schur complement of Σ in Σ. That is, the equation above is equivalent to inverting the overall covariance matrix, dropping the rows and columns corresponding to the variables being conditioned upon, and inverting back to get the conditional covariance matrix.


title: Multivariate normal distribution

text: Note that knowing that alters the variance, though the new variance does not depend on the specific value of a; perhaps more surprisingly, the mean is shifted by formula_171; compare this with the situation of not knowing the value of a, in which case x would have distribution


title: Multivariate normal distribution

text: An interesting fact derived in order to prove this result, is that the random vectors formula_173 and formula_174 are independent.


title: Multivariate normal distribution

text: In the bivariate case where x is partitioned into formula_175 and formula_176, the conditional distribution of formula_175 given formula_176 is


title: Multivariate normal distribution

text: Proof: the result is obtained by taking the expectation of the conditional distribution formula_185 above.


title: Multivariate normal distribution

text: To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra.


title: Multivariate normal distribution

text: Let be multivariate normal random variables with mean vector and covariance matrix Σ (standard parametrization for multivariate normal distributions). Then the joint distribution of is multivariate normal with mean vector and covariance matrix


title: Multivariate normal distribution

text: If is an affine transformation of formula_194 where c is an formula_195 vector of constants and B is a constant formula_196 matrix, then Y has a multivariate normal distribution with expected value and variance BΣB i.e., formula_197. In particular, any subset of the "X" has a marginal distribution that is also multivariate normal.


title: Multivariate normal distribution

text: Another corollary is that the distribution of , where b is a constant vector with the same number of elements as X and the dot indicates the dot product, is univariate Gaussian with formula_199. This result follows by using


title: Multivariate normal distribution

text: Observe how the positive-definiteness of Σ implies that the variance of the dot product must be positive.


title: Multivariate normal distribution

text: An affine transformation of X such as 2X is not the same as the sum of two independent realisations of X.


title: Multivariate normal distribution

text: The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean. Hence the multivariate normal distribution is an example of the class of elliptical distributions. The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix formula_42. The squared relative lengths of the principal axes are given by the corresponding eigenvalues.


title: Multivariate normal distribution

text: If is an eigendecomposition where the columns of U are unit eigenvectors and Λ is a diagonal matrix of the eigenvalues, then we have


title: Multivariate normal distribution

text: Moreover, U can be chosen to be a rotation matrix, as inverting an axis does not have any effect on "N"(0, Λ), but inverting a column changes the sign of U's determinant. The distribution "N"(μ, Σ) is in effect "N"(0, I) scaled by Λ, rotated by U and translated by μ.


title: Multivariate normal distribution

text: Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ yields a non-singular multivariate normal distribution. If any Λ is zero and U is square, the resulting covariance matrix UΛU is singular. Geometrically this means that every contour ellipsoid is infinitely thin and has zero volume in "n"-dimensional space, as at least one of the principal axes has length of zero; this is the degenerate case.


title: Multivariate normal distribution

text: "The radius around the true mean in a bivariate normal random variable, re-written in polar coordinates (radius and angle), follows a Hoyt distribution."


title: Multivariate normal distribution

text: In one dimension the probability of finding a sample of the normal distribution in the interval formula_203 is approximately 68.27%, but in higher dimensions the probability of finding a sample in the region of the standard deviation ellipse is lower.


title: Multivariate normal distribution

text: The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is straightforward.


title: Multivariate normal distribution

text: The Fisher information matrix for estimating the parameters of a multivariate normal distribution has a closed form expression. This can be used, for example, to compute the Cramér–Rao bound for parameter estimation in this setting. See Fisher information for more details.


title: Multivariate normal distribution

text: In Bayesian statistics, the conjugate prior of the mean vector is another multivariate normal distribution, and the conjugate prior of the covariance matrix is an inverse-Wishart distribution formula_212 . Suppose then that "n" observations have been made


title: Multivariate normal distribution

text: Multivariate normality tests check a given set of data for similarity to the multivariate normal distribution. The null hypothesis is that the data set is similar to the normal distribution, therefore a sufficiently small "p"-value indicates non-normal data. Multivariate normality tests include the Cox–Small test


title: Multivariate normal distribution

text: and Smith and Jain's adaptation of the Friedman–Rafsky test created by Larry Rafsky and Jerome Friedman.


title: Multivariate normal distribution

text: Mardia's test is based on multivariate extensions of skewness and kurtosis measures. For a sample {x, ..., x} of "k"-dimensional vectors we compute


title: Multivariate normal distribution

text: Under the null hypothesis of multivariate normality, the statistic "A" will have approximately a chi-squared distribution with degrees of freedom, and "B" will be approximately standard normal "N"(0,1).


title: Multivariate normal distribution

text: Mardia's kurtosis statistic is skewed and converges very slowly to the limiting normal distribution. For medium size samples formula_220, the parameters of the asymptotic distribution of the kurtosis statistic are modified For small sample tests (formula_221) empirical critical values are used. Tables of critical values for both statistics are given by Rencher for "k" = 2, 3, 4.


title: Multivariate normal distribution

text: Mardia's tests are affine invariant but not consistent. For example, the multivariate skewness test is not consistent against


title: Multivariate normal distribution

text: The BHEP test computes the norm of the difference between the empirical characteristic function and the theoretical characteristic function of the normal distribution. Calculation of the norm is performed in the L("μ") space of square-integrable functions with respect to the Gaussian weighting function formula_222. The test statistic is


title: Multivariate normal distribution

text: The limiting distribution of this test statistic is a weighted sum of chi-squared random variables, however in practice it is more convenient to compute the sample quantiles using the Monte-Carlo simulations.


title: Multivariate normal distribution

text: Suppose that observations (which are vectors) are presumed to come from one of several multivariate normal distributions, with known means and covariances. Then any given observation can be assigned to the distribution from which it has the highest probability of arising. This classification procedure is called Gaussian discriminant analysis.


title: Multivariate normal distribution

text: The classification performance, i.e. probabilities of the different classification outcomes, and the overall classification error, can be computed by the numerical method of ray-tracing (Matlab code).


title: Multivariate normal distribution

text: A widely used method for drawing (sampling) a random vector x from the "N"-dimensional multivariate normal distribution with mean vector μ and covariance matrix Σ works as follows:


title: Geographic information system

text: A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a broader sense, one may consider such a system to also include human users and support staff, procedures and workflows, body of knowledge of relevant concepts and methods, and institutional organizations.


title: Geographic information system

text: The uncounted plural, "geographic information systems", also abbreviated GIS, is the most common term for the industry and profession concerned with these systems. It is roughly synonymous with geoinformatics and part of the broader geospatial field, which also includes GPS, remote sensing, etc. Geographic information science, the academic discipline that studies these systems and their underlying geographic principles, may also be abbreviated as GIS, but the unambiguous GIScience is more common. GIScience is often considered a subdiscipline of geography within the branch of technical geography.


title: Geographic information system

text: Geographic information systems are utilized in multiple technologies, processes, techniques and methods. They are attached to various operations and numerous applications, that relate to: engineering, planning, management, transport/logistics, insurance, telecommunications, and business. For this reason, GIS and location intelligence applications are at the foundation of location-enabled services, which rely on geographic analysis and visualization.


title: Geographic information system

text: GIS provides the capability to relate previously unrelated information, through the use of location as the "key index variable". Locations and extents that are found in the Earth's spacetime are able to be recorded through the date and time of occurrence, along with x, y, and z coordinates; representing, longitude ("x"), latitude ("y"), and elevation ("z"). All Earth-based, spatial–temporal, location and extent references should be relatable to one another, and ultimately, to a "real" physical location or extent. This key characteristic of GIS has begun to open new avenues of scientific inquiry and studies.


title: Geographic information system

text: While digital GIS dates to the mid-1960s, when Roger Tomlinson first coined the phrase "geographic information system", many of the geographic concepts and methods that GIS automates date back decades earlier.


title: Geographic information system

text: One of the first known instances in which spatial analysis was used came from the field of epidemiology in the ""Rapport sur la marche et les effets du choléra dans Paris et le département de la Seine"" (1832). French geographer and cartographer, Charles Picquet created a map outlining the forty-eight Districts in Paris, using halftone color gradients, to provide a visual representation for the number of reported deaths due to cholera per every 1,000 inhabitants.


title: Geographic information system

text: In 1854, John Snow, an epidemiologist and physician, was able to determine the source of a cholera outbreak in London through the use of spatial analysis. Snow achieved this through plotting the residence of each casualty on a map of the area, as well as the nearby water sources. Once these points were marked, he was able to identify the water source within the cluster that was responsible for the outbreak. This was one of the earliest successful uses of a geographic methodology in pinpointing the source of an outbreak in epidemiology. While the basic elements of topography and theme existed previously in cartography, Snow's map was unique due to his use of cartographic methods, not only to depict, but also to analyze clusters of geographically dependent phenomena.


title: Geographic information system

text: The early 20th century saw the development of photozincography, which allowed maps to be split into layers, for example one layer for vegetation and another for water. This was particularly used for printing contours – drawing these was a labour-intensive task but having them on a separate layer meant they could be worked on without the other layers to confuse the draughtsman. This work was initially drawn on glass plates, but later plastic film was introduced, with the advantages of being lighter, using less storage space and being less brittle, among others. When all the layers were finished, they were combined into one image using a large process camera. Once color printing came in, the layers idea was also used for creating separate printing plates for each color. While the use of layers much later became one of the typical features of a contemporary GIS, the photographic process just described is not considered a GIS in itself -– as the maps were just images with no database to link them to.


title: Geographic information system

text: Two additional developments are notable in the early days of GIS: Ian McHarg's publication ""Design with Nature"" and its map overlay method and the introduction of a street network into the U.S. Census Bureau's DIME (Dual Independent Map Encoding) system.


title: Geographic information system

text: The first publication detailing the use of computers to facilitate cartography was written by Waldo Tobler in 1959. Further computer hardware development spurred by nuclear weapon research led to more widespread general-purpose computer "mapping" applications by the early 1960s.


title: Geographic information system

text: In 1960 the world's first true operational GIS was developed in Ottawa, Ontario, Canada, by the federal Department of Forestry and Rural Development. Developed by Dr. Roger Tomlinson, it was called the Canada Geographic Information System (CGIS) and was used to store, analyze, and manipulate data collected for the Canada Land Inventory, an effort to determine the land capability for rural Canada by mapping information about soils, agriculture, recreation, wildlife, waterfowl, forestry and land use at a scale of 1:50,000. A rating classification factor was also added to permit analysis.


title: Geographic information system

text: CGIS was an improvement over "computer mapping" applications as it provided capabilities for data storage, overlay, measurement, and digitizing/scanning. It supported a national coordinate system that spanned the continent, coded lines as arcs having a true embedded topology and it stored the attribute and locational information in separate files. As a result of this, Tomlinson has become known as the "father of GIS", particularly for his use of overlays in promoting the spatial analysis of convergent geographic data. CGIS lasted into the 1990s and built a large digital land resource database in Canada. It was developed as a mainframe-based system in support of federal and provincial resource planning and management. Its strength was continent-wide analysis of complex datasets. The CGIS was never available commercially.


title: Geographic information system

text: In 1964 Howard T. Fisher formed the Laboratory for Computer Graphics and Spatial Analysis at the Harvard Graduate School of Design (LCGSA 1965–1991), where a number of important theoretical concepts in spatial data handling were developed, and which by the 1970s had distributed seminal software code and systems, such as SYMAP, GRID, and ODYSSEY, to universities, research centers and corporations worldwide. These programs were the first examples of general purpose GIS software that was not developed for a particular installation, and was very influential on future commercial software, such as Esri ARC/INFO, released in 1983.


title: Geographic information system

text: By the late 1970s two public domain GIS systems (MOSS and GRASS GIS) were in development, and by the early 1980s, M&S Computing (later Intergraph) along with Bentley Systems Incorporated for the CAD platform, Environmental Systems Research Institute (ESRI), CARIS (Computer Aided Resource Information System), and ERDAS (Earth Resource Data Analysis System) emerged as commercial vendors of GIS software, successfully incorporating many of the CGIS features, combining the first generation approach to separation of spatial and attribute information with a second generation approach to organizing attribute data into database structures.


title: Geographic information system

text: In 1986, Mapping Display and Analysis System (MIDAS), the first desktop GIS product was released for the DOS operating system. This was renamed in 1990 to MapInfo for Windows when it was ported to the Microsoft Windows platform. This began the process of moving GIS from the research department into the business environment.


title: Geographic information system

text: By the end of the 20th century, the rapid growth in various systems had been consolidated and standardized on relatively few platforms and users were beginning to explore viewing GIS data over the Internet, requiring data format and transfer standards. More recently, a growing number of free, open-source GIS packages run on a range of operating systems and can be customized to perform specific tasks. The major trend of the 21st Century has been the integration of GIS capabilities with other Information technology and Internet infrastructure, such as relational databases, cloud computing, software as a service (SAAS), and mobile computing.


title: Geographic information system

text: The distinction must be made between a singular "geographic information system", which is a single installation of software and data for a particular use, along with associated hardware, staff, and institutions (e.g., the GIS for a particular city government); and "GIS software", a general-purpose application program that is intended to be used in many individual geographic information systems in a variety of application domains. Starting in the late 1970s, many software packages have been created specifically for GIS applications. Esri's ArcGIS, which includes ArcGIS Pro and the legacy software ArcMap, currently dominate the GIS Market. Other examples of GIS include Autodesk and MapInfo Professional and open source programs such as QGIS, GRASS GIS, MapGuide, and Hadoop-GIS. These and other desktop GIS applications include a full suite of capabilities for entering, managing, analyzing, and visualizing geographic data, and are designed to be used on their own.


title: Geographic information system

text: Starting in the late 1990s with the emergence of the Internet, as computer network technology progressed, GIS infrastructure and data began to move to servers, providing another mechanism for providing GIS capabilities. This was facilitated by standalone software installed on a server, similar to other server software such as HTTP servers and relational database management systems, enabling clients to have access to GIS data and processing tools without having to install specialized desktop software. These networks are known as distributed GIS. This strategy has been extended through the Internet and development of cloud-based GIS platforms such as ArcGIS Online and GIS-specialized software as a service (SAAS). The use of the Internet to facilitate distributed GIS is known as Internet GIS.


title: Geographic information system

text: An alternative approach is the integration of some or all of these capabilities into other software or information technology architectures. One example is a spatial extension to Object-relational database software, which defines a geometry datatype so that spatial data can be stored in relational tables, and extensions to SQL for spatial analysis operations such as overlay. Another example is the proliferation of geospatial libraries and application programming interfaces (e.g., GDAL, Leaflet, D3.js) that extend programming languages to enable the incorporation of GIS data and processing into custom software, including web mapping sites and location-based services in smartphones.


title: Geographic information system

text: The core of any GIS is a database that contains representations of geographic phenomena, modeling their "geometry" (location and shape) and their "properties" or "attributes". A GIS database may be stored in a variety of forms, such as a collection of separate data files or a single spatially-enabled relational database. Collecting and managing these data usually comprise the bulk of the time and financial resources of a project, far more than other aspects such as analysis and mapping.


title: Geographic information system

text: GIS uses spatio-temporal (space-time) location as the key index variable for all other information. Just as a relational database containing text or numbers can relate many different tables using common key index variables, GIS can relate otherwise unrelated information by using location as the key index variable. The key is the location and/or extent in space-time.


title: Geographic information system

text: Any variable that can be located spatially, and increasingly also temporally, can be referenced using a GIS. Locations or extents in Earth space–time may be recorded as dates/times of occurrence, and x, y, and z coordinates representing, longitude, latitude, and elevation, respectively. These GIS coordinates may represent other quantified systems of temporo-spatial reference (for example, film frame number, stream gage station, highway mile-marker, surveyor benchmark, building address, street intersection, entrance gate, water depth sounding, POS or CAD drawing origin/units). Units applied to recorded temporal-spatial data can vary widely (even when using exactly the same data, see map projections), but all Earth-based spatial–temporal location and extent references should, ideally, be relatable to one another and ultimately to a "real" physical location or extent in space–time.


title: Geographic information system

text: Related by accurate spatial information, an incredible variety of real-world and projected past or future data can be analyzed, interpreted and represented. This key characteristic of GIS has begun to open new avenues of scientific inquiry into behaviors and patterns of real-world information that previously had not been systematically correlated.


title: Geographic information system

text: GIS data represents phenomena that exist in the real world, such as roads, land use, elevation, trees, waterways, and states. The most common types of phenomena that are represented in data can be divided into two conceptualizations: discrete objects (e.g., a house, a road) and continuous fields (e.g., rainfall amount or population density). Other types of geographic phenomena, such as events (e.g., World War II), processes (e.g., suburbanization), and masses (e.g., soil) are represented less commonly or indirectly, or are modeled in analysis procedures rather than data.


title: Geographic information system

text: Traditionally, there are two broad methods used to store data in a GIS for both kinds of abstractions mapping references: raster images and vector. Points, lines, and polygons represent vector data of mapped location attribute references.


title: Geographic information system

text: A new hybrid method of storing data is that of identifying point clouds, which combine three-dimensional points with RGB information at each point, returning a "3D color image". GIS thematic maps then are becoming more and more realistically visually descriptive of what they set out to show or determine.


title: Geographic information system

text: GIS data acquisition includes several methods for gathering spatial data into a GIS database, which can be grouped into three categories: "primary data capture", the direct measurement phenomena in the field (e.g., remote sensing, the global positioning system); "secondary data capture", the extraction of information from existing sources that are not in a GIS form, such as paper maps, through digitization; and "data transfer", the copying of existing GIS data from external sources such as government agencies and private companies. All of these methods can consume significant time, finances, and other resources.