title: Ricky Williams

text: On July 22, 2006, Williams suffered a broken bone in his left arm during a game against the Saskatchewan Roughriders in Regina, Saskatchewan. He underwent surgery on July 23, 2006, to repair the broken bone. Shortly after injuring his arm, Williams suffered yet another injury after a door at the Argonauts' practice facility swung behind him and clipped the running back on his left achilles tendon requiring 16 stitches to close the gash. During his recovery, Williams received hyperbaric oxygen therapy in St. Catharines, Ontario to expedite his return from injury. In all, Williams missed two months of game action because of the injuries, returning on September 23, 2006, against the Calgary Stampeders.


title: Ricky Williams

text: In the 11 games that he played during 2006 CFL regular season, Williams rushed 109 times for 526 yards, scoring two touchdowns, with a long run of 35 yards. He caught 19 passes for 127 yards.


title: Ricky Williams

text: Williams stated his love for Toronto and mentioned the possibility of returning to the Canadian game during his professional career. "I was thinking it wouldn't be bad to come back up here and kind of follow the same steps as Pinner – play here a couple years and maybe get a chance to coach up here", Williams said. "Because I really like Toronto, I really like this organization … you can live here, you know? You feel like you have a life. I come to work, I go home, play with my kid, walk to the store. It's really nice. I get to teach. It's wonderful here." In another interview, he expressed further desire to remain in the CFL, "If I came back here, you can put me anywhere", he says. "Up here, I can play offense, defense, special teams. I can do everything. I can block, play tight end, running back, receiver — even play the line. The NFL is so structured — 'You do this.' Here I can do so much."


title: Ricky Williams

text: With the controversy over, the Argonauts signing Williams prompted outgoing CFL commissioner Tom Wright, in his final state of the league address, to introduce a new rule that would come in effect before the start of the 2007 CFL season that would prevent a player under suspension in the NFL from signing with a CFL club. This rule has been informally dubbed "The Ricky Williams Rule."


title: Ricky Williams

text: The new rule, however, was grandfathered so that players who were still playing in the league, such as Argonaut tackle Bernard Williams, who was suspended by the NFL for drug abuse and did not seek reinstatement when the ban ended, could continue playing.


title: Ricky Williams

text: On May 11, 2007, an anonymous source reported that Williams had failed a drug test again. The source indicated that NFL medical advisors had recommended to the commissioner that Williams not be allowed to apply for reinstatement that September.


title: Ricky Williams

text: Williams adhered to a strict regimen of multiple drug tests per week in 2007 as part of his attempt to be reinstated by the NFL. He practiced yoga, which, he claimed, helped him to stop using marijuana. In October 2007, NFL commissioner Roger Goodell granted his request for reinstatement. Williams returned for a "Monday Night Football" game on November 26, 2007. He rushed six times for 15 yards before Lawrence Timmons, a Pittsburgh Steelers linebacker, stepped on his right shoulder, tearing his pectoral muscle. The next day it was reported that he would miss the rest of the season, and on November 28, Williams was placed on injured reserve.


title: Ricky Williams

text: Williams bounced back in the 2008 season, rushing for 659 yards on 160 carries and scoring four touchdowns while playing in all 16 games for the Dolphins. He and Ronnie Brown ran the Wildcat formation together, resulting in an 11-5 season for the Dolphins.


title: Ricky Williams

text: In 2009, during the Dolphins ninth game, starting running back Ronnie Brown suffered a season-ending injury, and Williams, at age 32, became the starter for the remainder of the year. In Week 11, against the Carolina Panthers, he had 22 carries for 119 yards and two touchdowns to earn AFC Offensive Player of the Week. He finished the season with 1,121 yards rushing and a 4.7 yards per carry, along the way setting an NFL record of the longest time span (six years) between 1,000 yard seasons (2003–2009). Williams also became only the seventh player in NFL history to begin a season age 32 or older and reach 1,000 yards rushing during that season.


title: Ricky Williams

text: In the 2010 season, Williams carried 159 times for 673 yards and two touchdowns for the Dolphins while splitting duties, averaging 4.2 yards a carry at the age of 33.


title: Ricky Williams

text: Williams signed a two-year, $2.5 million contract with the Baltimore Ravens on August 8, 2011. Williams scored his first touchdown of the season against the Houston Texans on October 16. He finished the 2011 season with 444 rushing yards and two rushing touchdowns. On January 1, 2012, Williams surpassed the 10,000 career rushing yards mark and became the 26th player in the history of the NFL to do so. On February 7, 2012, Williams informed the Ravens of his retirement from the NFL.


title: Ricky Williams

text: Williams is a medical cannabis advocate. He once stated his "personal goal is to elevate the legitimacy of cannabis as a medicine and the respect of medical professionals for cannabis users." By 1999, Williams had several tattoos: one of a spider web on his shoulder, one of Mickey Mouse on his biceps, a barbed wire around his arm, one of a dagger on his pectoral, and a Gemini symbol on his other pectoral.


title: Ricky Williams

text: Williams has admitted being very shy and was diagnosed with social anxiety disorder, borderline personality disorder, and avoidant personality disorder with which he struggled to cope during his football career. Williams was treated with therapy and medication. Williams was briefly a spokesperson for the drug Paxil as treatment. He worked with the drug company GlaxoSmithKline to educate the public about the disorder. Williams later quit using Paxil and said that cannabis was a much better form of treatment.


title: Ricky Williams

text: Williams is a qualified yoga instructor. He has stated that one of his main reasons for joining the Canadian Football League's Toronto Argonauts was for the opportunity to teach free yoga lessons at a local Toronto yoga facility. It has been reported that Williams uses pranic healing, no-touch energy healing system, to recover from injuries. In 2009, Williams enrolled at Acupuncture and Massage College in Miami, Florida to study massage therapy and Japanese Shiatsu. In 2018, Williams co-founded an herbal wellness company with his second wife Linnea Miron named Real.


title: Ricky Williams

text: In May 2022, Williams legally changed his last name to Miron, his wife's last name, after they married.


title: Ricky Williams

text: The son of a minister, Williams was raised Southern Baptist and attended church twice a week during his childhood. He still self-identifies as a Christian, but his yoga study opened his mind to other religions, and his exact views on religion are difficult to label. He believes religions are cultural, and his beliefs are inclusive of at least some Christian, Muslim, Buddhist, and Hindu philosophies. Williams is in the first year of a master's program at Emperor's College of Traditional Oriental Medicine in Santa Monica, CA.


title: Ricky Williams

text: In 2015, Williams signed with global talent agency William Morris Endeavor (WME) for representation in media prior to being inducted into the College Football Hall of Fame.


title: Ricky Williams

text: Williams is a vegetarian. He was previously a vegan or at least had a meat-free diet. Tim Graham has reported that Greek yogurt is the only non-vegan food in Williams's diet. PETA has used video of him praising meatless alternatives to popular chicken dishes.


title: Billings, Montana

text: Billings is the largest city in the U.S. state of Montana, with a population of 117,116 as of the 2020 census. Located in the south-central portion of the state, it is the seat of Yellowstone County and the principal city of the Billings Metropolitan Area, which had a population of 184,167 in the 2020 census. It has a trade area of over 500,000.


title: Billings, Montana

text: Billings was nicknamed the "Magic City" because of its rapid growth from its founding as a railroad town in March 1882. With one of the largest trade areas in the United States, Billings is the trade and distribution center for much of Montana east of the Continental Divide, Northern Wyoming, and western portions of North Dakota and South Dakota. Billings is also the largest retail destination for much of the same area.


title: Billings, Montana

text: The city is experiencing rapid growth and a strong economy; it has had and is continuing to have the largest growth of any city in Montana. Parts of the metro area are seeing hyper growth. From 2000 to 2010 Lockwood, an eastern suburb, saw growth of 57.8%, the largest growth rate of any community in Montana. Billings has avoided the economic downturn that affected most of the nation from 2008 to 2012 as well as the housing bust. With more hotel accommodations than any area within a five-state region, the city hosts a variety of conventions, concerts, sporting events, and other rallies. With the Bakken oil development in eastern Montana and western North Dakota, the largest oil discovery in U.S. history, as well as the Heath shale oil discovery just north of Billings, the city's growth rate stayed high during the shale oil boom. Although the city is growing, its growth rate has diminished markedly with oil price declines in recent years.


title: Billings, Montana

text: Attractions in and around Billings include ZooMontana, Yellowstone Art Museum, Pompey's Pillar, Pictograph Cave, Chief Plenty Coups State Park. Little Bighorn Battlefield National Monument, Bighorn Canyon National Recreation Area, Red Lodge Mountain Resort, the Beartooth Highway, which connects Red Lodge and Yellowstone National Park. The northeast entrance to Yellowstone National Park is a little over from Billings.


title: Billings, Montana

text: The city is named for Frederick H. Billings, a former president of the Northern Pacific Railroad from Woodstock, Vermont. An earlier name for the area was Clark's Fork Bottom.


title: Billings, Montana

text: The Crow people, who are indigenous to the area, call the city . It means 'where they cut wood', and is named as such because of a sawmill built in the area by early white settlers. The Cheyenne name is and the Gros Ventre name is , both also named for the sawmill, or translations of the Crow name.


title: Billings, Montana

text: The downtown core and much of the rest of Billings is in the Yellowstone Valley, a canyon carved out by the Yellowstone River. Around 80 million years ago, the Billings area was on the shore of the Western Interior Seaway. The sea deposited sediment and sand around the shoreline. As the sea retreated, it left a deep layer of sand. Over millions of years, this sand was compressed into stone known as Eagle Sandstone. Over the last million years the river has carved its way down through this stone to form the canyon walls known as the Billings Rimrocks or the Rims.


title: Billings, Montana

text: The Pictograph Caves are about five miles south of downtown. These caves contain over 100 pictographs (rock paintings), the oldest of which is over 2,000 years old. Approximately 30,000 artifacts (including stone tools and weapons) have been excavated from the site. These excavations have proved the area has been occupied since at least 2600 BC until after 1800 AD.


title: Billings, Montana

text: The Crow Indians have called the Billings area home since about 1700. The present-day Crow Nation is just south of Billings.


title: Billings, Montana

text: In July 1806, William Clark (of the Lewis and Clark Expedition) passed through the Billings area. On July 25 he arrived at what is now known as Pompey's Pillar and wrote in his journal "... at 4 P M arrived at a remarkable rock, i ascended this rock and from its top had a most extensive view in every direction." Clark carved his name and the date into the rock, leaving the only remaining physical evidence of their expedition. He named the place Pompey's Tower, naming it after the son of his Shoshone interpreter and guide Sacajawea. In 1965, Pompey's Pillar was designated as a national historic landmark, and was proclaimed a national monument in January 2001. An interpretive center has been built next to the monument.


title: Billings, Montana

text: The area where Billings is today was known as Clark's Fork Bottom. Clark's Fork Bottom was to be the hub for hauling freight to Judith and Musselshell Basins. At the time these were some of the most productive areas of the Montana Territory. The plan was to run freight up Alkali Creek, now part of Billings Heights, to the basins and Fort Benton on the Hi-Line.


title: Billings, Montana

text: In 1877 settlers from the Gallatin Valley area of the Montana Territory formed Coulson the first town of the Yellowstone Valley. The town was started when John Alderson built a sawmill and convinced PW McAdow to open a general store and trading post on land Alderson owned on the bank of the Yellowstone River. The store went by the name of Headquarters, and soon other buildings and tents were being built as the town began to grow. At this time before the coming of the railroad, most goods coming to and going from the Montana Territory were carried on paddle riverboats. It is believed it was decided to name the new town Coulson in an attempt to attract the Coulson Packet Company that ran riverboats between St Louis and many points in the Montana Territory. In spite of their efforts the river was traversed only once by paddle riverboat to the point of the new town.


title: Billings, Montana

text: Coulson was a rough town of dance halls and saloons and not a single church. The town needed a sheriff and the famous mountain man John "Liver-Eating" Johnson took the job. Many disagreements were settled with a gun in the coarse Wild West town. Soon a graveyard was needed and Boothill Cemetery was created. It was called Boothill because most of the people in it were said to have died with their boots on. Today, Boothill Cemetery sits within Billings' city limits and is the only remaining physical evidence of Coulson's existence.


title: Billings, Montana

text: When the railroad came to the area, Coulson residents were sure the town would become the railroads hub and Coulson would soon be the Territories largest city. The railroad only had claim to odd sections and it had two sections side-by-side about two miles west of Coulson. Being able to make far more money by creating a new town on these two sections the railroad decided to create the new town of Billings, the two towns existed side by side for a short time with a trolley even running between them. However, most of Coulson's residents moved to the new booming town of Billings. In the end Coulson faded away with the last remains of the town disappearing in the 1930s. Today Coulson Park, a Billings city park, sits on the river bank where Coulson once was.


title: Billings, Montana

text: Named after Northern Pacific Railway president Frederick H. Billings, the city was founded in 1882. The Railroad formed the city as a western railhead for its further westward expansion. At first the new town had only three buildings but within just a few months it had grown to over 2,000. This spurred Billings' nickname of the Magic City because, like magic, it seemed to appear overnight.


title: Billings, Montana

text: The nearby town of Coulson appeared a far more likely site. Coulson was a rough-and-tumble town where arguments were often followed by gunplay. Liver-Eating Johnson was a lawman in Coulson. Perhaps the most famous person to be buried in Coulson's Boothill cemetery is H.M. "Muggins" Taylor, the scout who carried the news of Custer's Last Stand at the Battle of Little Bighorn to the world. Most buried here were said to have died with their boots on. The town of Coulson had been on the Yellowstone River, which made it ideal for the commerce steamboats brought up the river. However, when the Montana & Minnesota Land Company oversaw the development of potential railroad land, they ignored Coulson, and platted the new town of Billings just a couple of miles to the northwest. Coulson quickly faded away; most of her residents were absorbed into Billings. Yet, for a short time, the two towns coexisted; a trolley even ran between them. But ultimately there was no future for Coulson as Billings grew. Though it stood on the banks of the Yellowstone River only a couple of miles from the heart of present-day downtown Billings, the city of Billings never built on the land where Coulson once stood. Today Coulson Park sits along the banks of the Yellowstone where the valley's first town once stood.


title: Billings, Montana

text: By the 1910 census, Billings' population had risen to 10,031 ranking it the sixth fastest-growing community in the nation. Billings became an energy center in the early years of the twentieth century with the discovery of oil fields in Montana and Wyoming. Then the discovery of large natural gas and coal reserves secured the city's rank as first in energy. In the early 20th century, its served as regional trading center and energy hub for eastern Montana and northern Wyoming, an area then known as the Midland Empire.


title: Billings, Montana

text: After World War II, Billings became the region's major financial, medical and cultural center. Billings has had rapid growth from its founding; in its first 50 years growth was, at times, as high as 200 to 300 percent per decade.


title: Billings, Montana

text: Billings growth has remained robust throughout the years, and in the 1950s, it had a growth rate of 66 percent. The 1973 oil embargo by OPEC spurred an oil boom in eastern Montana, northern Wyoming and western North Dakota. With this increase in oil production, Billings became the headquarters for energy sector companies. In 1975 and 1976, the Colstrip coal-fire generation plants 1 and 2 were completed; plants 3 and 4 started operating in 1984 and 1986.


title: Billings, Montana

text: In the 1970s and 1980s, Billings saw major growth in its downtown core; the first high-rise buildings to be built in Montana were erected. In 1980, the 22-floor Sheraton Hotel was completed. Upon its completion, it was declared "the tallest load-bearing brick masonry building in the world" by the Brick Institute of America. During the 1970s and 1980s, other major buildings were constructed in the downtown core; the Norwest Building (now Wells Fargo), Granite Tower, Sage Tower, the MetraPark arena, the TransWestern Center, many new city-owned parking garages, and the First Interstate Center, the tallest building in a five-state area.


title: Billings, Montana

text: With the completion of large sections of the interstate system in Montana in the 1970s, Billings became a shopping destination for an ever-larger area. The 1970s and 1980s saw new shopping districts and shopping centers developed in the Billings area. In addition to the other shopping centers, two new malls were developed, and Rimrock Mall was redeveloped and enlarged, on what was then the city's west end. Cross Roads Mall was built in Billings Heights, and West Park Plaza mall in midtown. Several new business parks were also developed on the city's west end during this period.


title: Billings, Montana

text: Billings was affected by the 1980 eruption of Mount St. Helens in May; the city received about an inch of ash on the ground. The Yellowstone fires of 1988 blanketed Billings in smoke for weeks.


title: Billings, Montana

text: In the 1990s, the service sector in the city increased with the development of new shopping centers built around big box stores such as Target, Walmart and Office Depot, all of which built multiple outlets in the Billings area. With the addition of more interchange exits along I-90, additional hotel chains and service industry outlets are being built in Billings. Development of business parks and large residential developments on the city's west end, South Hills area, Lockwood, and the Billings Heights were all part of the 1990s. Billings received the All-America City Award in 1992.


title: Billings, Montana

text: In the 21st century, Billings saw the development of operations centers in the city's business parks and downtown core by such national companies as GE, Wells Fargo and First Interstate Bank. It also saw renewed growth in the downtown core with the addition of many new buildings, new parking garages and a new MET Transit Center, and in 2002 Skypoint was completed. Downtown also saw a renaissance of the historic areas within the downtown core as building after building was restored. In 2007, Billings was designated a Preserve America Community.


title: Billings, Montana

text: With the completion of the Shiloh interchange exit off Interstate 90, the TransTech Center was developed and more hotel development occurred as well. In 2010 the Shiloh corridor was open for business with the completion of the Shiloh parkway, a multi-lane street with eight roundabouts. More shopping centers were developed in the 21st century. One of the newest is Shiloh Crossing, which brought the first Kohl's department store to Montana. Other new centers include Billings Town Square with Montana's first Cabela's, and West Park Promenade, Montana's first open-air shopping mall. In 2009, "Fortune Small Business" magazine named Billings the best small city in which to start a business. Billings saw continued growth with the largest actual growth of any city in Montana. On June 20, 2010 (Father's Day), a tornado touched down in the downtown core and Heights sections of Billings. The MetraPark Arena and area businesses suffered major damage.


title: Billings, Montana

text: In the 2010s, Eastern Montana and North Dakota have experienced an energy boom due to the Bakken formation, the largest oil discovery in U.S. history. In August 2016, a high-rise complex called the One Big Sky Center was proposed for downtown Billings. If built, it would be the tallest building in Montana and Montana's first building to meet or exceed the mark.


title: Billings, Montana

text: Two-thirds of the city is in the Yellowstone Valley and the South Hills area and one-third in the Heights-Lockwood area. The city is divided by the Rims, long cliffs, also called the Rimrocks. The Rims run to the north and east of the downtown core, separating it from the Heights to the north and Lockwood to the east, with the cliffs to the north being tall and to the east of downtown, the face rises . The elevation of Billings is above sea level. The Yellowstone River runs through the southeast portion of the city. According to the United States Census Bureau, the city has an area of , of which is land and is water.


title: Billings, Montana

text: Around Billings, seven mountain ranges can be viewed. The Bighorn Mountains have over 200 lakes and two peaks that rise to over : Cloud Peak, at and Black Tooth Mountain, at . The Pryor Mountains directly south of Billings rise to a height of and are unlike any other landscape in Montana. They are also home the Pryor Mountain Wild Horse Range. The Beartooth Mountains are the location of Granite Peak, which at is the highest point in the state of Montana. The Beartooth Highway, a series of steep zigzags and switchbacks along the Montana–Wyoming border, rises to . It was called "the most beautiful drive in America" by Charles Kuralt. The Beartooth Mountains are just northeast of Yellowstone National Park. The Crazy Mountains to the west rise to a height of at Crazy Peak, the tallest peak in the range. Big Snowy Mountains, with peaks of , are home to Crystal Lake. The Bull Mountains are a low-lying heavily forested range north of Billings Heights. The Absaroka Range stretches about across the Montana–Wyoming border, and at its widest, forming the eastern boundary of Yellowstone National Park.


title: Billings, Montana

text: Downtown Billings has a hot-summer humid continental climate (Köppen: "Dfa") depending on the isotherm used, closely bordering on semi-arid (Köppen: "BSk"), with dry, hot summers, and cold, dry winters. However, areas outside of downtown can have a hot-summer continental climate, even with the isotherm, due to the urban heat island effect, as exemplified by the Billings Logan International Airport. In the summer, the temperature can rise to over on an average of 1 to 3 days per year, while the winter will bring temperatures below on an average of 12.9 days per year. The snowfall averages a year, but because of warm chinook winds that pass through the region during the winter, snow does not usually accumulate heavily or remain on the ground for long: the greatest depth has been on April 5, 1955, after a huge storm which dumped of water equivalent precipitation as snow in the previous three days under temperatures averaging .


title: Billings, Montana

text: The snowiest year on record was 2017–18, with , topping the 2013–14 previous record of . The first freeze of the season on average arrives by October 6 and the last is May 5. Spring and autumn in Billings are usually mild, but brief. Winds, while strong at times, are considered light compared with the rest of Montana and the Rocky Mountain Front.


title: Billings, Montana

text: Due to its location, Billings is susceptible to severe summer weather as well. On June 20, 2010, a tornado touched down in the Billings Heights and Downtown sections of the city. The tornado was accompanied by hail up to golf ball size, dangerous cloud-to-ground lightning, and heavy winds. The tornado destroyed a number of businesses and severely damaged the 12,000-seat MetraPark Arena.


title: Billings, Montana

text: Billings has many sections that comprise the whole of the city. The sections are often defined by Billings unique physical characteristics. For example, a cliff known as the "Rims" separates the Heights from downtown Billings.


title: Billings, Montana

text: The south side of Billings is probably the oldest residential area in the city, and it is the city's most culturally diverse neighborhood. South Park is an old growth City park, host to several food fairs and festivals in the summer months. The Bottom Westend Historic District is home to many of Billings' first mansions. Midtown, the most densely populated portion of the city is in the midst of gentrification on a level few, if any, areas in Montana have ever seen. New growth is mainly concentrated on Billings West End, where Shiloh Crossing is a new commercial development, anchored by Scheels, Montana's largest retail store. Residentially, the West End is characterized by upper income households. Denser, more urban growth is occurring in Josephine Crossing, one of Billings' many new contemporary neighborhoods. Downtown is a blend of small businesses and office space, together with restaurants and a walkable brewery district. The Heights, defined as the area of the city northeast of the Metra, is predominantly residential, and a new school was recently constructed to accommodate growth in the neighborhood.


title: Billings, Montana

text: Billings is the principal city of the Billings Metropolitan Statistical Area. The metropolitan area consists of three counties: Yellowstone, Stillwater, and Carbon. The population of the entire metropolitan area was at 184,167 in the 2020 Census.


title: Billings, Montana

text: As of the census of 2010, there were 104,170 people, 43,945 households, and 26,194 families residing in the city. The population density was . There were 46,317 housing units at an average density of . The racial makeup of the city was 89.6% White, 4.4% Native American, 0.8% Black, 0.7% Asian, 0.1% Pacific Islander, 1.4% from other races, and 2.9% from two or more races. Hispanic or Latino of any race were 5.2% of the population.


title: Billings, Montana

text: There were 43,945 households, of which 28.9% had children under the age of 18 living with them, 43.7% were married couples living together, 11.3% had a female householder with no husband present, 4.6% had a male householder with no wife present, and 40.4% were non-families. 32.6% of all households were made up of individuals, and 12% had someone living alone who was 65 years of age or older. The average household size was 2.29 and the average family size was 2.90.


title: Billings, Montana

text: In the city, the population was spread out, with 22.6% of residents under the age of 18; 9.8% between the ages of 18 and 24; 26.3% from 25 to 44; 26.3% from 45 to 64; and 15% who were 65 years of age or older. The median age in the city was 37.5 years. The gender makeup of the city was 48.3% male and 51.7% female.


title: Billings, Montana

text: As of 2000 the median income for a household in the city was $35,147, and the median income for a family was $45,032. Males had a median income of $32,525 versus $21,824 for females. The per capita income for the city was $19,207. About 9.2% of families and 12.0% of the population were below the poverty line, including 16.5% of those under age 18 and 7.0% of those age 65 or over. 29.4% of the population had a bachelor's degree or higher.


title: Billings, Montana

text: Billings' location was essential to its economic success. Billings future as a major trade and distribution center was basically assured from its founding as a railroad hub due to its geographic location. As Billings quickly became the region's economic hub, it outgrew the other cities in the region. The Billings trade area serves over a half million people. A major trade and distribution center, the city is home to many regional headquarters and corporate headquarters. With Montana having no sales tax, Billings is a retail destination for much of Wyoming, North and South Dakota as well as much of Montana east of the Continental Divide. $1 out of every $7 spent on retail purchases in Montana is being spent in Billings. The percentage of wholesale business transactions done in Billings is even stronger: Billings accounts for more than a quarter of the wholesale business for the entire state (these figures do not include Billings portion of sales for Wyoming and the Dakotas). Billings is an energy center; Billings sits amidst the largest coal reserves in the United States as well as large oil and natural gas fields.


title: Billings, Montana

text: In 2009, "Fortune Small Business" magazine named Billings the best small city in which to start a business. Billings has a diverse economy including a large and rapidly growing medical corridor that includes inpatient and outpatient health care. Billings has a large service sector including retail, hospitality and entertainment. The metro area is also home to 3 oil refineries, a sugar beet refining plant, commercial and residential construction, building materials manufacturing and distribution, professional services, financial services, banking, trucking, higher education (4 campuses, 19 others have a physical presence/classes), auto parts wholesaling and repair services, passenger and cargo air, cattle, media, printing, wheat and barley farming, milk processing, heavy equipment sales and service, business services, consumer services, food distribution, agricultural chemical manufacturing and distribution, energy exploration and production, surface and underground mining, metal fabrication, and many others providing a diverse and robust economy.


title: Billings, Montana

text: Corporate headquarters include Stillwater Mining Company, Kampgrounds of America, First Interstate Bank, and others.


title: Billings, Montana

text: The Alberta Bair Theater is a 1,400-seat performing arts venue noted for its 20-ton capacity hydraulic lift that raises and lowers the stage apron. Opened in 1931 and originally called the Fox Theater, it was renamed in 1987 in honor of Alberta Bair and her substantial donations that helped fund the building's renovation. Her father, Charles M. Bair, homesteaded the land the theater now occupies and she was born in a nearby house that still stands today.


title: Billings, Montana

text: Built in 1950, the Shrine Auditorium is a smaller, cost-effective venue that hosts national shows. It seats 2,340 for concerts and offers 550 off-street parking spots.


title: Billings, Montana

text: Dehler Park is the new multi-use stadium that replaced Cobb Field and Athletic Park swimming pool in the summer of 2008. Cobb Field was a baseball stadium that was the home of the Billings Mustangs, the Pioneer League Rookie Affiliate of the Cincinnati Reds, from 1948 through 2007. Cobb Field was named after Bob Cobb, who was responsible for bringing professional baseball with the Mustangs to Billings. Cobb Field also hosted home games for local American Legion baseball teams. In 2006, Billings voters approved $12 million to be spent on constructing a new multi-use sports facility. Cobb Field was demolished in 2007 and construction of Dehler Park began at the end of the 2007 baseball season. The park debuted on June 29, 2008, when the Billings Scarlets faced the Bozeman Bucks in American Legion regular-season play. The new Dehler Park has a capacity of 3,500 to over 6,000.


title: Billings, Montana

text: Wendy's Field at Daylis Stadium is a local stadium used for high school games. It is next to Billings Senior High.


title: Billings, Montana

text: Centennial Ice Arena is home to the Billings Amateur Hockey League, Figure Skating Clubs and Adult Hockey.


title: Billings, Montana

text: The Babcock Theater is a 750-seat performing arts theater in Billings, Montana. It was built in 1907 and at the time was considered the largest theater between Minneapolis and Seattle. Today, after extensive renovations, it hosts a variety of national acts.


title: Billings, Montana

text: This 4,000-seat venue primarily hosts Yellowjacket sports, local events and some national touring events. This facility has gyms and racket ball courts as well as an Olympic-size pool with bleachers for aquatic events.


title: Billings, Montana

text: Fortin Center is a 3,000-seat arena on the campus of Rocky Mountain College it is primarily used for the Rocky Mountain sports events.


title: Billings, Montana

text: With eight microbreweries in the metropolitan area, Billings has more breweries than any community in Montana. The downtown breweries are, Yellowstone Valley Brewing Co., Thirsty Street Tap Room, Angry Hank's Tap Room, Carters Brewery, and Überbrew. Another nearby brewery, Red Lodge Ales Brewing Co., is in Red Lodge. Downtown Billings also has a distillery that makes a variety of handcrafted spirits. Trailhead Spirits is in the former train depot complex. Canyon Creek Brewery opened at the end of 2013 on Billings' west end. Another offering, the Last Chance Pub, opened downtown in 2016.


title: Billings, Montana

text: Billings is the county seat of Yellowstone County, the most populous county in Montana. It is also the location of the James F. Battin Federal Courthouse, one of five federal courthouses for the District of Montana.


title: Billings, Montana

text: Billings is governed via the mayor council system. There are ten members of the city council who are elected from one of five wards with each ward electing two members. The mayor is elected in a citywide vote. Both the mayor and council members are officially nonpartisan. The city charter, also called the Billings, Montana City Code (BMCC) was established 1977.


title: Billings, Montana

text: Unlike some other cities in Montana, Billings' city ordinances do not contain provisions that forbid discrimination on the basis of sexual orientation or gender identity. An effort to pass a non-discrimination ordinance in Billings failed in 2014, after then-mayor Tom Hanel cast a tie-breaking vote against it at the conclusion of a meeting that lasted 8.5 hours. An effort to introduce an NDO measure to the City Council was briefly floated in September 2019 by a city council member, but was abandoned approximately a month later.


title: Billings, Montana

text: Billings has five school districts: Billings Public Schools, District 3, Elder Grove School District, Independent School District, and Canyon Creek School District. Billings Public Schools consists of 22 elementary schools, six middle schools, and three high schools (Senior High, Skyview High, and West High) that have approximately 15,715 students and 1,850 full-time employees. District 3, Independent, and Elder Grove School Districts each have one elementary school, those being Blue Creek Elementary, Elder Grove Elementary, and Independent Elementary, respectively. Canyon Creek School District operates Canyon Creek School, which serves grades K-8.


title: Billings, Montana

text: Billings has three institutions of higher learning. Montana State University Billings (MSU Billings) is part of the state university system, while Rocky Mountain College and Yellowstone Baptist College are private.


title: Billings, Montana

text: Montana State University Billings was founded in 1927 as Eastern Montana Normal College to train teachers. The name was shortened to Eastern Montana College in 1949, and it was given its present name when the Montana State University System reorganized in 1994. The university offers associate/bachelor's/master's degrees and certificates in fields such as business, education, and medicine. Around 5,000 students attend MSU Billings.


title: Billings, Montana

text: City College at MSU Billings was established in 1969 as the Billings Vocational-Technical Education Center. Its governance was passed to the Montana University System Board of Regents in 1987, when it became known as the College of Technology. It was officially merged with MSU Billings (then known as Eastern Montana College) in 1994. The name was changed to the present name in 2012. Known as the "comprehensive two-year college arm" of MSU Billings, the college offers degrees and programs in a variety of fields, including automotive, business, computer technology, and nursing.


title: Billings, Montana

text: Through the marriage of three institutions of higher learning Rocky Mountain College is Montana's oldest college. Rocky Mountain College (or RMC) was founded in 1878. The campus that became RMC was known as the Billings Polytechnic Institute until 1947, when it joined the Montana Collegiate Institute in Deer Lodge (Montana's first institution of higher learning) and Intermountain Union College in Helena to form to Rocky Mountain College. During the 2013 fall semester, there were 1,068 students attending Rocky Mountain College. The college offers 50 majors offered in 24 different fields including art, education, music, psychology, and theater. RMC is affiliated with the United Church of Christ, the United Methodist Church, and the Presbyterian Church (U.S.A.).


title: Billings, Montana

text: Yellowstone Baptist College is a small private Christian college in western Billings. It offers one degree: Bachelor of Arts in Christian Studies/Leadership. The YBC is affiliated with the Southern Baptist Convention and has close ties with Oklahoma Baptist University in Shawnee, Oklahoma. The YBC also plans to open a nondenominational branch called the Yellowstone Bible Institute in early 2013.


title: Billings, Montana

text: The largest media market in Montana and Wyoming, Billings is serviced by a variety of print media. Newspaper service includes the "Billings Gazette", a daily morning broadsheet newspaper printed in Billings, Montana, and owned by Lee Enterprises. It is the largest daily newspaper in Montana, with a Sunday circulation of 52,000 and a weekday circulation of 47,000. It publishes three editions: the state edition, which circulates in most of Eastern Montana and all of South Central Montana; the Wyoming edition, which circulates in Northern Wyoming; and the city edition, which circulates in Yellowstone County. "Yellowstone County News" is the next leading print newspaper, owned by Jonathan & Tana McNiven. It is published on a weekly basis and provides news and columns for "Yellowstone County and the communities of Lockwood, Shepherd, Huntley, Worden, Ballanatine, Pompey's Pillar, Custer and Billings." It is also recognized as the Publication of Record for both the City of Billings and Yellowstone County. Other publications include other more specialized weekly and monthly publications. Billings also has several community magazines including "Magic City Magazine" and "Yellowstone Valley Woman".


title: Billings, Montana

text: The Billings Beet also provides the region with satirical news. The Billings area has four major non-news television stations, two major news television stations, one community television station, four PBS channels and several Low-Power Television (LPTV) channels. It is also served by twenty-two commercial radio stations and Yellowstone Public Radio (NPR).


title: Billings, Montana

text: Billings Logan International Airport is close to downtown; it sits on top of the Rims, a cliff that overlooks the downtown core. Scheduled passenger service and air cargo flights operate from this airfield.


title: Billings, Montana

text: The Laurel Municipal Airport is a publicly owned public-use airport in Laurel, Montana, southwest of downtown Billings. It has three runways exclusively serving privately operated general aviation aircraft and helicopters.


title: Billings, Montana

text: The Billings METropolitan Transit is Billings' public transit system. MET Transit provides fixed-route and paratransit bus service to the City of Billings. All MET buses are accessible by citizens who use wheelchairs and other mobility devices. They are wheelchair lift-equipped and accessible to all citizens who are unable to use the stairs. MET buses are equipped with bike racks for their bike-riding passengers. There are Westend and Downtown transit centers allowing passengers to connect with all routes. The Billings Bus Terminal is served by Express Arrow, Greyhound and Jefferson Lines which also provide regional and interstate bus service.


title: Billings, Montana

text: Billings has an extensive trail system running throughout the metro area. The rapidly expanding trail system, known as the Heritage trail system, has a large variety of well-maintained trails and pathways.


title: Billings, Montana

text: "Bicycling" magazine ranked Billings among the nation's 50 most bike-friendly communities. In 2012, the Swords Park Trail was named the Montana State Trail of the Year and received an Environmental and Wildlife Compatibility award from the Coalition for Recreational Parks.


title: Billings, Montana

text: Interstate 90 runs east–west through the southern portion of Billings, serving as a corridor between Billings Heights, Lockwood, Downtown, South Hills, Westend, Shiloh, and Laurel. East of Downtown, between Billings Heights and Lockwood, Interstate 90 connects with Interstate 94, which serves as an east–west corridor between Shepherd, Huntley, Lockwood, Downtown, South Hills, Westend, Shiloh, and Laurel via its connection with I-90.


title: Billings, Montana

text: The 2012 Billings area I-90 corridor planning study recommends many improvements to the corridor from Laurel through Lockwood. Among the improvements recommended are construction of new east and west bound bridges over the Yellowstone River, each bridge having three to four traffic lanes. Also recommended are construction of additional east and west bound traffic lanes from Shiloh to Johnson Lane and reconstruction of many of the bridges, interchanges and on-off ramps along the corridor at a cost of $114 million.


title: Billings, Montana

text: The Billings Bypass is a project designed to offer an alternative route into Billings Heights, to create a new and more direct connection between Billings and Lockwood and to connect I-90 with Montana Highway 87 and Old Highway 312. The study portion of the project is nearing its completion. Right of way acquisition should begin in 2013 along with final design followed by construction.


title: Billings, Montana

text: Montana Highway 3 is a north–south highway that runs along the edge of the North Rims connecting Downtown and the Westend with the Rehberg Ranch, Indian Cliffs and Billings Heights. U.S. Highway 87 runs through the center of Billings Heights and is known as Main Street within the city limits. This is the busiest section of roadway in the state of Montana. It connects to U.S. Highway 87 East, which runs through Lockwood as Old Hardin Road.


title: Billings, Montana

text: There is currently no service, though until 1979 Amtrak's "North Coast Hiawatha" stopped at the Billings Depot, serving a Chicago to Seattle route. Before Amtrak, Billings was well-served by Northern Pacific, Great Northern, and Chicago, Burlington, and Quincy railroads with direct routes to Kansas City, Denver, Chicago, Great Falls, and the West Coast. (Billings was the northern and western terminus for the Chicago, Burlington and Quincy Railroad).


title: Billings, Montana

text: The city's rapidly growing health care sector employed nearly 13,000 people in 2012; they earned $641 million in wages, or about 20 percent of all wages in the city. Employment doubled in 25 years and wage rates in constant dollars grew by 162 percent.


title: Billings, Montana

text: St. Vincent Healthcare was founded in 1898 by the Sisters of Charity of Leavenworth as St. Vincent Hospital. The name was changed to the present name in 2000. The hospital and its 30 clinics employ approximately 2,100 people and receive more than 400,000 patient visits each year. St. Vincent Healthcare is run by the Sisters of Charity of Leavenworth Health System, which operates health care facilities in Colorado, Kansas, and Montana.


title: Billings, Montana

text: Billings Clinic started in 1911 as the general practice of Dr. Arthur J. Movius. By 1939, three new general practitioners had joined Dr. Movius's practice and the name was changed to The Billings Clinic. Billings Deaconess Hospital (founded in 1907) merged with Billings Clinic in 1990 to form the current hospital. Billings Clinic now employs around 3,400 people and is one of the largest employers in Montana. In July 2012, Billings Clinic received a score of 72/100 for patient safety from Consumer Reports, making it the safest hospital of the 1,159 hospitals rated. Additionally, in January 2013, Billings Clinic was added to the Mayo Clinic Care Network, only the 12th hospital nationally to be added to the network and the only such health system in Montana.


title: Billings, Montana

text: Other medical facilities include the Northern Rockies Radiation Oncology Center, Rimrock Foundation (addiction treatment both inpatient and outpatient), Advanced Care Hospital of Montana (a 40-bed long-term acute-care hospital), South Central Montana Mental Health Center, Billings VA Community-Based Outpatient Clinic, Billings Clinic Research Center (pharmaceutical field trials, osteoporosis are two long-time focuses), Billings MRI, City/County Public Health's Riverstone Health, HealthSouth Surgery Center and Physical Therapy offices, Baxter/Travenol BioLife plasma collection center, and many independent practices.


title: Billings, Montana

text: The Billings Police Department is the main law enforcement agency in Billings. It is the largest city police force in Montana, with about 136 sworn officers and 80 civilian employees. There are nine police beats.


title: Billings, Montana

text: The Billings Fire Department was founded in 1883 as a volunteer fire company named the Billings Fire Brigade. The Yellowstone Hook and Ladder Company was founded in 1886; that company was disbanded in 1888 after the mayor criticized the group for how that handled a fire, leaving the town without a fire department for almost six months. The last volunteer fire company, Maverick Hose Company, served as the city's fire department until 1918. The modern fire department has seven stations, employs 114 people, and received a class three rating by ISO.


title: Billings, Montana

text: The tallest building in Billings and Montana as well as a five-state region is the First Interstate Center, which stands at and 20 floors above ground level. Billings is also home to the world's tallest load-bearing brick building, the DoubleTree Tower, which stands . With a floor count of 22 floors above ground level, the Crowne Plaza is the tallest hotel in the city and state. It was the tallest from 1980 to 1985. The Wells Fargo Building, formerly the Norwest Bank Building, was the tallest building in Montana from 1977 until 1980.


title: SWIFT

text: The Society for Worldwide Interbank Financial Telecommunication (SWIFT), legally S.W.I.F.T. SC, is a Belgian cooperative society providing services related to the execution of financial transactions and payments between banks worldwide. Its principal function is to serve as the main messaging network through which international payments are initiated. It also sells software and services to financial institutions, mostly for use on its proprietary "SWIFTNet", and assigns ISO 9362 Business Identifier Codes (BICs), popularly known as "SWIFT codes".


title: SWIFT

text: The SWIFT messaging network is a component of the global payments system. SWIFT acts as a carrier of the "messages containing the payment instructions between financial institutions involved in a transaction". However, the organization does not manage accounts on behalf of individuals or financial institutions, and it does not hold funds from third parties. It also does not perform clearing or settlement functions. After a payment has been initiated, it must be settled through a payment system, such as TARGET2 in Europe. In the context of cross-border transactions, this step often takes place through correspondent banking accounts that financial institutions have with each other.


title: SWIFT

text: As of 2018, around half of all high-value cross-border payments worldwide used the SWIFT network, and in 2015, SWIFT linked more than 11,000 financial institutions in over 200 countries and territories, who were exchanging an average of over 32 million messages per day (compared to an average of 2.4 million daily messages in 1995).


title: SWIFT

text: Though widely utilized, SWIFT has been criticized for its inefficiency. In 2018, the London-based "Financial Times" noted that transfers frequently "pass through multiple banks before reaching their final destination, making them time-consuming, costly and lacking transparency on how much money will arrive at the other end". SWIFT has since introduced an improved service called "Global Payments Innovation" (GPI), claiming it was adopted by 165 banks and was completing half its payments within 30 minutes.


title: SWIFT

text: As a cooperative society under Belgian law, SWIFT is owned by its member financial institutions. It is headquartered in La Hulpe, Belgium, near Brussels; its main building was designed by Ricardo Bofill Taller de Arquitectura and completed in 1989. The chairman of SWIFT is Yawar Shah of Pakistan, and its CEO is Javier Pérez-Tasso of Spain. SWIFT hosts an annual conference, called Sibos, specifically aimed at the financial services industry.


title: SWIFT

text: SWIFT was founded in Brussels on 3 May 1973 under the leadership of its inaugural Swedish CEO, Carl Reuterskiöld (1973–1989), a former employee at Wallenberg-owned Skandinaviska Enskilda Banken, and was supported by 239 banks in 15 countries. Before its establishment, international financial transactions were communicated over Telex, a public system involving manual writing and reading of messages. It was set up out of fear of what might happen if a single private and fully American entity controlled global financial flows – which before was First National City Bank (FNCB) of New York – later Citibank. In response to FNCB's protocol, FNCB's competitors in the US and Europe pushed an alternative "messaging system that could replace the public providers and speed up the payment process". SWIFT started to establish common standards for financial transactions and a shared data processing system and worldwide communications network designed by Logica and developed by the Burroughs Corporation. Fundamental operating procedures and rules for liability were established in 1975, and the first message was sent in 1977. SWIFT's first international (non-European) operations centre was inaugurated by Governor John N. Dalton of Virginia in 1979.


title: SWIFT

text: SWIFT has become the industry standard for syntax in financial messages. Messages formatted to SWIFT standards can be read and processed by many well-known financial processing systems, whether or not the message travelled over the SWIFT network. SWIFT cooperates with international organizations for defining standards for message format and content. SWIFT is also "Registration authority" (RA) for the following ISO standards:


title: SWIFT

text: In RFC 3615 "<nowiki>urn:swift:</nowiki>" was defined as Uniform Resource Names (URNs) for SWIFT FIN.


title: SWIFT

text: The SWIFT secure messaging network is run from three data centres, located in the United States, the Netherlands, and Switzerland. These centres share information in near real-time. In case of a failure in one of the data centres, another is able to handle the traffic of the complete network. SWIFT uses submarine communications cables to transmit its data.


title: SWIFT

text: Shortly after opening its third data centre in Switzerland in 2009, SWIFT introduced new distributed architecture with two messaging zones, European and Trans-Atlantic, so data from European SWIFT members no longer mirrored the U.S. data centre. European zone messages are stored in the Netherlands and in part of the Swiss operating centre; Trans-Atlantic zone messages are stored in the United States and in another part of the Swiss operating centre that is segregated from the European zone messages. Countries outside of Europe were by default allocated to the Trans-Atlantic zone, but could choose to have their messages stored in the European zone.


title: SWIFT

text: SWIFT moved to its current IP network infrastructure, known as SWIFTNet, from 2001 to 2005, providing a total replacement of the previous X.25 infrastructure. The process involved the development of new protocols that facilitate efficient messaging, using existing and new message standards. The adopted technology chosen to develop the protocols was XML, where it now provides a wrapper around all messages legacy or contemporary. The communication protocols can be broken down into:


title: SWIFT

text: SWIFT provides a centralized store-and-forward mechanism, with some transaction management. For bank A to send a message to bank B with a copy or authorization involving institution C, it formats the message according to standards and securely sends it to SWIFT. SWIFT guarantees its secure and reliable delivery to B after the appropriate action by C. SWIFT guarantees are based primarily on high redundancy of hardware, software, and people.


title: SWIFT

text: During 2007 and 2008, the entire SWIFT network migrated its infrastructure to a new protocol called SWIFTNet Phase 2. The main difference between Phase 2 and the former arrangement is that Phase 2 requires banks connecting to the network to use a Relationship Management Application (RMA) instead of the former bilateral key exchange (BKE) system. According to SWIFT's public information database on the subject, RMA software should eventually prove more secure and easier to keep up-to-date; however, converting to the RMA system meant that thousands of banks around the world had to update their international payments systems to comply with the new standards. RMA completely replaced BKE on 1 January 2009.


title: SWIFT

text: Under 3 above, SWIFT provides turn-key solutions for members, consisting of linkage clients to facilitate connectivity to the SWIFT network and CBTs or "computer based terminals" which members use to manage the delivery and receipt of their messages. Some of the more well-known interfaces and CBTs provided to their members are:


title: SWIFT

text: There are four key areas that SWIFT services fall under in the financial marketplace: securities, treasury & derivatives, trade services. and payments-and-cash management.


title: SWIFT

text: Swift Ref, the global payment reference data utility, is SWIFT's unique reference data service. Swift Ref sources data direct from data originators, including central banks, code issuers and banks making it easy for issuers and originators to maintain data regularly and thoroughly. SWIFTRef constantly validates and cross-checks data across the different data sets.


title: SWIFT

text: SWIFT offers a secure person-to-person messaging service, SWIFTNet Mail, which went live on 16 May 2007. SWIFT clients can configure their existing email infrastructure to pass email messages through the highly secure and reliable SWIFTNet network instead of the open Internet. SWIFTNet Mail is intended for the secure transfer of sensitive business documents, such as invoices, contracts and signatories, and is designed to replace existing telex and courier services, as well as the transmission of security-sensitive data over the open Internet. Seven financial institutions, including HSBC, FirstRand Bank, Clearstream, DnB NOR, Nedbank, and Standard Bank of South Africa, as well as SWIFT piloted the service.


title: SWIFT

text: A series of articles published on 23 June 2006 in "The New York Times", "The Wall Street Journal", and the "Los Angeles Times" revealed a program, named the Terrorist Finance Tracking Program, which the US Treasury Department, Central Intelligence Agency (CIA), and other United States governmental agencies initiated after the 11 September attacks to gain access to the SWIFT transaction database.


title: SWIFT

text: After the publication of these articles, SWIFT quickly came under pressure for compromising the data privacy of its customers by allowing governments to gain access to sensitive personal information. In September 2006, the Belgian government declared that these SWIFT dealings with American governmental authorities were a breach of Belgian and European privacy laws.


title: SWIFT

text: In response, and to satisfy members' concerns about privacy, SWIFT began a process of improving its architecture by implementing a distributed architecture with a two-zone model for storing messages (see Operations centres).


title: SWIFT

text: Concurrently, the European Union negotiated an agreement with the United States government to permit the transfer of intra-EU SWIFT transaction information to the United States under certain circumstances. Because of concerns about its potential contents, the European Parliament adopted a position statement in September 2009, demanding to see the full text of the agreement and asking that it be fully compliant with EU privacy legislation, with oversight mechanisms emplaced to ensure that all data requests were handled appropriately. An interim agreement was signed without European Parliamentary approval by the European Council on 30 November 2009, the day before the Lisbon Treaty—which would have prohibited such an agreement from being signed under the terms of the codecision procedure—formally came into effect. While the interim agreement was scheduled to come into effect on 1 January 2010, the text of the agreement was classified as "EU Restricted" until translations could be provided in all EU languages and published on 25 January 2010.


title: SWIFT

text: On 11 February 2010, the European Parliament decided to reject the interim agreement between the EU and the US by 378 to 196 votes. One week earlier, the parliament's civil liberties committee had already rejected the deal, citing legal reservations.


title: SWIFT

text: In March 2011, it was reported that two mechanisms of data protection had failed: EUROPOL released a report complaining that requests for information from the US had been too vague (making it impossible to make judgments on validity) and that the guaranteed right for European citizens to know whether their information had been accessed by US authorities had not been put into practice.


title: SWIFT

text: "Der Spiegel" reported in September 2013 that the National Security Agency (NSA) widely monitors banking transactions via SWIFT, as well as credit card transactions. The NSA intercepted and retained data from the SWIFT network used by thousands of banks to securely send transaction information. SWIFT was named as a "target", according to documents leaked by Edward Snowden. The documents revealed that the NSA spied on SWIFT using a variety of methods, including reading "SWIFT printer traffic from numerous banks". In April 2017, a group known as the Shadow Brokers released files allegedly from the NSA which indicate that the agency monitored financial transactions made through SWIFT.


title: SWIFT

text: The European Union issued the first set of sanctions against Belarus - the first was introduced on 27 February 2022, which banned certain categories of Belarusian items in the EU, including timber, steel, mineral fuels and tobacco. After the Lithuanian prime minister proposed disconnecting Belarus from SWIFT, the European Union, which does not recognise Lukashenko as the legitimate President of Belarus, started to plan an extension of the sanctions already issued against Russian entities and top officials to its ally.


title: SWIFT

text: In January 2012, the advocacy group United Against Nuclear Iran (UANI) implemented a campaign calling on SWIFT to end all relations with Iran's banking system, including the Central Bank of Iran. UANI asserted that Iran's membership in SWIFT violated US and EU financial sanctions against Iran as well as SWIFT's own corporate rules.


title: SWIFT

text: Consequently, in February 2012, the U.S. Senate Banking Committee unanimously approved sanctions against SWIFT aimed at pressuring it to terminate its ties with blacklisted Iranian banks. Expelling Iranian banks from SWIFT would potentially deny Iran access to billions of dollars in revenue using SWIFT but not from using IVTS. Mark Wallace, president of UANI, praised the Senate Banking Committee.


title: SWIFT

text: Initially SWIFT denied that it was acting illegally, but later said that "it is working with U.S. and European governments to address their concerns that its financial services are being used by Iran to avoid sanctions and conduct illicit business". Targeted banks would be—amongst others—Saderat Bank of Iran, Bank Mellat, Post Bank of Iran and Sepah Bank. On 17 March 2012, following agreement two days earlier between all 27 member states of the Council of the European Union and the Council's subsequent ruling, SWIFT disconnected all Iranian banks that had been identified as institutions in breach of current EU sanctions from its international network and warned that even more Iranian financial institutions could be disconnected from the network.


title: SWIFT

text: In February 2016, most Iranian banks reconnected to the network following the lift of sanctions due to the Joint Comprehensive Plan of Action.


title: SWIFT

text: Similarly, in August 2014 the UK planned to press the EU to block Russian use of SWIFT as a sanction due to Russian military intervention in Ukraine. However, SWIFT refused to do so. SPFS, a Russia-based SWIFT equivalent, was created by the Central Bank of Russia as a backup measure.


title: SWIFT

text: During the 2021–2022 Russo-Ukrainian crisis, the United States developed preliminary possible sanctions against Russia, but excluded banning Russia from SWIFT. Following the 2022 Russian invasion of Ukraine, the foreign ministers of Lithuania, Latvia, and Estonia called for Russia to be cut off from SWIFT. However, other EU member states were reluctant, both because European lenders held most of the nearly $30 billion in foreign banks' exposure to Russia and because Russia had developed the SPFS alternative. The European Union, United Kingdom, Canada, and the United States finally agreed to remove select Russian banks from the SWIFT messaging system in response to the 2022 Russian invasion of Ukraine; the governments of France, Germany, Italy and Japan individually released statements alongside the EU.


title: SWIFT

text: In 2014, SWIFT rejected calls from pro-Palestinian activists to revoke Israeli banks' access to its network.


title: SWIFT

text: In 2016 an $81 million theft from the Bangladesh central bank via its account at the New York Federal Reserve Bank was traced to hacker penetration of SWIFT's Alliance Access software, according to a "New York Times" report. It was not the first such attempt, the society acknowledged, and the security of the transfer system was undergoing new examination accordingly. Soon after the reports of the theft from the Bangladesh central bank, a second, apparently related, attack was reported to have occurred on a commercial bank in Vietnam.


title: SWIFT

text: Both attacks involved malware written to both issue unauthorized SWIFT messages and to conceal that the messages had been sent. After the malware sent the SWIFT messages that stole the funds, it deleted the database record of the transfers then took further steps to prevent confirmation messages from revealing the theft. In the Bangladeshi case, the confirmation messages would have appeared on a paper report; the malware altered the paper reports when they were sent to the printer. In the second case, the bank used a PDF report; the malware altered the PDF viewer to hide the transfers.


title: SWIFT

text: In May 2016, Banco del Austro (BDA) in Ecuador sued Wells Fargo after Wells Fargo honoured $12 million in fund transfer requests that had been placed by thieves. In this case, the thieves sent SWIFT messages that resembled recently cancelled transfer requests from BDA, with slightly altered amounts; the reports do not detail how the thieves gained access to send the SWIFT messages. BDA asserts that Wells Fargo should have detected the suspicious SWIFT messages, which were placed outside of normal BDA working hours and were of an unusual size. Wells Fargo claims that BDA is responsible for the loss, as the thieves gained access to the legitimate SWIFT credentials of a BDA employee and sent fully authenticated SWIFT messages.


title: SWIFT

text: In the first half of 2016, an anonymous Ukrainian bank and others—even "dozens" that are not being made public—were variously reported to have been "compromised" through the SWIFT network and to have lost money.


title: SWIFT

text: In March 2022, Swiss newspaper "Neue Zürcher Zeitung" reported about the increased security precautions by the State Police of Thurgau at the SWIFT data centre in Diessenhofen. After most of the Russian banks have been excluded from the private payment system, the risk of sabotage was considered higher. Inhabitants of the town described the large complex as a "fortress" or "prison" where frequent security check of the fenced property are conducted.


title: Vineeth Sreenivasan

text: Vineeth Sreenivasan (born 1 October 1984) is an Indian playback singer, actor, film director, screenwriter, producer, lyricist, creative director and dubbing artist. He predominantly works in the Malayalam cinema. He is the son of actor and screenwriter Sreenivasan.


title: Vineeth Sreenivasan

text: Vineeth Sreenivasan is the eldest son of Malayalam screenwriter and actor Sreenivasan and Vimala. He completed his primary education from nursery to 10th standard at Rani Jai Higher Secondary School. He graduated in mechanical engineering from KCG College of Technology, Chennai.


title: Vineeth Sreenivasan

text: He made his acting debut playing one of the main protagonists in the Malayalam film "Cycle", which did well at the box office. He did his second movie role with his father in the movie "Makante Achan".


title: Vineeth Sreenivasan

text: Vineeth won the AMMA Best Male Singer Award 2008 for his songs "Mampullikkavil" and "Jillu Jillu" and also the Best Male new face of the year 2008 by Asianet, for his role in "Cycle". Vineeth wrote the script and Lyrics and debuted as director for the movie "Malarvadi Arts Club" with seven new young actors. He won the Asiavision award for the best debutant director for Malarvadi Arts Club. "Thattathin Marayathu" is the second movie in which he was the screenwriter, director and playback singer. His third movie "Thira" was released in 2013, in which he introduced his younger brother Dhyan Sreenivasan.


title: Vineeth Sreenivasan

text: Vineeth married Divya Narayanan on 18 October 2012, after an eight-year-long relationship since 30 March 2004. She was his junior at KCG College of Technology in Chennai. The couple had a son Vihaan Divya Vineeth on 30 June 2017.


title: Vineeth Sreenivasan

text: Editor Ranjan Abraham, music composer Shaan Rahman, cinematographer Jomon T. John, and actor Aju Varghese have worked on five movies. Sreenivasan, Nivin Pauly, and Deepak Parambol acted in three films.


title: Union Public Service Commission

text: The Union Public Service Commission (ISO: ), commonly abbreviated as UPSC, is India's premier central recruitment agency for recruitment of all the Group 'A' officers under Government of India . It is responsible for appointments to and examinations for all of the Group 'A' posts of all the central government establishments which also includes all of the central public sector undertakings and all of the central autonomous bodies. While Department of Personnel and Training is the central personnel agency in India.


title: Union Public Service Commission

text: The agency's charter is granted by Part XIV of the Constitution of India, titled as "Services Under the Union and the States." The commission is mandated by the Constitution for appointments to the services of the Union and All India Services. It is also required to be consulted by the Government in matters relating to the appointment, transfer, promotion and disciplinary matters. The commission reports directly to the President and can advise the Government through him. Although, such advice is not binding on the Government. Being a constitutional authority, UPSC is amongst the few institutions which function with both autonomy and freedom, along with the country’s higher judiciary and lately the Election Commission.


title: Union Public Service Commission

text: The commission is headquartered at Dholpur House, in New Delhi and functions through its own secretariat. Dr. Manoj Soni has been the Chairman of UPSC since 5 April 2022.


title: Union Public Service Commission

text: Established on 1 October 1926 as Public Service Commission, it was later reconstituted as Federal Public Service Commission by the Government of India Act 1935; only to be renamed as today's Union Public Service Commission after the independence.


title: Union Public Service Commission

text: The Royal Commission on the superior Civil Services in India was set up under the chairmanship of Lord Lee of Fareham by the British Government in 1923. With equal numbers of Indian and British members, the commission submitted its report in 1924, recommending setting up of a Public Service Commission. The Lee Commission proposed that 40% of future entrants should be British, 40% Indians directly recruited, and 20% Indians promoted from the provincial services.


title: Union Public Service Commission

text: This led to the establishment of the first Public Service Commission on 1 October 1926 under the chairmanship of Sir Ross Barker. A mere limited advisory function was granted to the Public Service Commission and the leaders of the freedom movement continually stressed on this aspect, which then resulted in the setting up of a Federal Public Service Commission under the Government of India Act 1935.


title: Union Public Service Commission

text: The Federal Public Service Commission became the Union Public Service Commission after independence. It was given a constitutional status with under of Constitution of India on 26 January 1950.


title: Union Public Service Commission

text: Articles 315 to 323 of Part XIV of the constitution, titled as "Services Under the Union and the States", provide for a Public Service Commission for the Union and for each state. Accordingly, as per "Art. 315", at Union level, Union Public Service Commission is envisaged by it. UPSC is amongst the few institutions which function with both autonomy and freedom, along with the country’s higher judiciary and lately the Election Commission.


title: Union Public Service Commission

text: As per "Art. 316", the Chairman and other members of Union Public Service Commission shall be appointed by the President. In case the office of the Chairman becomes vacant his duties shall be performed by one of the other members of the Commission as the President may appoint for the purpose.


title: Union Public Service Commission

text: Also, nearly half of the members of the Commission shall be persons who at the dates of their respective appointments have held office for at least ten years either under the Government of India or under the Government of a State. A member of a Union Public Service Commission shall hold office for a term of six years from the date on which he enters upon his office or until he attains the age of sixty-five years, whichever is earlier. Under "Art 318," the President is empowered to determine number of members of the Commission and their conditions of service. Further, he can make provision with respect to the number of members of the staff of the Commission and their conditions of service too. Also, conditions of service cannot be varied to his disadvantage after his appointment.


title: Union Public Service Commission

text: As per "Art 319", a person who holds office as Chairman shall, on the expiration of his term of office, be ineligible for re-appointment to that office. But, a member other than the Chairman of the Union Public Service Commission shall be eligible for appointment as the Chairman of the Union Public Service Commission, or as the Chairman of a State Public Service Commission, but not for any other employment either under the Government of India or under the Government of a State. Also, the Chairman of a State Public Service Commission shall be eligible for appointment as the Chairman or any other member of the Union Public Service Commission.


title: Union Public Service Commission

text: As per "Art. 317", the Chairman or any other member of a Public Service Commission shall only be removed from their office by order of the President on the ground of "misbehaviour" after the Supreme Court, on reference being made to it by the President, has, on inquiry reported that the Chairman or such other member ought to be removed. The President may suspend the Chairman or other member of the Commission until report of the Supreme Court is received.


title: Union Public Service Commission

text: As per "Art. 320," it shall be the duty of the Union Public Service Commissions to conduct examinations for appointments to the services of the Union. It shall also assist two or more States, if requested so, in framing and operating schemes of joint recruitment for any services.


title: Union Public Service Commission

text: It shall be the duty of a Union Public Service Commission to advise on any matter referred to them; provided that the President has not made any regulations specifying the matters in which it shall not be necessary for Union Public Service Commission to be consulted.


title: Union Public Service Commission

text: As per "Art. 322", the expenses of the Union Public Service Commission, including any salaries, allowances and pensions payable to or in respect of the members or staff of the Commission, shall be charged on the Consolidated Fund of India.


title: Union Public Service Commission

text: As per "Art. 321", an Act made by Parliament may provide for the exercise of additional functions by the Union Public Service Commission w.r.t. services of the Union.


title: Union Public Service Commission

text: As per "Art. 323", it will be the duty of the Union Commission to annually present a report to the President of the work done by the Commission. On receipt of such report, the President shall present a copy before each House of Parliament; together with a memorandum, if any, explaining the reasons where the advice of the Commission was not accepted by him.


title: Union Public Service Commission

text: The Commission consists of the chairman and other members appointed by The President of India. Usually, the Commission consists of 9 to 11 members including the chairman. Every member holds office for a term of six years or until he attains the age of sixty-five years, whichever is earlier.


title: Union Public Service Commission

text: The terms and conditions of service of chairman and members of the Commission are governed by the Union Public Service Commission (Members) Regulations, 1969.


title: Union Public Service Commission

text: The chairman and any other member of the Commission can submit his resignation at any time to the President of India. He may be removed from his office by the President of India on the ground of misbehaviour (only if an inquiry of such misbehavior is made and upheld by Supreme Court) or if he is adjudged insolvent, or engages during his term of office in any paid employment outside the duties of his office, or in the opinion of the President unfit to continue in office by reason of infirmity of mind or body.


title: Union Public Service Commission

text: The Commission is serviced by a Secretariat headed by a Secretary with four Additional Secretaries, a number of Joint Secretaries, Deputy Secretaries and other supporting staff. The secretariat, for administrative purpose, is further divided into divisions, each undertaking having a specific responsibility:


title: Union Public Service Commission

text: The institute is currently having seven members including the Chairman against its sanctioned strength of ten members.


The 2022 United States Senate election in Alaska was held on November 8, 2022. Incumbent three-term Republican U.S. Senator Lisa Murkowski won reelection to a fourth term, defeating fellow Republican Kelly Tshibaka and Democrat Patricia Chesbro.


title: 2022 United States Senate election in Alaska

text: After the voter approval of Ballot Measure 2 during the 2020 Alaska elections, this was the first U.S. Senate election in Alaska to be held under a new election process. All candidates ran in a nonpartisan blanket top-four primary on August 16, 2022, and the top four candidates advanced to the general election, where voters will utilize ranked-choice voting.


text: Murkowski was appointed to the Senate in 2002 by her father, Frank Murkowski, who served as a U.S. senator from Alaska from 1981 until he was elected to become Governor of Alaska. Murkowski has won three Senate elections since then, including a notable write-in campaign in the 2010 election, although she has never won an election with an outright majority of the vote.


text: Murkowski was the only Republican senator running for reelection in 2022 who voted to convict former president Donald Trump in his second impeachment trial in 2021. On March 16, 2021, the Alaska Republican Party voted to censure Murkowski and announced that it would recruit a Republican challenger in the 2022 election cycle. Following Murkowski's opposition to some of Trump's initiatives and her vote to convict him, Trump endorsed Tshibaka and campaigned against Murkowski. The Alaska Republican Party endorsed Tshibaka; Republican Senate leader Mitch McConnell and the National Republican Senatorial Committee supported Murkowski.


text: In addition to Murkowski and Tshibaka, Democrat Pat Chesbro and Republican Buzz Kelley also advanced to the general election. On September 13, Kelley suspended his campaign and endorsed Tshibaka. Murkowski received a plurality of first-place votes, but because no candidate received a majority of the votes in the first round, the instant runoff was triggered. Murkowski won reelection in the maximum round, winning most of the second-choice votes from Chesbro's voters. Murkowski is the only senator never to win a majority of the vote in the first round of a Senate election in three or more elections, as she only received a majority of votes in this election via the third round of ranked choice voting.


title: Boss Level

text: Boss Level is a 2020 American science fiction action film directed by Joe Carnahan and written by Carnahan and Chris and Eddie Borey, from a story by the Boreys. It stars Frank Grillo as a retired special forces soldier who tries to escape a never-ending time loop that results in his death. Mel Gibson, Naomi Watts and Michelle Yeoh co-star.


title: Boss Level

text: The film was originally announced in 2012 as "Continue", and was developed by Carnahan at 20th Century Fox, but it did not move forward. "Boss Level" was formally announced in November 2017, and was produced by Carnahan, Grillo, Randall Emmett and George Furla. Filming took place in Georgia from March to May 2018. The film was originally scheduled to be released by Entertainment Studios Motion Pictures on August 16, 2019, but was delayed. It was released in the United States on March 5, 2021, by Hulu.


title: Boss Level

text: Roy Pulver, a retired Delta Force soldier in Atlanta, has been stuck in a time loop, and has learned the day's patterns through many previous loops. He wakes at 07:00 AM each day, avoids an assassin in his apartment and an attack by a gunman in a helicopter outside his window, then escapes his apartment before it explodes. He has been able to elude more assassins throughout the morning, but finds himself unable to figure out how to survive a final attack at 12:47 PM, waking up back in his apartment on the next loop.


title: Boss Level

text: On the day before Roy entered the loop, his estranged wife Jemma had asked Roy to visit her at defense contractor Dynow Labs under the pretense of a job interview. The two argue over Joe, their son, whom Jemma has led to believe that Roy is just a family friend. When Colonel Clive Ventor, head of Dynow, discovers Roy near Jemma's highly classified project, he has him escorted out, but not before Jemma obtains a sample of Roy's hair.


title: Boss Level

text: In one loop, Roy tries to call Jemma but instead reaches Ventor, who tells him that Jemma died from a lab accident the day before. Roy becomes suspicious. On a later loop, he finds Joe at Underground Atlanta, skipping school for a video game tournament. Roy spends the day with Joe but does not mention Jemma's death. The assassins arrive to kill Roy, and Roy uses his body to protect Joe, telling him as he dies that he is his father.


title: Boss Level

text: When Roy next wakes, he realizes that the assassins had followed him using a dental tracking device implanted by Alice, his date from the night before (a dental hygienist). Through more trial-and-error loops, Roy finds a way to remove the tracker and sneak into Dynow, killing several guards and assassins, but is always stopped by Ventor. Ventor reveals to Roy that Jemma's project is the Osiris Spindle, a quantum device capable of rewriting history, which Ventor plans to use to set himself up as the world's dictator. Ventor admits he was responsible for Jemma's death after an argument the night before. As she had started the Spindle and no one else knows how to operate it, Ventor warns Roy the Spindle will destroy the world if it runs too long.


title: Boss Level

text: On further loops, Roy makes the connection to the Egyptian god of the afterlife, Osiris, and he realizes that Jemma must have placed him in the Spindle to stop Ventor. While he is able to further infiltrate Dynow and kill Ventor, Roy learns the assassins were sent to kill Joe, and arrives too late. As he mourns over Joe, the Osiris Spindle explodes and destroys the world.


title: Boss Level

text: Roy spends several loops in a despondent state, then decides to spend several more loops with Joe, staying with him until the Spindle's explosion. In one loop, he learns that Jemma had called Joe that morning, later than he previously thought she was still alive, and realizes he can save her. After determining the exact time and place she died at Ventor's hands in Dynow, fourteen minutes after he wakes up, Roy uses the next loop to hijack the helicopter, get to Dynow, kill the waiting assassins, and stop Ventor before he kills Jemma.


title: Boss Level

text: Roy tells Jemma he has been spending his loops with Joe, and that he has seen the end of the world. Jemma tells Roy that he has to enter the Osiris Spindle in order to reset it and prevent the world from ending but also warns that it may cause him to cease from existing. Roy kisses Jemma before entering the spindle as Jemma looks on in awe.


title: Boss Level

text: In addition, Sheaun McKinney plays Dave, the counter surveillance expert, and Armida Lopez plays Esmeralda the chauffeur while the remaining assassins are: Buster Reeves as Mr. Good Morning; Eric Etebari as Roy #2; Quinton "Rampage" Jackson and Rashad Evans as the German Twins; Adam Simon as Loudmouth; Aaron Beelner as Marshall / Kaboom; and Michael Tourek as Smiley. Director Joe Carnahan cameos as a patron in the bar.


title: Boss Level

text: In January 2012, Joe Carnahan announced that he was working on the film, originally titled "Continue", for 20th Century Fox, and described it as ""Groundhog Day" as an action movie", inspired by video game rules. In May 2012, it was reported that Fox was moving forward with the project. In September 2012, Carnahan posted screen tests that he had filmed with actor Frank Grillo on Twitter, saying he was sharing them "to show you how cool this movie could have been..."


title: Boss Level

text: In November 2017, it was reported that Grillo and Mel Gibson were negotiating to star in the film, now titled "Boss Level", with Carnahan writing and directing. Further casting continued in March 2018 with the additions of Will Sasso, Naomi Watts, Annabelle Wallis and Rob Gronkowski. Filming began that month in Savannah, Georgia. Ken Jeong, Mathilde Ollivier, Selina Lo and Michelle Yeoh joined the cast the following month.


title: Boss Level

text: In April 2018, filming took place in Atlanta, including in Pullman Yard, the Oakland City MARTA station, and near the Georgia Aquarium. Filming also took place in Decatur. A restaurant scene was filmed in Atlanta on May 12 and 13, 2018. On May 13, "Screen Daily" reported that filming had wrapped. The film's budget was $45 million.


title: Boss Level

text: In April 2018, Entertainment Studios Motion Pictures acquired U.S. distribution rights to the film. It was scheduled to be released on August 16, 2019, but missed its release date.<ref name="/Film"></ref>


title: Boss Level

text: A special free advance screening of the film, sponsored by entertainment website Collider, was held at the ArcLight Cinemas in Hollywood on February 11, 2020, followed by a session with Grillo and Carnahan.


title: Boss Level

text: In June 2020, Entertainment Studios dropped the film. In November 2020, the U.S. distribution rights were acquired in an eight-figure deal by Hulu, which was later revealed to be worth $11,750,000. The film was released on March 5, 2021.


title: Boss Level

text: In July 2021 Blumhouse Productions sued the producers of the film for breach of contract. Blumhouse asserts that they were brought in to recut the film after the original version failed to secure distribution, but have not been compensated for their work, which was to be 5% of the acquisition fee paid by Hulu. Blumhouse also sued Hulu for continuing to stream their cut of the film after being sent multiple cease and desist notices.


title: Boss Level

text: On the review aggregation website Rotten Tomatoes, the film has an approval rating of 73%, based on 83 reviews, with an average rating of 6.50/10. The site's critics consensus reads: ""Boss Level" powers up the increasingly crowded time-loop genre with a gleefully over-the-top sci-fi action thriller that revels in its own excess." On Metacritic, the film has a weighted average score of 56 out of 100, based on 16 critics, indicating "mixed or average reviews".


title: Boss Level

text: Writing for IndieWire, Christian Blauvelt gave the film a grade of B and said, "It's a star part, and Grillo commands it. Most importantly, he gets you to invest in Roy enough that, even without a controller in your hands, you never feel like you're simply watching someone else play a videogame. With no pixels in sight, Grillo gives "Boss Level" the thing most videogame movie riffs lack: a pulse."


title: K-nearest neighbors algorithm

text: In statistics, the k"-nearest neighbors algorithm (k"-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the "k" closest training examples in a data set. The output depends on whether "k"-NN is used for classification or regression:


title: K-nearest neighbors algorithm

text: "k"-NN is a type of classification where the function is only approximated locally and all computation is deferred until function evaluation. Since this algorithm relies on distance for classification, if the features represent different physical units or come in vastly different scales then normalizing the training data can improve its accuracy dramatically.


title: K-nearest neighbors algorithm

text: Both for classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that the nearer neighbors contribute more to the average than the more distant ones. For example, a common weighting scheme consists in giving each neighbor a weight of 1/"d", where "d" is the distance to the neighbor.


title: K-nearest neighbors algorithm

text: The neighbors are taken from a set of objects for which the class (for "k"-NN classification) or the object property value (for "k"-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required.


title: K-nearest neighbors algorithm

text: Suppose we have pairs formula_1 taking values in formula_2, where is the class label of , so that formula_3 for formula_4 (and probability distributions formula_5). Given some norm formula_6 on formula_7 and a point formula_8, let formula_9 be a reordering of the training data such that formula_10.


title: K-nearest neighbors algorithm

text: The training examples are vectors in a multidimensional feature space, each with a class label. The training phase of the algorithm consists only of storing the feature vectors and class labels of the training samples.


title: K-nearest neighbors algorithm

text: In the classification phase, "k" is a user-defined constant, and an unlabeled vector (a query or test point) is classified by assigning the label which is most frequent among the "k" training samples nearest to that query point.


title: K-nearest neighbors algorithm

text: A commonly used distance metric for continuous variables is Euclidean distance. For discrete variables, such as for text classification, another metric can be used, such as the overlap metric (or Hamming distance). In the context of gene expression microarray data, for example, "k"-NN has been employed with correlation coefficients, such as Pearson and Spearman, as a metric. Often, the classification accuracy of "k"-NN can be improved significantly if the distance metric is learned with specialized algorithms such as Large Margin Nearest Neighbor or Neighbourhood components analysis.


title: K-nearest neighbors algorithm

text: A drawback of the basic "majority voting" classification occurs when the class distribution is skewed. That is, examples of a more frequent class tend to dominate the prediction of the new example, because they tend to be common among the "k" nearest neighbors due to their large number. One way to overcome this problem is to weight the classification, taking into account the distance from the test point to each of its "k" nearest neighbors. The class (or value, in regression problems) of each of the "k" nearest points is multiplied by a weight proportional to the inverse of the distance from that point to the test point. Another way to overcome skew is by abstraction in data representation. For example, in a self-organizing map (SOM), each node is a representative (a center) of a cluster of similar points, regardless of their density in the original training data. "K"-NN can then be applied to the SOM.


title: K-nearest neighbors algorithm

text: The best choice of "k" depends upon the data; generally, larger values of "k" reduces effect of the noise on the classification, but make boundaries between classes less distinct. A good "k" can be selected by various heuristic techniques (see hyperparameter optimization). The special case where the class is predicted to be the class of the closest training sample (i.e. when "k" = 1) is called the nearest neighbor algorithm.


title: K-nearest neighbors algorithm

text: The accuracy of the "k"-NN algorithm can be severely degraded by the presence of noisy or irrelevant features, or if the feature scales are not consistent with their importance. Much research effort has been put into selecting or scaling features to improve classification. A particularly popular approach is the use of evolutionary algorithms to optimize feature scaling. Another popular approach is to scale features by the mutual information of the training data with the training classes.


title: K-nearest neighbors algorithm

text: In binary (two class) classification problems, it is helpful to choose "k" to be an odd number as this avoids tied votes. One popular way of choosing the empirically optimal "k" in this setting is via bootstrap method.


title: K-nearest neighbors algorithm

text: The most intuitive nearest neighbour type classifier is the one nearest neighbour classifier that assigns a point to the class of its closest neighbour in the feature space, that is formula_11.


title: K-nearest neighbors algorithm

text: As the size of training data set approaches infinity, the one nearest neighbour classifier guarantees an error rate of no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data).


title: K-nearest neighbors algorithm

text: The -nearest neighbour classifier can be viewed as assigning the nearest neighbours a weight formula_12 and all others weight. This can be generalised to weighted nearest neighbour classifiers. That is, where the th nearest neighbour is assigned a weight formula_13, with formula_14. An analogous result on the strong consistency of weighted nearest neighbour classifiers also holds.


title: K-nearest neighbors algorithm

text: Let formula_15 denote the weighted nearest classifier with weights formula_16. Subject to regularity conditions, which in asymptotic theory are conditional variables which require assumptions to differentiate among parameters with some criteria. On the class distributions the excess risk has the following asymptotic expansion


title: K-nearest neighbors algorithm

text: The optimal weighting scheme formula_22, that balances the two terms in the display above, is given as follows: set formula_23,


title: K-nearest neighbors algorithm

text: With optimal weights the dominant term in the asymptotic expansion of the excess risk is formula_28. Similar results are true when using a bagged nearest neighbour classifier.


title: K-nearest neighbors algorithm

text: "k"-NN is a special case of a variable-bandwidth, kernel density "balloon" estimator with a uniform kernel.


title: K-nearest neighbors algorithm

text: The naive version of the algorithm is easy to implement by computing the distances from the test example to all stored examples, but it is computationally intensive for large training sets. Using an approximate nearest neighbor search algorithm makes "k-"NN computationally tractable even for large data sets. Many nearest neighbor search algorithms have been proposed over the years; these generally seek to reduce the number of distance evaluations actually performed.


title: K-nearest neighbors algorithm

text: "k-"NN has some strong consistency results. As the amount of data approaches infinity, the two-class "k-"NN algorithm is guaranteed to yield an error rate no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data). Various improvements to the "k"-NN speed are possible by using proximity graphs.


title: K-nearest neighbors algorithm

text: where formula_30is the Bayes error rate (which is the minimal error rate possible), formula_31 is the "k-"NN error rate, and is the number of classes in the problem. For formula_32 and as the Bayesian error rate formula_30 approaches zero, this limit reduces to "not more than twice the Bayesian error rate".


title: K-nearest neighbors algorithm

text: There are many results on the error rate of the nearest neighbour classifiers. The -nearest neighbour classifier is strongly (that is for any joint distribution on formula_34) consistent provided formula_35 diverges and formula_36 converges to zero as formula_37.


title: K-nearest neighbors algorithm

text: Let formula_38 denote the nearest neighbour classifier based on a training set of size . Under certain regularity conditions, the excess risk yields the following asymptotic expansion


title: K-nearest neighbors algorithm

text: The choice formula_23 offers a trade off between the two terms in the above display, for which the formula_43-nearest neighbour error converges to the Bayes error at the optimal (minimax) rate formula_28.


title: K-nearest neighbors algorithm

text: The K-nearest neighbor classification performance can often be significantly improved through (supervised) metric learning. Popular algorithms are neighbourhood components analysis and large margin nearest neighbor. Supervised metric learning algorithms use the label information to learn a new metric or pseudo-metric.