In statistics and computational geometry , the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space . Given a set of points in d -dimensional space, a centerpoint of the set is a point such that any hyperplane that goes through that point divides the set of points in two roughly equal subsets: the smaller part should have at least a 1/( d + 1) fraction of the points. Like the median, a centerpoint need not be one of the data points. Every non-empty set of points (with no duplicates) has at least one centerpoint.
24-440: (Redirected from Centrepoint ) Centerpoint (alternatively spelled centrepoint ) may refer to: Centerpoint (geometry) , a generalization of the median to two or more dimensions Organizations [ edit ] CenterPoint Energy , an electric and natural gas utility in the U.S.A. CenterPoint Properties , Chicago industrial real estate developer Centrepoint (charity) ,
48-549: A PhD in mathematics after completing a doctoral dissertation titled "On denumerability in topology ". During World War II , Tukey worked at the Fire Control Research Office and collaborated with Samuel Wilks and William Cochran . He is claimed to have helped design the U-2 spy plane. After the war, he returned to Princeton, dividing his time between the university and AT&T Bell Laboratories . In 1962, Tukey
72-399: A Tukey median (and therefore also a centerpoint) may be constructed in time O( n + n log n ). A randomized algorithm that repeatedly replaces sets of d + 2 points by their Radon point can be used to compute an approximation to a centerpoint of any point set, in the sense that its Tukey depth is linear in the sample set size, in an amount of time that
96-437: A Tukey median must be a centerpoint, but not every centerpoint is a Tukey median. Both terms are named after John Tukey . For a different generalization of the median to higher dimensions, see geometric median . A simple proof of the existence of a centerpoint may be obtained using Helly's theorem . Suppose there are n points, and consider the family of closed half-spaces that contain more than dn /( d + 1) of
120-807: A UK charitable trust for homeless young people Centrepoint Theatre , a theatre and theatre company in Palmerston North, New Zealand Places [ edit ] Sydney Tower , also known as Centrepoint Tower, in Sydney, New South Wales, Australia Westfield Sydney , a shopping centre under the Sydney Tower Centerpoint Mall (Toronto) , Ontario, Canada Centrepointe , a neighbourhood in Ottawa, Ontario, Canada Centre Point Sabah , in Kota Kinabalu, Sabah, Malaysia Centrepoint (commune) ,
144-561: A building See also [ edit ] Center Point (disambiguation) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Centerpoint . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Centerpoint&oldid=1184175227 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description
168-604: A former commune in Albany, New Zealand SM City Sta. Mesa , Manila, Philippines, formerly known as SM Centerpoint The Centrepoint , a shopping centre in Singapore Centre Point , an office building in central London, England Centerpoint, Ohio , United States, an unincorporated community Centerpointe Mall , Grand Rapids, Michigan, United States Centerpoint Medical Center , Independence, Missouri, United States CentrePointe, Lexington , Kentucky, United States,
192-764: A key role in the design and conduct of the National Assessment of Educational Progress . He was awarded the National Medal of Science by President Nixon in 1973. He was awarded the IEEE Medal of Honor in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform (FFT) algorithm ". Tukey retired in 1985. He died in New Brunswick, New Jersey , on July 26, 2000. Early in his career Tukey worked on developing statistical methods for computers at Bell Labs , where he invented
216-426: A matching pair but the vintage was such that it was hard to tell. ... Carefully and deliberately a list of headings was chalked on the blackboard. The words came too, not many, like overweight parcels, delivered at a slow unfaltering pace. ... When it was complete, Tukey turned to face the audience and the podium ... "Comments, queries, suggestions?" he asked the audience ... As he waited for a response, he clambered onto
240-520: Is also credited with coining the term bit and the first published use of the word software . Tukey was born in New Bedford, Massachusetts , in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a B.A. in 1936 and M.S. in 1937 in chemistry, from Brown University , before moving to Princeton University , where in 1939 he received
264-517: Is different from Wikidata All article disambiguation pages All disambiguation pages Centerpoint (geometry) Closely related concepts are the Tukey depth of a point (the minimum number of sample points on one side of a hyperplane through the point) and a Tukey median of a point set (a point maximizing the Tukey depth). A centerpoint is a point of depth at least n /( d + 1), and
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#1732854880056288-535: Is polynomial in the dimension. John Tukey John Wilder Tukey ( / ˈ t uː k i / ; June 16, 1915 – July 26, 2000) was an American mathematician and statistician , best known for the development of the fast Fourier Transform (FFT) algorithm and box plot . The Tukey range test , the Tukey lambda distribution , the Tukey test of additivity , and the Teichmüller–Tukey lemma all bear his name. He
312-486: The Tukey lambda distribution , Tukey's test of additivity , Tukey's lemma , and the Tukey window all bear his name. He is also the creator of several little-known methods such as the trimean and median-median line , an easier alternative to linear regression . In 1974, he developed, with Jerome H. Friedman , the concept of the projection pursuit . John Tukey contributed greatly to statistical practice and data analysis in general. In fact, some regard John Tukey as
336-635: The Human Male , which summarized "A random selection of three people would have been better than a group of 300 chosen by Mr. Kinsey". From 1960 to 1980, Tukey helped design the NBC television network polls used to predict and analyze elections. He was also a consultant to the Educational Testing Service, the Xerox Corporation, and Merck & Company. During the 1970s and early 1980s, Tukey played
360-436: The assumptions underlying their use; the need to amass experience of the behaviour of specific methods of analysis in order to provide guidance on their use; the importance of allowing the possibility of data's influencing the choice of method by which they are analysed; the need for statisticians to reject the role of "guardian of proven truth", and to resist attempts to provide once-for-all solutions and tidy over-unifications of
384-472: The father of data science. At the very least, he pioneered many of the key foundations of what came later to be known as data science. Making sense of data has a long history and has been addressed by statisticians, mathematicians, scientists, and others for many many years. During the 1960s, Tukey challenged the dominance at the time of what he called "confirmatory data analysis", statistical analyses driven by rigid mathematical configurations. Tukey emphasized
408-410: The first program for viewing multivariate data, was conceived by him during the early 1970s. This coupling of data analysis and computer science is what is now called data science. Tukey articulated the important distinction between exploratory data analysis and confirmatory data analysis , believing that much statistical methodology placed too great an emphasis on the latter. Though he believed in
432-597: The importance of having a more flexible attitude towards data analysis and of exploring data carefully to see what structures and information might be contained therein. He called this "exploratory data analysis" (EDA). In many ways, EDA was a precursor to data science. Tukey also realized the importance of computer science to EDA. Graphics are an integral part of EDA methodology and, while much of Tukey's work focused on static displays (such as box plots) that could be drawn by hand, he realized that computer graphics would be much more effective for studying multivariate data. PRIM-9,
456-431: The podium and manoeuvred until he was sitting cross-legged facing the audience. ... We in the audience sat like spectators at the zoo waiting for the great bear to move or say something. But the great bear appeared to be doing the same thing, and the feeling was not comfortable. While working with John von Neumann on early computer designs, Tukey introduced the word bit as a portmanteau of binary digit . The term bit
480-521: The points. Fewer than n /( d + 1) points are excluded from any one of these halfspaces, so the intersection of any subset of d + 1 of these halfspaces must be nonempty. By Helly's theorem, it follows that the intersection of all of these halfspaces must also be nonempty. Any point in this intersection is necessarily a centerpoint. For points in the Euclidean plane , a centerpoint may be constructed in linear time . In any dimension d ,
504-458: The subject; the iterative nature of data analysis; implications of the increasing power, availability, and cheapness of computing facilities; the training of statisticians. Tukey's lectures were described to be unusual. McCullagh described his lecture given in London in 1977: Tukey ambled to the podium, a great bear of a man dressed in baggy pants and a black knitted shirt. These might once have been
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#1732854880056528-461: The term bit in 1947. His statistical interests were many and varied. He is particularly remembered for his development with James Cooley of the Cooley–Tukey FFT algorithm . In 1970, he contributed significantly to what is today known as the jackknife —also termed Quenouille–Tukey jackknife. He introduced the box plot in his 1977 book, "Exploratory Data Analysis". Tukey's range test ,
552-437: The utility of separating the two types of analysis, he pointed out that sometimes, especially in natural science , this was problematic and termed such situations uncomfortable science . A. D. Gordon offered the following summary of Tukey's principles for statistical practice: ... the usefulness and limitation of mathematical statistics; the importance of having methods of statistical analysis that are robust to violations of
576-734: Was elected to the American Philosophical Society . He became a full professor at 35 and founding chairman of the Princeton statistics department in 1965. Among many contributions to civil society , Tukey served on a committee of the American Statistical Association that produced a report critiquing the statistical methodology of the Kinsey Report , Statistical Problems of the Kinsey Report on Sexual Behavior in
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