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Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be…

Machine Learning · Statistics 2014-04-08 Sohan Seth , Manuel J. A. Eugster

Archetypal analysis serves as an exploratory tool that interprets a collection of observations as convex combinations of pure (extreme) patterns. When these patterns correspond to actual observations within the sample, they are termed…

Methodology · Statistics 2026-01-12 Aleix Alcacer , Irene Epifanio

Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this…

Applications · Statistics 2023-01-11 Benjamin S. Baumer , Gregory J. Matthews , Quang Nguyen

Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the…

Machine Learning · Statistics 2018-12-31 Jesús Moliner , Irene Epifanio

Archetypal analysis represents each individual member of a set of data vectors as a mixture (a constrained linear combination) of the pure types or archetypes of the data set. The archetypes are themselves required to be mixtures of the…

Astrophysics · Physics 2009-11-07 B. H. P. Chan , D. A. Mitchell , L. E. Cram

Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed $k$, the method finds a convex polytope with $k$ vertices, called archetype points, such that the polytope is…

Statistics Theory · Mathematics 2022-04-19 Braxton Osting , Dong Wang , Yiming Xu , Dominique Zosso

Archetypes are typical population representatives in an extremal sense, where typicality is understood as the most extreme manifestation of a trait or feature. In linear feature space, archetypes approximate the data convex hull allowing…

Computer Vision and Pattern Recognition · Computer Science 2020-02-04 Sebastian Mathias Keller , Maxim Samarin , Fabricio Arend Torres , Mario Wieser , Volker Roth

Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between…

Machine Learning · Computer Science 2019-11-15 David van Dijk , Daniel Burkhardt , Matthew Amodio , Alex Tong , Guy Wolf , Smita Krishnaswamy

Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose…

Applications · Statistics 2020-06-30 Ismael Cabero , Irene Epifanio

A new approach in team sports analysis consists in studying positioning and movements of players during the game in relation to team performance. State of the art tracking systems produce spatio-temporal traces of players that have…

Applications · Statistics 2017-07-06 Rodolfo Metulini , Marica Manisera , Paola Zuccolotto

Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and…

Applications · Statistics 2026-05-06 Paul-Hieu V. Nguyen , James M. Smoliga , Benton Lindaman , Sameer K. Deshpande

The use of statistical methods in sport analytics has gained a rapidly growing interest over the last decade, and nowadays is common practice. In particular, the interest in understanding and predicting an athlete's performance throughout…

Methodology · Statistics 2021-01-21 Patric Dolmeta , Raffaele Argiento , Silvia Montagna

Predicting outcomes in sports is important for teams, leagues, bettors, media, and fans. Given the growing amount of player tracking data, sports analytics models are increasingly utilizing spatially-derived features built upon player…

Machine Learning · Computer Science 2022-07-29 Peter Xenopoulos , Claudio Silva

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and…

Physics and Society · Physics 2023-01-20 Nick James , Max Menzies , Howard Bondell

Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…

Methodology · Statistics 2016-09-02 Irene Epifanio

In recent years, analytics has started to revolutionize the game of basketball: quantitative analyses of the game inform team strategy, management of player health and fitness, and how teams draft, sign, and trade players. In this review,…

Applications · Statistics 2020-07-22 Zachary Terner , Alexander Franks

Technological advances have paved the way for collecting high-resolution network data in basketball, football, and other team-based sports. Such data consist of interactions among players of competing teams indexed by space and time.…

Applications · Statistics 2024-02-14 Nicholas Grieshop , Yong Feng , Guanyu Hu , Michael Schweinberger

Computer Vision developments are enabling significant advances in many fields, including sports. Many applications built on top of Computer Vision technologies, such as tracking data, are nowadays essential for every top-level analyst,…

Computer Vision and Pattern Recognition · Computer Science 2023-01-19 Tiago Mendes-Neves , Luís Meireles , João Mendes-Moreira

In sports, there is a constant effort to improve metrics which assess player ability, but there has been almost no effort to quantify and compare existing metrics. Any individual making a management, coaching, or gambling decision is…

Applications · Statistics 2016-10-03 Alexander Franks , Alexander D'Amour , Daniel Cervone , Luke Bornn

In this paper, we explore some of the applications of computer vision to sports analytics. Sport analytics deals with understanding and discovering patterns from a corpus of sports data. Analysing such data provides important performance…

Computer Vision and Pattern Recognition · Computer Science 2020-04-15 Neha Bhargava , Fabio Cuzzolin
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