K-nearest neighbors algorithm: Difference between revisions

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{{Distinguish|k-means clustering}}

{{DISPLAYTITLE:''k''-nearest neighbors algorithm}}

In [[statistics]], the '''''k''-nearest neighbors algorithm''' ('''''k''-NN''') is a [[Non-parametric statistics|non-parametric]] [[supervised learning]] method first developed by [[Evelyn Fix]] and [[Joseph Lawson Hodges Jr.|Joseph Hodges]] in 1951,<ref>{{Cite report | last1=Fix | first1=Evelyn | last2= Hodges | first2=Joseph L. | title=Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties | issue=Report Number 4, Project Number 21-49-004 | year=1951 | url=https://apps.dtic.mil/dtic/tr/fulltext/u2/a800276.pdf | archive-url=https://web.archive.org/web/20200926212807/https://apps.dtic.mil/dtic/tr/fulltext/u2/a800276.pdf | url-status=dead | archive-date=September 26, 2020 | publisher=USAF School of Aviation Medicine, Randolph Field, Texas}}</ref> and later expanded by [[Thomas M. Cover|Thomas Cover]].<ref>{{cite journal |last=Altman |first=Naomi S. |author-link=Naomi Altman |title=An introduction to kernel and nearest-neighbor nonparametric regression |journal=The American Statistician |volume=46 |issue=3 |year=1992 |pages=175–185 |doi=10.1080/00031305.1992.10475879|hdl=1813/31637 |url=https://ecommons.cornell.edu/bitstream/1813/31637/1/BU-1065-MA.pdf |hdl-access=free }}</ref> It is used for [[statistical classification|classification]] and [[regression analysis|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:

:* In ''k-NN classification'', the output is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its ''k'' nearest neighbors (''k'' is a positive [[integer]], typically small). If ''k''&nbsp;=&nbsp;1, then the object is simply assigned to the class of that single nearest neighbor.