Editing Cluster analysis (section)

{{Short description|Grouping a set of objects by similarity}}
[[File:Cluster-2.svg|thumb|The result of a cluster analysis shown as the coloring of the squares into three clusters]]
{{Machine learning}}

'''Cluster analysis''' or '''clustering''' is the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a '''cluster''') are more [[Similarity measure|similar]] (in some specific sense defined by the analyst) to each other than to those in other groups (clusters). It is a main task of [[exploratory data analysis]], and a common technique for [[statistics|statistical]] [[data analysis]], used in many fields, including [[pattern recognition]], [[image analysis]], [[information retrieval]], [[bioinformatics]], [[data compression]], [[computer graphics]] and [[machine learning]].

Cluster analysis refers to a family of algorithms and tasks rather than one specific [[algorithm]]. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small [[Distance function|distances]] between cluster members, dense areas of the data space, intervals or particular [[statistical distribution]]s. Clustering can therefore be formulated as a [[multi-objective optimization]] problem. The appropriate clustering algorithm and parameter settings (including parameters such as the [[Metric (mathematics)|distance function]] to use, a density threshold or the number of expected clusters) depend on the individual [[data set]] and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of [[knowledge discovery]] or interactive multi-objective optimization that involves trial and failure. It is often necessary to modify [[data preprocessing]] and model parameters until the result achieves the desired properties.

Besides the term ''clustering'', there are a number of terms with similar meanings, including ''automatic [[Statistical classification|classification]]'', ''[[numerical taxonomy]]'', ''botryology'' (from {{langx|el|βότρυς}} {{gloss|grape}}), ''typological analysis'', and ''[[Community structure|community detection]]''. The subtle differences are often in the use of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest.

Cluster analysis originated in anthropology by Driver and Kroeber in 1932<ref>{{Cite journal|last=Driver and Kroeber|date=1932|title=Quantitative Expression of Cultural Relationships|url=http://dpg.lib.berkeley.edu/webdb/anthpubs/search?all=&volume=31&journal=1&item=5|journal=University of California Publications in American Archaeology and Ethnology|volume=Quantitative Expression of Cultural Relationships|pages=211–256|publisher=University of California Press|publication-place=Berkeley, CA|publication-date=1932|access-date=2019-02-18|archive-date=2020-12-06|archive-url=https://web.archive.org/web/20201206053117/https://dpg.lib.berkeley.edu/webdb/anthpubs/search?all=&volume=31&journal=1&item=5|url-status=dead}}</ref> and introduced to psychology by [[Joseph Zubin]] in 1938<ref>{{Cite journal|last=Zubin|first=Joseph|date=1938|title=A technique for measuring like-mindedness.|journal=The Journal of Abnormal and Social Psychology|language=en|volume=33|issue=4|pages=508–516|doi=10.1037/h0055441|issn=0096-851X}}</ref> and [[Robert Tryon]] in 1939<ref>{{cite book | title = Cluster Analysis: Correlation Profile and Orthometric (factor) Analysis for the Isolation of Unities in Mind and Personality | first = Robert C. | last = Tryon | author-link = Robert Tryon | publisher = Edwards Brothers | year = 1939}}</ref> and famously used by [[Raymond Cattell|Cattell]] beginning in 1943<ref>{{cite journal | last = Cattell | first = R. B. | date = 1943 | title = The description of personality: Basic traits resolved into clusters | journal = Journal of Abnormal and Social Psychology | volume = 38 | issue = 4 | pages = 476–506 | doi=10.1037/h0054116}}</ref> for trait theory classification in [[personality psychology]].