Editing Dimensionality reduction (section)

{{short description|Process of reducing the number of random variables under consideration}}
{{For|dimensional reduction in physics|dimensional reduction}}

'''Dimensionality reduction''', or '''dimension reduction''', is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its [[intrinsic dimension]]. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often [[sparse matrix|sparse]] as a consequence of the [[curse of dimensionality]], and analyzing the data is usually [[computational complexity theory#Intractability|computationally intractable]]. Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as [[signal processing]], [[speech recognition]], [[neuroinformatics]], and [[bioinformatics]].<ref name="dr_review">{{cite journal |last1=van der Maaten |first1=Laurens |last2=Postma |first2=Eric |last3=van den Herik |first3=Jaap |date=October 26, 2009 |title=Dimensionality Reduction: A Comparative Review |url=https://members.loria.fr/moberger/Enseignement/AVR/Exposes/TR_Dimensiereductie.pdf |journal=J Mach Learn Res |volume=10 |pages=66–71}}</ref>

Methods are commonly divided into linear and nonlinear approaches.<ref name="dr_review"/> Linear approaches can be further divided into [[feature selection]] and [[feature extraction]].<ref>{{cite book |last1=Pudil |first1=P. |last2=Novovičová |first2=J. |editor1-first=Huan |editor1-last=Liu |editor2-first=Hiroshi |editor2-last=Motoda |doi=10.1007/978-1-4615-5725-8_7 |chapter=Novel Methods for Feature Subset Selection with Respect to Problem Knowledge |title=Feature Extraction, Construction and Selection |pages=101 |year=1998 |isbn=978-1-4613-7622-4}}</ref> Dimensionality reduction can be used for [[noise reduction]], [[data visualization]], [[cluster analysis]], or as an intermediate step to facilitate other analyses.