Editing Principal component analysis (section)

== History ==

PCA was invented in 1901 by [[Karl Pearson]],<ref>{{Cite journal|author=Pearson, K. |author-link=Karl Pearson |year=1901 |title=On Lines and Planes of Closest Fit to Systems of Points in Space |journal=Philosophical Magazine |volume=2 |issue=11 |pages=559–572 |doi=10.1080/14786440109462720|s2cid=125037489 |url=https://zenodo.org/record/1430636 }}</ref> as an analogue of the [[principal axis theorem]] in mechanics; it was later independently developed and named by [[Harold Hotelling]] in the 1930s.<ref>Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. ''[[Journal of Educational Psychology]]'', '''24''', 417–441, and 498–520.<br> {{cite journal |last1=Hotelling |first1=H |year=1936 |title=Relations between two sets of variates |journal=[[Biometrika]] |volume=28 |issue=3/4|pages=321–377 |doi=10.2307/2333955|jstor=2333955}}</ref> Depending on the field of application, it is also named the discrete [[Karhunen–Loève theorem|Karhunen–Loève]] transform (KLT) in [[signal processing]], the [[Harold Hotelling|Hotelling]] transform in multivariate quality control, [[proper orthogonal decomposition]] (POD) in mechanical engineering, [[singular value decomposition]] (SVD) of '''X''' (invented in the last quarter of the 19th century<ref>
{{cite journal |last1=Stewart|first1=G. W. |year=1993 |title=On the early history of the singular value decomposition |journal=[[SIAM Review]] |volume=35 |issue=4|pages=551–566|doi=10.1137/1035134|url=http://purl.umn.edu/1868 |hdl=1903/566 |hdl-access=free }}</ref>), [[Eigendecomposition|eigenvalue decomposition]] (EVD) of '''X'''<sup>T</sup>'''X''' in linear algebra, [[factor analysis]] (for a discussion of the differences between PCA and factor analysis see Ch.&nbsp;7 of Jolliffe's ''Principal Component Analysis''),<ref name="Jolliffe2002">{{Cite book |last=Jolliffe |first=I. T. |url=http://link.springer.com/10.1007/b98835 |title=Principal Component Analysis |date=2002 |publisher=Springer-Verlag |isbn=978-0-387-95442-4 |series=Springer Series in Statistics |location=New York |language=en |doi=10.1007/b98835}}</ref> [[Eckart–Young theorem]] (Harman, 1960), or [[empirical orthogonal functions]] (EOF) in meteorological science (Lorenz, 1956), empirical eigenfunction decomposition (Sirovich, 1987), quasiharmonic modes (Brooks et al., 1988), [[Spectral theorem|spectral decomposition]] in noise and vibration, and [[Mode shape|empirical modal analysis]] in structural dynamics.