Principal component analysis: Difference between revisions

Revision as of 18:07, 21 October 2024

Revision as of 18:29, 21 October 2024

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== Details ==

PCA is defined as an [[orthogonal transformation|orthogonal]] [[linear transformation]] on a real [[inner product space]] that transforms the data to a new [[coordinate system]] such that the greatest variance by some scalar projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on.<ref name="Jolliffe2002"/><ref name="greenacreetal2022"/>

Consider an <math>n \times p</math> data [[Matrix (mathematics)|matrix]], '''X''', with column-wise zero [[empirical mean]] (the sample mean of each column has been shifted to zero), where each of the ''n'' rows represents a different repetition of the experiment, and each of the ''p'' columns gives a particular kind of feature (say, the results from a particular sensor).

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|s2cid=254965361

|url=http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-492087

|doi-access=free

}}</ref>

<ref name="greenacreetal2022">{{cite journal

|first1=M. |last1=Greenacre

|first2=P.J.F. |last2=Groenen

|first3=T. |last3=Hastie

|first4=A. |last4=Iodice d'Enza

|first5=A. |last5=Markos

|first6=E. |last6=Tuzhilina

|year=2022

|title=Principal Component Analysis

|journal=Nature Reviews Methods Primers

|volume=2

|issue=100

|doi=10.1038/s43586-022-00184-w

|s2cid=254965361

|url=https://doi.org/10.1038/s43586-022-00184-w

|doi-access=free

}}</ref>