Editing Canonical correlation (section)

==Practical uses==
A typical use for canonical correlation in the experimental context is to take two sets of variables and see what is common among the two sets.<ref>{{cite book|last= Sieranoja|first=S.|author2=Sahidullah, Md| author3=Kinnunen, T.| author4= Komulainen, J.| author5= Hadid, A.|title=2018 IEEE 3rd International Conference on Signal and Image Processing (ICSIP) |chapter=Audiovisual Synchrony Detection with Optimized Audio Features |date=July 2018|pages=377–381 |doi=10.1109/SIPROCESS.2018.8600424 |isbn=978-1-5386-6396-7 |s2cid=51682024 |url=http://urn.fi/urn:nbn:fi-fe2020041415345 |chapter-url=http://cs.joensuu.fi/pages/tkinnu/webpage/pdf/audiovisual_synchrony_2018.pdf}}</ref> For example, in psychological testing, one could take two well established multidimensional [[personality tests]] such as the [[Minnesota Multiphasic Personality Inventory]] (MMPI-2) and the [[Neuroticism Extraversion Openness Personality Inventory|NEO]]. By seeing how the MMPI-2 factors relate to the NEO factors, one could gain insight into what dimensions were common between the tests and how much variance was shared. For example, one might find that an [[Extraversion and introversion|extraversion]] or [[neuroticism]] dimension accounted for a substantial amount of shared variance between the two tests.

One can also use canonical-correlation analysis to produce a model equation which relates two sets of variables, for example a set of performance measures and a set of explanatory variables, or a set of outputs and set of inputs. Constraint restrictions can be imposed on such a model to ensure it reflects theoretical requirements or intuitively obvious conditions. This type of model is known as a maximum correlation model.<ref>{{Cite journal | last1 = Tofallis | first1 = C. | title = Model Building with Multiple Dependent Variables and Constraints | doi = 10.1111/1467-9884.00195 | journal = Journal of the Royal Statistical Society, Series D | volume = 48 | issue = 3 | pages = 371–378 | year = 1999 | arxiv = 1109.0725| s2cid = 8942357 }}</ref>

Visualization of the results of canonical correlation is usually through bar plots of the coefficients of the two sets of variables for the pairs of canonical variates showing significant correlation. Some authors suggest that they are best visualized by plotting them as heliographs, a circular format with ray like bars, with each half representing the two sets of variables.<ref>{{Cite book | last1 = Degani | first1 = A. | last2 = Shafto | first2 = M. | last3 = Olson | first3 = L. | doi = 10.1007/11783183_11 | chapter = Canonical Correlation Analysis: Use of Composite Heliographs for Representing Multiple Patterns | title = Diagrammatic Representation and Inference | series = Lecture Notes in Computer Science | volume = 4045 | pages = 93 | year = 2006 | isbn = 978-3-540-35623-3 | chapter-url = http://ti.arc.nasa.gov/m/profile/adegani/Composite_Heliographs.pdf| citeseerx = 10.1.1.538.5217 }}</ref>