Editing Correlation (section)

===Nearest valid correlation matrix===
In some applications (e.g., building data models from only partially observed data) one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to the way it has been computed).

In 2002, Higham<ref>{{cite journal|title=Computing the nearest correlation matrix—a problem from finance|journal=IMA Journal of Numerical Analysis|date=2002|first=Nicholas J.|last=Higham|volume=22|issue=3|pages=329–343|doi=10.1093/imanum/22.3.329|citeseerx=10.1.1.661.2180}}</ref> formalized the notion of nearness using the [[Frobenius norm]] and provided a method for computing the nearest correlation matrix using the [[Dykstra's projection algorithm]], of which an implementation is available as an online Web API.<ref>{{Cite web|url=https://portfoliooptimizer.io/|title=Portfolio Optimizer |website=portfoliooptimizer.io|access-date=2021-01-30}}</ref>

This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure<ref>{{cite journal|title=Computing a Nearest Correlation Matrix with Factor Structure.|journal= SIAM J. Matrix Anal. Appl.|date=2010|first1=Rudiger|last1=Borsdorf|first2=Nicholas J.|last2=Higham|first3=Marcos|last3=Raydan|volume=31|issue=5|pages=2603–2622|doi=10.1137/090776718|url= http://eprints.maths.manchester.ac.uk/1523/1/SML002603.pdf}}</ref>) and numerical (e.g. usage the [[Newton's method]] for computing the nearest correlation matrix<ref>{{cite journal|title=A quadratically convergent Newton method for computing the nearest correlation matrix.|journal= SIAM J. Matrix Anal. Appl.|date=2006|first1=HOUDUO|last1=Qi|first2=DEFENG|last2=Sun|volume=28|issue=2|pages=360–385|doi=10.1137/050624509}}</ref>) results obtained in the subsequent years.