Partial least squares regression: Difference between revisions

Revision as of 15:55, 17 December 2019

Revision as of 23:39, 5 January 2020

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'''Partial least squares regression''' ('''PLS regression)''') is a [[statistics|statistical]] method that bears some relation to [[principal component regression|principal components regression]]; instead of finding [[hyperplane]]s of maximum [[variance]] between the response and independent variables, it finds a [[linear regression]] model by projecting the [[predicted variable]]s and the [[observable variable]]s to a new space. Because both the ''X'' and ''Y'' data are projected to new spaces, the PLS family of methods are known as bilinear factor models. Partial least squares discriminant analysis (PLS-DA) is a variant used when the Y is categorical.

PLS is used to find the fundamental relations between two [[matrix (mathematics)|matrices]] (''X'' and ''Y''), i.e. a [[latent variable]] approach to modeling the [[covariance]] structures in these two spaces. A PLS model will try to find the multidimensional direction in the ''X'' space that explains the maximum multidimensional variance direction in the ''Y'' space. PLS regression is particularly suited when the matrix of predictors has more variables than observations, and when there is [[multicollinearity]] among ''X'' values. By contrast, standard regression will fail in these cases (unless it is [[Tikhonov regularization|regularized]]).