partial linear squares

The method of partial linear squares in statistics bears some relation to principal component analysis; instead of finding the hyperplanes of maximum variance, it finds a linear model describing some predicted variables in terms of other observable variables. It is used to find the fundamental relations between two 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. It was first introduced by the Swedish statistician Svante Wold. The modern (and arguably, more correct, according to Wold) long form for PLS is Projection to Latent Structures. It is widely applied in the field of chemometrics, and more recently, in chemical engineering process data. (See John F. MacGregor.)

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