Wold, Herman

PLS was originally proposed by Herman Wold (Wold, 1982 Wold et al., 1984) to address situations involving a modest number of observations, highly collinear variables, and data with noise in both the X- and Y-data sets. It is therefore designed to analyze the variations between two data sets, X, Y). Although PLS is similar to PCA in that they both model the A -data variance, the resulting X space model in PLS is a rotated version of the PCA model. The rotation is defined so that the scores of X data maximize the covariance of X to predict the Y-data. 

Partial least squares was developed in the 1960s by Herman Wold, working in the field of econometrics. His son, Svante Wold, introduced PLS to the field of chemistry and further developed the method [16], Application of these powerful methods to interesting chemical problems produced innovative solutions to chemical problems previously thought to be intractable. In many ways, the introduction of multivariate methods of analysis into the discipline of chemistry was revolutionary. 

Partial least-squares regression (PLSR) is a multivariate data analytical technique designed to handle intercorrelated regressors. It is based on Herman Wold s general PLS principle [1], in which complicated, multivariate systems analysis problems are solved by a sequence of simple least-squares regressions. 

Partial least squares is a loose term for a family of philosophically and technically related multivariate modeling methods derived from Herman Wold s basic concepts of iterative fitting of bilinear models... 

The PLS approach was developed around 1975 by Herman Wold and co-workers for the modeling of complicated data sets in terms of chains of matrices (blocks), so-called path models . Herman Wold developed a simple but efficient way to estimate the parameters in these models called NIPALS (nonlinear iterative partial least squares). This led, in turn, to the acronym PLS for these models, where PLS stood for partial least squares . This term describes the central part of the estimation, namely that each model parameter is iteratively estimated as the slope of a simple bivariate regression (least squares) between a matrix column or row as the y variable, and another parameter vector as the x variable. So, for instance, in each iteration the PLS weights w are re-estimated as u X/(u u). Here denotes u transpose, i.e., the transpose of the current u vector. The partial in PLS indicates that this is a partial regression, since the second parameter vector (u in the... 

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