SIMPLS: An alternative approach to partial least squares regression. de Jong, S. Chemometrics and Intelligent Laboratory Systems, 18(3):251--263, March, 1993. 00778
SIMPLS: An alternative approach to partial least squares regression [link]Paper  doi  abstract   bibtex   
De Jong, S., 1993. SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18: 251–263. A novel algorithm for partial least squares (PLS) regression, SIMPLS, is proposed which calculates the PLS factors directly as linear combinations of the original variables. The PLS factors are determined such as to maximize a covariance criterion, while obeying certain orthogonality and normalization restrictions. This approach follows that of other traditional multivariate methods. The construction of deflated data matrices as in the nonlinear iterative partial least squares (NIPALS)-PLS algorithm is avoided. For univariate y SIMPLS is equivalent to PLS1 and closely related to existing bidiagonalization algorithms. This follows from an analysis of PLS1 regression in terms of Krylov sequences. For multivariate Y there is a slight difference between the SIMPLS approach and NIPALS-PLS2. In practice the SIMPLS algorithm appears to be fast and easy to interpret as it does not involve a breakdown of the data sets.
@article{ de_jong_simpls:_1993,
  title = {{SIMPLS}: {An} alternative approach to partial least squares regression},
  volume = {18},
  issn = {0169-7439},
  shorttitle = {{SIMPLS}},
  url = {http://www.sciencedirect.com/science/article/pii/016974399385002X},
  doi = {10.1016/0169-7439(93)85002-X},
  abstract = {De Jong, S., 1993. SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18: 251–263.

A novel algorithm for partial least squares (PLS) regression, SIMPLS, is proposed which calculates the PLS factors directly as linear combinations of the original variables. The PLS factors are determined such as to maximize a covariance criterion, while obeying certain orthogonality and normalization restrictions. This approach follows that of other traditional multivariate methods. The construction of deflated data matrices as in the nonlinear iterative partial least squares (NIPALS)-PLS algorithm is avoided. For univariate y SIMPLS is equivalent to PLS1 and closely related to existing bidiagonalization algorithms. This follows from an analysis of PLS1 regression in terms of Krylov sequences. For multivariate Y there is a slight difference between the SIMPLS approach and NIPALS-PLS2. In practice the SIMPLS algorithm appears to be fast and easy to interpret as it does not involve a breakdown of the data sets.},
  number = {3},
  urldate = {2013-11-03TZ},
  journal = {Chemometrics and Intelligent Laboratory Systems},
  author = {de Jong, Sijmen},
  month = {March},
  year = {1993},
  note = {00778},
  pages = {251--263}
}
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