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“The partial least squares algorithm: a truncated Cayley-Hamilton series approximation used to solve the regression problem”

Authors: David Di Ruscio,
Affiliation: Telemark University College
Reference: 1998, Vol 19, No 3, pp. 117-140.

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Keywords: Least squares, Cayley-Hamilton, PLS

Abstract: In this paper it is shown that the PLS algorithm for univariate data is equivalent to using a truncated Cayley-Hamilton polynomial expression of degree 1 less than a less than r for the matrix inverse inv(X“X) in R^(rxr) used to compute the LS solution. Furthermore, the a coefficients in this polynomial are computed as the LS optimal solution (minimizing parameters) to the prediction error. The resulting solution is non-iterative. The solution can be expressed in terms of one matrix inverse and is given by BPLS = Ka * inv(Ka“*X“*X*Ka)*Ka“*X“*Y where Ka in R^(rxr) is the controllability (Krylov) matrix for the pair (X“X,X“Y).

PDF PDF (3422 Kb)        DOI: 10.4173/mic.1998.3.1

DOI forward links to this article:
  [1] Maryam Ghadrdan, Chriss Grimholt and Sigurd Skogestad (2013), doi:10.1021/ie400542n

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  title={{The partial least squares algorithm: a truncated Cayley-Hamilton series approximation used to solve the regression problem}},
  author={Di Ruscio, David},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


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