## “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. |

**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 (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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**BibTeX:**

@article{MIC-1998-3-1,

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},

volume={19},

number={3},

pages={117--140},

year={1998},

doi={10.4173/mic.1998.3.1},

publisher={Norwegian Society of Automatic Control}

};