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A PLS kernel algorithm for data sets with many variables and fewer objects. Part 1: Theory and algorithm by Stefan Rännar; Fredrik Lindgren; Paul Geladi; Svante Wold is a Chemistry article available to read on EtoBox.

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A fast PLS regression algorithm dealing with large data matrices with many variables (K) and fewer objects (N) is presented. For such data matrices the classical algorithm is computer-intensive and memory-demanding. Recently, Lindgren et al. (J. Chemometrics, 7,45-49 (1993)) developed a quick and efficient kernel algorithm for the case with many objects and few variables. The present paper is focused on the opposite case, i.e. many variables and fewer objects. A kernel algorithm is presented based on eigenvectors to the 'kernel' matrix XXTYYT, which is a square, non-symmetric matrix of size N x N, where N is the number of objects. Using the kernel matrix and the association matrices XX' (N x N) and YY' (N x N), it is possible to calculate all score and loading vectors and hence conduct a complete PLS regression including diagnostics such as R 2 . This is done without returning to the original data matrices X and Y. The algorithm is presented in equation form, with proofs of some new properties and as MATLAB code.

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Author

Stefan Rännar; Fredrik Lindgren; Paul Geladi; Svante Wold

Publisher

Wiley

Published

1994

Language

EN

Field

Chemistry (Physical Sciences)