The kernel algorithm for PLS

Journal of Chemometrics - Tập 7 Số 1 - Trang 45-59 - 1993
Fredrik Lindgren1, Paul Geladi1, Svante Wold1
1Research Group for Chemometrics, Department of Organic Chemistry, University of Umea, S‐901 87 Umea, Sweden

Tóm tắt

AbstractA fast and memory‐saving PLS regression algorithm for matrices with large numbers of objects is presented. It is called the kernel algorithm for PLS. Long (meaning having many objects, N) matrices X (N × K) and Y (N × M) are condensed into a small (K × K) square ‘kernel’ matrix XTYYTX of size equal to the number of X‐variables. Using this kernel matrix XTYYTX together with the small covariance matrices XTX (K × K), XTY (K × M) and YTY (M × M), it is possible to estimate all necessary parameters for a complete PLS regression solution with some statistical diagnostics. The new developments are presented in equation form. A comparison of consumed floating point operations is given for the kernel and the classical PLS algorithm. As appendices, a condensed matrix algebra version of the kernel algorithm is given together with the MATLAB code.

Từ khóa


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Thông tin xuất bản

Journal of Chemometrics

Tập 7 Số 1

45-59

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