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

Abstract

A 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


Tài liệu tham khảo

Jöreskog K., 1982, System under Indirect Observation: Causality, Structure, Prediction

Martens H., 1983, Progress in Cereal Chemistry and Technology, 607

Wold S., 1983, Matrix Pencils, 286, 10.1007/BFb0062108

Wold H., 1966, Research Papers in Statistics, 411

Wold H., 1966, Multivariate Analysis, 391

10.1137/0905052

Wold S., 1984, Mathematics and Statistics in Chemistry, Chemometrics, 17

10.1016/0003-2670(86)80028-9

10.1080/03610918808812681

10.1002/cem.1180020306

10.1016/S0003-2670(00)86335-7

10.1002/cem.1180030209

10.1016/0169-7439(89)80112-1

10.1016/0169-7439(89)80049-8

10.1002/cem.1180050206

Lindgren F., 1991, Proc. Symp. on Applied Statistics, Copenhagen, January 1991

10.1016/0165-9936(92)80118-P

10.1016/0169-7439(92)80121-J

10.1016/0169-7439(87)80096-5

G.Strang Linear Algebra and Its Applications Harcourt Brace Jovanovich (1988).

10.1002/0471725331

10.1016/0169-7439(92)80093-J

Wold S., 1978, Technometrics, 20, 379, 10.1080/00401706.1978.10489693

SIMCA Software Manual Umetri AB. S‐901 87 Umetri Sweden.

Wold S., 1981, Proc. Symp. on Applied Statistics, Copenhagen, January, 1981

ERDAS Software Manual

F.LindgrenandP.Geladi Illustrative examples of PLS regression on multivariate Images in preparation.

Thông tin
Thông tin xuất bản

Journal of Chemometrics

Tập 7 Số 1

45-59

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