A PLS KERNEL ALGORITHM FOR DATA SETS WITH MANY VARIABLES AND FEWER OBJECTS .1. THEORY AND ALGORITHM

A fast PLS regression algorithm dealing with large data matrices with many variables (K) and fewer objects (N) is presented. For such data m atrices the classical algorithm is computer-intensive and memory-deman ding. Recently, Lindgren et al. (J. Chemometrics, 7, 45-49 (1993)) dev eloped a quick and efficient kernel algorithm for the case with many o bjects and few variables. The present paper is focused on the opposite case, i.e. many variables and fewer objects. A kernel algorithm is pr esented based on eigenvectors to the 'kernel' matrix XX(T)YY(T), which is a square, non-symmetric matrix of size N x N, where N is the numbe r of objects. Using the kernel matrix and the association matrices XX( T) (N x N) and YY(T) (N x N), it is possible to calculate all score an d loading vectors and hence conduct a complete PLS regression includin g diagnostics such as R2. This is done without returning to the origin al data matrices X and Y. The algorithm is presented in equation form, with proofs of some new properties and as MATLAB code.