The kernel algorithm for PLS

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 X T YY T X of size equal to the number of X ‐variables. Using this kernel matrix X T YY T X together with the small covariance matrices X T X ( K × K ), X T Y ( K × M ) and Y T Y ( 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.