Ole-Christian Galbo Engstrøm
Partial least squares is a workhorse for calibration, particularly where you have many correlated measurements and few samples, and the Improved Kernel PLS algorithms are already among the fastest implementations available. This paper speeds up two steps they share.
The change to computing the X rotations is instructive. It replaces term-by-term accumulation with direct evaluation using the same number of multiplications, so on paper nothing improved. The gain is entirely in how the work maps onto modern hardware: accumulating term by term forces each step to wait for the previous one, while direct evaluation lets many multiplications proceed at once.
That is a good illustration of where performance actually lives now. Counting operations stopped being a reliable proxy for speed once processors became wide, and an algorithm that exposes parallelism beats an equivalent one that serialises.
Improved Kernel Partial Least Squares (IKPLS) algorithms 1 and 2 are among the fastest PLS calibration algorithms. This article focuses on two shared steps, the computation of the $\mathbf{X}$ rotations, $\mathbf{R}$, and the $\mathbf{Y}$ loadings, $\mathbf{Q}$, and accelerates both. For $\mathbf{R}$, term-by-term accumulation is replaced by a direct evaluation strategy that requires the same number of multiplications but parallelizes better on modern hardware. For…
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