Kernel PLS regression on wavelet transformed NIR spectra for prediction of sugar content of apple

A kernel PLS algorithm was implemented to estimate the sugar content of Golden Delicious apples based on NIR reflectance spectra in the range of 800–1690 nm. Covariance, Gaussian and polynomial kernel functions were considered. All kernels, except the covariance kernel, incorporate tuning parameters which were optimised by computer experiments. The calibration results were insensitive to the actual value of the tuning parameters over a wide range. No significant difference between the RMSEP values obtained with different kernels was obtained, irrespective of the applied transformation (none, log(1/R), Kubelka–Munck) or first order derivative calculation. A wavelet compression procedure was implemented to speed up the computation of the kernel Gram matrices. It was shown that the kernel Gram matrix computed with the approximation and detail coefficients of the wavelet transformed spectra converges in norm to the real kernel Gram matrix. The time required for calculating the kernel Gram matrix is inversely proportional to the compression ratio. It was shown that a compression ratio of up to 25 did not affect the accuracy of the kernel PLS calibration models.