A nonlinear calibration transfer method based on joint kernel subspace

A nonlinear strategy is proposed to develop calibration transfer method with the available joint spectral data composed of the master and slave spectra of standard samples. Its core idea is to minimize the instrument-induced spectral variation in the reproducing kernel Hilbert space (RKHS) where the joint spectral data is implicitly mapped by proper kernel function. The nonlinear feature representation of master or slave spectra are reconstructed by singular value decomposition (SVD) in the RKHS. Then the transferred feature of slave spectra approaching the reconstructed feature of master spectra in the RKHS can be acquired by the procedure that (1) calculates the transfer matrix to match the maser and slave kernel features in the joint kernel subspace and (2) utilizes the transferred slave kernel feature to reconstruct the nonlinear feature representation of slave spectra. As a better feature representation suited for multivariate calibration, both the reconstructed feature of master calibration spectra and the transferred feature of slave test spectra are derived in the RKHS. A kernel partial least squares (KPLS) model built on the former is applied to the latter. The KPLS master calibration model is equivalent to a partial least squares (PLS) model built with the corresponding reconstructed master kernel feature in the joint kernel subspace. By exploiting the kernel eigenvector representations and kernel trick, a series of computationally less demanding formulas with linear operation is derived to realize the nonlinear calibration model, termed as joint kernel subspace based calibration transfer (JKSCT). JKSCT is compared with boxcar signal transfer (BST), piecewise direct standardization (PDS), multi-level simultaneous component analysis (MSCA), canonical correlation analysis based calibration transfer (CCACT), generalized least squares (GLS), slope and bias correction (SBC), spectral space transformation (SST), external parameter orthogonalization (EPO) and double competitive adaptive reweighted sampling (DCARS) on three spectral datasets. Experimental results show that JKSCT performs at least comparable with the DCARS or SST, and frequently better than the other methods.

Automated summary

The proposed nonlinear strategy reconstructs the feature representation of master/slave spectra in RKHS using SVD, aiming at minimizing instrument-induced spectral variations and transferring features between master and slave spectra. The KPLS model built on the transferred features shows good performance in multivariate calibration, outperforming several existing calibration transfer methods on spectral datasets.