Chemical rank estimation by noise perturbation in functional principal component analysis

Some kinds of chemical data are not only univariate or multivariate observations of classical statistics, but also functions observed continuously. Such special characters of the data, if being handled efficiently, will certainly improve the predictive accuracy. In this paper, a novel method, named noise perturbation in functional principal component analysis (NPFPCA), was proposed to determine the chemical rank of two-way data. In NPFPCA, after noise addition to the measured data, the smooth eigenvectors can be obtained by functional principal component analysis (FPCA). The eigenvectors representing noise are sensitive to the perturbation, on the other hand, those representing chemical components are not. Therefore, by comparing the difference of eigenvectors obtained by FPCA with noise perturbation and by traditional principal component analysis (PCA), the chemical rank of the system can be achieved accurately. Several simulated and real chemical data sets were analyzed to demonstrate the efficiency of the proposed method.