The chemical rank estimation for excitation-emission matrix fluorescence data by region-based moving window subspace projection technique and Monte Carlo simulation

A novel method, region-based on moving window subspace projection technique (RMWSPT) coupled with Monte Carlo simulation, was developed for the chemical rank estimation of excitation-emission matrix (EEM) fluorescence data arrays. RMWSPT determines the chemical rank by performing singular value decomposition (SVD) on the unfolded matrices of original data array and the subarrays yielded by a moving window, and through employing the subspace projection technique on the difference between the corresponding sub-bands of the significant eigenvectors and those of subarrays. Compared with the traditional methods, it utilizes the information from eigenvectors combined with the projection residual sum of squares values to estimate the rank of the EEM data arrays instead of using the eigenvalues. Two simulated and two real EEM data arrays were analyzed to demonstrate the excellent performance of the RMWSPT. Moreover, its performance was compared with that of other three factor-determining methods, i.e., factor indicator function (IND), the core consistency diagnostic (CORCONDIA) test and two-mode subspace comparison (TMSC) approaches. The results showed that the newly proposed method can accurately and quickly determine the chemical rank to fit the trilinear model, and it can deal with more complex situations in the presence of severe collinearity and trace concentration. The RMWSPT method thus lights a new avenue to determine the chemical rank of EEM data arrays and may hold great potential to be extended as a promising alternative for the chemical rank estimation.