A novel method to estimate the chemical rank of three-way data for second-order calibration

• SWATLD-MCS can accurately estimate the chemical rank of three-way data.
• SWATLD-MCS resists the effects of severe collinearity and high noise levels.
• SWATLD-MCS can decrease computation burden and save the analytical time.
• This method can be extended to estimate the chemical rank of higher-order data.

A novel method, self-weighted alternating trilinear decomposition with Monte Carlo simulation (SWATLD-MCS), is developed to determine the chemical rank of three-way data for second-order calibration. The proposed method estimates the chemical rank by comparing the values of sorted mean relative-concentration (SMRC), which are obtained from SWATLD by decomposing one pseudo three-way data array created by Monte Carlo simulation. The results for two simulated and two real three-way data sets are presented, in comparison with other two factor-determining methods, i.e., ADD-ONE-UP and the core consistency diagnostic (CORCONDIA). These results demonstrate that this new method can accurately estimate chemical ranks of complex systems even when heavy collinearity and high-intensity noise are present. Also the method has a lower computational burden than competitive methods, which saves overall analysis time. In addition, this new methodology can be extended to: i) other second-order calibration algorithms, being insensitive to excessive factors, can be used with this method; ii) the chemical rank of higher-order data can be determined by this method, using higher-order calibration algorithms.