A new method to determine the number of chemical components of four-way data from mixtures

Determining the number of chemical components in mixtures is a crucial step in four-way data analysis. However, few works about true four-way component-determining method are developed to estimate the optimum number of components of four-way data arrays. In this paper, a new method is proposed for the determination of the number of chemical components of four-way data from complicated chemical systems, namely, alternating weighted quadrilinear decomposition incorporating Monte Carlo simulation (AWQLD-MCS), as an extension of self-weighted alternating trilinear decomposition incorporating Monte Carlo simulation. The performance of the newly developed method has been demonstrated by two simulated and two real four-way data arrays. The results show that the proposed method can accurately and quickly estimate the number of components to fit the quadrilinear model. Moreover, the newly suggested method is compared with the other three component-determining methods, i.e., the core consistency diagnostic (CORCONDIA) test, the ADD-ONE-UP truncating and fitting method (ADD-ONE-UP) and factor indicator function (IND). It is found that the new method has the fast analytical speed and the strong ability of anti-noise-interference and anticollinearity in practical application, indicating that it is a promising alternative for four-way component determination in quadrilinear decomposition.