Advanced chemometric algorithm coupled to subspace projection technique between original and pseudo samples: A snapshot of chemical rank estimation for high-order data

Abstract A new method, “advanced chemometric algorithm coupled to subspace projection technique between original and pseudo samples (ACA-SPOPS)”, is proposed for the first time for chemical rank estimation of three-way data arrays. In ACA-SPOPS, self-weighted alternating trilinear decomposition (SWATLD) algorithm is used to create pseudo samples to produce a pseudo array. Singular value decomposition (SVD) is then performed on the unfolded matrices of both pseudo array and original array. The chemical rank can be accordingly determined via the subspace projection technique. The performance of ACA-SPOPS has been demonstrated by both simulated and experimental data arrays. By comparing with four other widely used methods, namely core consistency diagnostic (CORCONDIA) test, ADD-ONE-UP truncating and fitting (ADD-ONE-UP), two-mode subspace comparison (TMSC) and subspace projection of pseudo high-way data array (SPPH), the results showed that this new method possessed better analytical performance than many other ones, in terms of noise, collinearity, concentration and computation speed. Moreover, the ACA-SPOPS method may be further applied for processing higher-order data arrays by accordingly extending the SWATLD algorithm to higher dimensions.