Novel Sexalinear Decomposition Algorithm for Analyzing the Chemical Sexalinear Data Array

ABSTRACT With the development of analytical instrument towards more and more high‐way and complex, it is very important and meaningful work to obtain ultra‐high‐way chemical data and explore its analytical methods. In this paper, a novel and excellent six‐way algorithm combination method (six‐way ACM) was proposed. In addition, a real chemically meaningful ultra‐high‐way sexalinear data array was obtained and constructed for the first time. The proposed six‐way data array has highly collinearity, which puts forward higher requirements for parsing this data array to a certain extent. To verify the feasibility of the proposed algorithm, it was used to analyze the above real sexalinear six‐way data array and a series of simulated six‐way data arrays with different noise levels. The results of real data and simulated data demonstrate that the proposed method can be well used in the analysis of six‐way data arrays and shows fascinating performance, including insensitive to excessive number of components, fast convergence speed, and suitable for high collinearity and high noise data. Compared with three‐way, four‐way, and five‐way calibration methods, the six‐way ACM provides higher sensitivity, a lower limit of detection, a lower limit of quantification, and more stable and accurate results, showing an outstanding “higher‐order advantages” and better ability to handle collinearity problems. This work provides not only data analysis method for high‐order instruments that may emerge in the future but also real data support and methodological reference for theoretical research on high‐order tensor algebra.