Theory of medium‐rank second‐order calibration with restricted‐Tucker models

Abstract

Abstract If an analytical instrument or instrumental method gives a response matrix when analyzing a pure analyte, the instrument or instrumental method is called a second‐order method. Second‐order methods that generate a response matrix for a pure analyte of rank one are called rank‐one second‐order methods. If the response matrix of a pure analyte is not rank one, essentially two cases exist: medium rank (between two and five) and high rank (greater than five). Subsequently, medium‐ and high‐rank second‐order calibration tries to use medium‐ and high‐rank second‐order methods to analyze for analytes of interest in a mixture. A particular advantage of second‐order methods is the ability to analyze for analytes of interest in a mixture which contains unknown interferences. Keeping this advantage is the challenge on moving away from rank‐one second‐order calibration methods. In this paper a medium‐rank second‐order calibration method is proposed based on least‐squares restricted Tucker models. With this method the second‐order advantage is retained.