THEORY OF MEDIUM-RANK 2ND-ORDER CALIBRATION WITH RESTRICTED-TUCKER MODELS

If an analytical instrument or instrumental method gives a response ma trix when analyzing a pure analyte, the instrument or instrumental met hod is called a second-order method. Second-order methods that generat e 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 f ive) and high rank (greater than five). Subsequently, medium- and high -rank second-order calibration tries to use medium- and high-rank seco nd-order methods to analyze for analytes of interest in a mixture. A p articular advantage of second-order methods is the ability to analyze for analytes of interest in a mixture which contains unknown interfere nces. Keeping this advantage is the challenge on moving away from rank -one second-order calibration methods. In this paper a medium-rank sec ond-order calibration method is proposed based on least-squares restri cted Tucker models. With this method the second-order advantage is ret ained.