Recent advances in chemical multi-way calibration with second-order or higher-order advantages: Multilinear models, algorithms, related issues and applications

This review discusses the recent advances in both theories and analytical applications of multi-way calibrations based on various high-order analytical data. In the theory part, we focus on some aspects of multi-way calibration, such as multilinear models and their extensions, multi-way calibration algorithms with second-order or higher-order advantages, and other fundamental issues. According to different types of high-order instrument signals, recent applications of second-, third-, and fourth-order calibrations are then discussed, and their contributions to green analytical chemistry are highlighted.