Multiway calibration method is gaining more and more attentions in the field of analytical science. It is a smart and green quantitative analysis strategy based on "mathematical separation" for Complex chemical systems when combined with advanced analytical instruments capable of generating multidimensional arrays,e.g.HPLC-DAD,EEMs and LC-MS.It enables one to quantify the component(s) of analytical interest even in the presence of unknown interferences not included in the calibration samples,and then it has the "second-order advantage" or "higher-order advantage",and makes the final goal of analytical chemistry achievable even without the aid of Complex separation procedures.These multiway calibration methods could be applied to resolve different problems of qualitative and quantitative analysis in Complex chemical systems.The performances of these algorithms have been evaluated by using the simulated and real experimental datasets.They have been utilized to simultaneous or direct determinations of multiple component(s) of analytical interest in many fields suchas pharmaceutical,biomedical,environmental,food sciences.The main points on successful applications of these chemometric methods combined with advanced analytical instruments have been also summarized.Some recent developments on the theories and their applications of multiway calibration methodologies including second-and third-order calibrationare also reviewed in detail.
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