Analytical advantages of multivariate data processing. One, two, three, infinity?

Multidimensional data are being abundantly produced by modern analytical instrumentation, calling for new and powerful data-processing techniques. Research in the last two decades has resulted in the development of a multitude of different processing algorithms, each equipped with its own sophisticated artillery. Analysts have slowly discovered that this body of knowledge can be appropriately classified, and that common aspects pervade all these seemingly different ways of analyzing data. As a result, going from univariate data (a single datum per sample, employed in the well-known classical univariate calibration) to multivariate data (data arrays per sample of increasingly complex structure and number of dimensions) is known to provide a gain in sensitivity and selectivity, combined with analytical advantages which cannot be overestimated. The first-order advantage, achieved using vector sample data, allows analysts to flag new samples which cannot be adequately modeled with the current calibration set. The second-order advantage, achieved with second- (or higher-) order sample data, allows one not only to mark new samples containing components which do not occur in the calibration phase but also to model their contribution to the overall signal, and most importantly, to accurately quantitate the calibrated analyte(s). No additional analytical advantages appear to be known for third-order data processing. Future research may permit, among other interesting issues, to assess if this "1, 2, 3, infinity" situation of multivariate calibration is really true.