Local principal component models, rank maps and contextuality for curve resolution and multi-way calibration inference

Abstract

Abstract Geladi, P. and Wold, S., 1987. Local principal component models, rank maps and contextuality for curve resolution and multi-way calibration inference. Chemometrics and Intelligent Laboratory Systems , 2: 273–281. Hyphenated methods in analytical chemistry (e.g. liquid chromatography—ultraviolet spectrometry or gas chromatography—mass spectrometry) benefit from the use of curve resolution and multi-way analysis methods. Curve resolution methods, however, are often difficult to apply and the results difficult to interpret, because one always tries to find overall factors. Multi-way analysis methods need data reduction in the variable × variable space. This paper proposes the use of local principal component models, mainly to estimate local rank. By shifting the geometrical position of the local models, a rank map is obtained. This rank map and its contextuality can be used for finding empty regions, one-constituent regions and overlapping constituent regions. This kind of inference offers valuable a priori knowledge for further application of curve resolution and calibration methods. The method of rank mapping also detects regions of nonlinearity and extreme high noise, something that curve resolution methods fail to do. A rapid microcomputer program has been developed and the algorithm is given in the text.