THE AMT APPROACH IN CHEMOMETRICS - FIRST FORAYS

摘要

The 'Angle Measure Technique' (AMT) was introduced in 1994 by Robert Andrle as a new method for characterizing the complexity of geomorphic lines. AMT was proposed as an alternative to fractal analysis (in which the statistical measure of the complexity of a feature, e.g. an angular line, is assumed constant over the range of scales of measurement) for this purpose. Instead, AMT was designed to delineate changes in complexity of a geomorphic feature as a function of scale. In this paper we induct this approach into chemometrics and give several didactic and application examples. Initially it is instructive to view AMT as an analogy to Fourier transformation, but only concerning the way that AMT spectra can be used in further practical data analysis. The AMT approach has profound implications for analysis of both 1D and 2D measurement series in which 'noise' is dominant. AMT characterizes the noise part as well as quasi-periodic phenomena of a measurement series in a novel fashion as a function of a scale factor s. AMT derives complexity spectra which can often be used directly in furthering other specific data analytic objectives, e.g. as X-input for multivariate calibration or for interpretative purposes. AMT in fact creates a new domain of general data analysis, the scale domain, which complements the time and frequency domains of signal analysis. We here develop AMT so as to be able to work on any general 'measurement series', including, but far from restricted to, time series, image analysis and process chemometrics. A software program for generic AMT analysis has been developed, with which we have begun a series of forays into chemometric applications, some of which are delineated here in order to appreciate the potential of AMT. We also illustrate the method with a detailed example from food science, namely AMT spectra derived from textured bread imagery, which can be well calibrated with respect to sensory attributes (product volume, porosity). This type of application will be of great value in product and process optimization (certainly not only in food science). This example serves as an exemplar for direct at-line imaging for general quality or process control and automation, i.e. non-invasive on-line or at-line process analysis. We have further developed the original AMT concept in several ways, notably by a 'mean-difference Y' complexity measure and an augmented standard deviation addition as well as 'automated' X/Y-axis scalings. A central issue in interpretative AMT analysis relates to 'optimal scaling' (Y-axis and/or X-axis scaling). We have only barely begun approaching this complex issue, but AMT analysis would appear not to be fatally hampered even if not optimally scaled. For comparative studies the scaling is irrelevant.