By Lydia I. Kronsjo
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First, there is the still growing mass of data. An example is an image 18 where each pixel is no longer characterized by a grey scale or by a colour but instead by a complete spectrum. Supposing that the spectrum is measured at 1024 wavenumbers, this represents a stack of 1024 images of a typical size of 512x512 pixels, which should all be treated together by multivariate procedures! Secondly, data have become increasingly complex. In high resolution NMR, for example, spectra are measured in two and higher dimensions and contain an enormous amount of information on the secondary and tertiary structure of large molecules.
4. 9 and a single set of data was obtained. 7 and s estimated from the range, using eq. 26. The estimation with eq. 29. The range is rarely used forn > 15. 10) In the same way as we can pool variances to obtain a common estimate of the standard deviation from a set of the standard deviations, we can pool ranges. When there are k sets of n data, then: _ A: R = (l/k)lRj where Rj is the range of thejth set of data. 6. 27. R is used less often than s, because it is more vulnerable to extreme values.
27. 28. 29. 30. 31. 32. 33. 34. G. van Marlen and A. Dijkstra, Information theory applied to selection of peaks for retrieval of mass spectra. Anal. , 48 (1976) 595-598. L. Massart and L. Kaufman, Operations research in analytical chemistry. Anal. , 47 (1975) 1244A-1253A. Arbeitskreis Automation in der Analyse, System Theorie in der Analytik. I. Definitionen und Interpretationen Systemtheoretischer Grundbegriffe. Zeit. Anal. Chemie, 256 (1971) 257-270. Arbeitskreis Automation in der Analyse, System Theorie in der Analytik.
Algorithms: Their complexity and efficiency by Lydia I. Kronsjo