Analytical data dimensionality

Dimensionality of analytical data. Analytical data are present either in the form of measured values yt or analytical results x,. Multivariate data, i.e., results of m variables (e.g., analyte concentrations) measured at n different samples, are mostly represented in the form of data sets and data matrices ... 

So, we can imagine a future of the representation techniques in which three-dimensional coloured figures with a pleasant (or otherwise) accompaniment are used to represent food analytical data with clear relationships to the food quality and origin. We leave to the reader s imagination the evaluation of the possibilities offered by the other human senses in the field of data representation. 

Other sulfur-bonding adducts of the Rh4+ core have been reported for thiols,338 thioethers,305,335 alkyl sulfides,291 293,336 thiourea derivatives,339-341 and benzothiadiazole.342 Reaction ofNCX- (X = S, Se) with [Rh2(02CMe)4] is reported to lead to the anionic 1 1 adduct [Rh2(02CMe)4(NCX)]-, 343 A structure has not been reported, but based on analytical data, one-dimensional chains with bridging NCX- anions were proposed.343... 

Botschwina later used a doubly polarized basis set to study this complex, along with a CEPA-1 treatment of electron correlation. The ab initio energetics were fit to an analytic four-dimensional function in order to elucidate anharmonic effects. The results at various levels of theory are presented in Table 3.64 along with experimentally measured quantities. Comparison of the SCF and CEPA-1 data suggests that while correlation yields major changes in the frequencies themselves, the shifts that occur upon complexation are surprisingly insensitive to correlation. The same is true of introduction of anharmonicity with one major exception. Whereas the frequency shifts of the stretches of the HCN proton acceptor molecule are little affected by introduction of anharmonicity, the red shift of HP is increased by 46% from 168 to 245 cm . This latter result is in near perfect agreement with... 

Fig. A series of three-dimensional quasitemary diagrams of the same analytical data with various comer definitions, (a) All the analysed elements are defined in the comers of the diagram, (b) P and S are replace by Fe and Ti, (c) Fe and Ti are replaced by Ca and Mg, (d) conventional ternary diagram with Si, Ca, and K defining a comer each. The column heights represent the relative content of the material with the elemental composition as controlled by the definitions in the comers.

Buvari-Barcza and co-workers [77] showed, by comparing several com-plexing agents, that y-CD is the best host for solubilising C6q fullerene in a water environment. The interaction of C6q and y-CD forms a C6o-(y-CD)2 inclusion complex. The analytical data and solid state NMR indicated that the essentially 1 2 complex exists as two different forms. In the violet colored form, unhydrated C60 is included, while in the brownish one, C q is also hydrated. The inner diameter of the y-cyclodextrin is only 0.95 nm while the diameter of C6q is estimated to be 1.0 nm. Because of this dimensional difference, complete inclusion is inconceivable, but the secondary hydroxyls of the y-CD rims can be connected by hydrogen bonds and possibly mediated by water molecules (Fig. 29). 

The power of principal components analysis is in providing a mathematical transformation of our analytical data to a form with reduced dimensionality. From the results, the similarity and difference between objects and samples can often be better assessed and this makes the technique of prime importance in chemometrics. Having introduced the methodology and basics here, future chapters will consider the use of the technique as a data preprocessing tool. 

M. Wolkenstein, Optimization of the Visualization Process for Three-Dimensional Analytical Data, PhD Thesis, Vienna University of Technology, Vienna, Austria, 1998. 

M. Wolkenstein, H. Hutter and M. Grasserbauer, Visualization of N-Dimensional Analytical Data on Personal Computers, Trends in Analytical Chemistry, 17 (3) (1998), 120-128. 

Grouping of analytical data is possible either by means of clustering methods or by projecting the high-dimensional data onto lower dimensional space. Since there is no supervisor in the sense of known membership of objects to classes, these methods are performed in an unsupervised manner. 

PCA can often be so effective and efficient in reducing the dimensionality of analytical data that it can provide immediate visual indication of patterns within data and is a commonly employed exploratory technique. 

Both unfolded and three-dimensional regression models gave satisfactory predictions of almost all the sensorial parameters, which characterised the quality of ABTM samples. In particular, the aromatic parameters are better modelled, probably due to nature of the employed analytical data, that is volatile organic compounds. 

An example of the results obtained in the form of a chromatoelectropherogram can be seen in Figure 9.6. The contour type data display showed the three variables that were studied, namely chromatographic elution time, electrophoretic migration time, and relative absorbance intensity. Peptides were cleanly resolved by using this two-dimensional method. Neither method alone could have separated the analytes under the same conditions. The most notable feature of this early system was that (presumably) all of the sample components from the first dimension were analyzed by the second dimension, which made this a truly comprehensive multidimensional technique. 

---