Chemometrics reduction

J.M. Deane, Data reduction using principal components analysis. In Multivariate Pattern Recognition in Chemometrics, R. Brereton (Ed.). Chapter 5, Elsevier, Amsterdam, 1992, pp. 125-165. 

Since reproducibility of the flow system is critical to obtaining reproducibility, one approach has been to substitute lower-performance columns (50-to 100-p packings) operated at higher temperatures.1 Often, improvements in detection and data reduction can substitute for resolution. Chemometric principles are a way to sacrifice chromatographic efficiency but still obtain the desired chemical information. An example of how meaningful information can be derived indirectly from chromatographic separation is the use of system or vacancy peaks to monitor chemical reactions such as the titration of aniline and the hydrolysis of aspirin to salicylic acid.18... 

Data reduction and interpretation are much aided by computer methods and the high speed of current microcomputers facilitates the real-time processing and display of data. The principle of extracting as much information as possible from analytical measurements through the application of statistical and other mathematical methods, usually with the aid of appropriate computer software, is known as chemometrics (p. 13). 

Nowadays, generating huge amounts of data is relatively simple. That means Data Reduction and Interpretation using multivariate statistical tools (chemometrics), such as pattern recognition, factor analysis, and principal components analysis, can be critically important to extracting useful information from the data. These subjects have been introduced in Chapters 5 and 6. 

Recall, the standard deviation of the added noise in Y was lxlO-3. It is reached approximately after the removal of 3 sets of eigenvectors (at t=4). Note that, from a strictly statistical point of view, it is not quite appropriate to use Matlab s std function for the determination of the residual standard deviation since it doesn t properly take into account the gradual reduction in the degrees of freedom in the calculation of R. But it is not our intention to go into the depths of statistics here. For more rigorous statistical procedures to determine the number of significant factors, we refer to the relevant chemometrics literature on this topic. 

It is vain to address the subsequent objective of CSE-reduction without unconditional commitment to and respect for me rules for sampling correctness. All pertinent specifications were given above. Nobody and no science (chemometrics included) will be able to escape from neglect without suffering significant scientific and economic penalties. 

The outcome of this is that although not easily interpretable by inspection (as for example in mid-infrared absorbance spectra) the NIR spectra of hydrocarbon streams possess a very high information content. Use of suitable chemometric methods allows for the reduction of this information content into extremely powerful predictive models for not only chemical compositional properties, but also bulk physical and fuel properties of hydrocarbon process streams and prodncts. ... 

The proper conduct of complex exposure studies requires that the quality of the data be well defined and the statistical basis be sufficient to support rule making if necessary. These requirements, from study design through chemical analysis to data reduction and interpretation, focused our attention on the application of chemometric techniques to environmental problems. 

Erikson, L., Vervoom, H., and Peijnenburg, W.J., Multivariate QSAR modelling of the rate of reductive dehalogenation of haloalkanes,. Chemometrics, 10, 483-492, 1996. 

The simplest and most widely used chemometric technique is Principal Component Analysis (PCA). Its objective is to accomplish orthogonal projection and in that process identify the minimum number of sensors yielding the maximum amount of information. It removes redundancies from the data and therefore can be called a true data reduction tool. In the PCA terminology, the eigenvectors have the meaning of Principal Components (PC) and the most influential values of the principal component are called primary components. Another term is the loading of a variable i with respect to a PQ. 

Fig. 8.3. A Acquired high SNR data and simulated noisy spectra (peak-to-peak noise = 0.001, 0.01, 0.1, and 0.4 a.u.), showing the degradation in data quality. Spectra are offset for clarity. B Spectra after noise reduction demonstrate the dramatic gains possible by chemometric methods. C Noise reduction was implemented to classify breast tissue and application of noise rejection allowed the same quality of classification (accuracy) to be recovered at higher noise levels. D In another example, image fidelity (here the nitrile stretching vibrational mode at 2227 cm-1) is much enhanced as a result of spectral noise rejection A and C are reproduced from Reddy and Bhargava, Submitted [165], D is reproduced from [43]...

Principal component analysis is a popular statistical method that tries to explain the covariance structure of data by means of a small number of components. These components are linear combinations of the original variables, and often allow for an interpretation and a better understanding of the different sources of variation. Because PCA is concerned with data reduction, it is widely used for the analysis of high-dimensional data, which are frequently encountered in chemometrics. PCA is then often the first step of the data analysis, followed by classification, cluster analysis, or other multivariate techniques [44], It is thus important to find those principal components that contain most of the information. 

Petersen, L. (2004), Representative mass reduction in samphng—A critical survey of techniques and hardware, Chemometr. Intell. Lab. Syst., 74, 95-114. 

Pattern Recognition. The application of computers to build descriptive or predictive models (i.e., find patterns) of information from input datasets. The techniques of pattern recognition overlap those used in statistics, chemometrics, and data mining, and include data display, description, and reduction, unsupervised methods such as cluster analy-... 

The classical PCA is non-robust and sensitive to deviations of error distribution from the normal assumption, the PC directions being influenced by the presence of outlier(s). In PP PCA, the PC directions are determinated by the the inherent structure of the main body of the data. Using some robust projective index, the influence of the outliers is thus substantially reduced. The distorted appearance or misrepresentation of the projected data structure in the PC subspace caused by the presence of outlier(s) could be eliminated in PP PCA. This characteristic feature of PP PCA is essential for obtaining reliable results for exploratory data analysis, calibration and resolution in analytical chemometrics where PCA is used for dimension reduction. 

The use of several variables in describing objects increases the complexity of the data and therefore the —> model complexity, noise, variable correlation, redundancy of information provided by the variables, and unbalanced information and not useful information give the data an intrinsic complexity that must be resolved. This happens in the case of spectra, each constituted, for example, by 800-1000 digitalized signals, which are highly correlated variables. Usually, —> variable reduction and variable selection improve the quality of models (in particular, their predictive power) and information extracted from models. Chemometrics provides several useful tools able to check the different kinds of information contained in the data [Frank and Todeschini, 1994]. 

Structure/Response Correlations, data set, chemometrics, statistical indices. Principal Component Analysis, similarity/diversity, validation, variable selection, and variable reduction... 

Holmes, E., J. K. Nicholson, A. W. Nicholls, J. C. Lindon, S. C. Connor, S. Policy, and J. Connelly. 1998. The identification of novel biomarkers of renal toxicity using automatic data reduction techniques and PCA of proton NMR spectra of urine. Chemometrics and Intelligent Laboratory Systems 44 245-255... 

Principal component analysis and partial least squares analysis are chemometric tools for extracting and rationalizing the information from any multivariate description of a biological system. Complexity reduction and data simplification are two of the most important features of such tools. PCA and PLS condense the overall information into two smaller matrices, namely the score plot (which shows the pattern of compounds) and the loading plot (which shows the pattern of descriptors). Because the chemical interpretation of score and loading plots is simple and straightforward, PCA and PLS are usually preferred to other nonlinear methods, especially when the noise is relatively high. ... 

---