Data interpretation clustering

Evidence of the appHcation of computers and expert systems to instmmental data interpretation is found in the new discipline of chemometrics (qv) where the relationship between data and information sought is explored as a problem of mathematics and statistics (7—10). One of the most useful insights provided by chemometrics is the realization that a cluster of measurements of quantities only remotely related to the actual information sought can be used in combination to determine the information desired by inference. Thus, for example, a combination of viscosity, boiling point, and specific gravity data can be used to a characterize the chemical composition of a mixture of solvents (11). The complexity of such a procedure is accommodated by performing a multivariate data analysis. 

The objective functions for both k-means clustering and the F-nearest neighbor heuristic given by Eqs. (20) and (21) use information only from the inputs. Because of this capacity to cluster data, local methods are particularly useful for data interpretation when the clusters can be assigned labels. 

Data interpretation methods can be categorized in terms of whether the input space is separated into different classes by local or nonlocal boundaries. Nonlocal methods include those based on linear and nonlinear projection, such as PLS and BPN. The class boundary determined by these methods is unbounded in at least one direction. Local methods include probabilistic methods based on the probability distribution of the data and various clustering methods when the distribution is not known a priori. 

The bottleneck in utilizing Raman shifted rapidly from data acquisition to data interpretation. Visual differentiation works well when polymorph spectra are dramatically different or when reference samples are available for comparison, but is poorly suited for automation, for spectrally similar polymorphs, or when the form was previously unknown [231]. Spectral match techniques, such as are used in spectral libraries, help with automation, but can have trouble when the reference library is too small. Easily automated clustering techniques, such as hierarchical cluster analysis (HCA) or PCA, group similar spectra and provide information on the degree of similarity within each group [223,230]. The techniques operate best on large data sets. As an alternative, researchers at Pfizer tested several different analysis of variance (ANOVA) techniques, along with descriptive statistics, to identify different polymorphs from measurements of Raman... 

The advent of analytical techniques capable of providing data on a large number of analytes in a given specimen had necessitated that better techniques be employed in the assessment of data quality and for data interpretation. In 1983 and 1984, several volumes were published on the application of pattern recognition, cluster analysis, and factor analysis to analytical chemistry. These treatises provided the theoretical basis by which to analyze these environmentally related data. The coupling of multivariate approaches to environmental problems was yet to be accomplished. 

Moreover, the interpretation of experimental data on clusters in solution requires more elaborate theoretical models to include the solvation effects around the structure of a small metal cluster. New kinetic models must be developed to describe nucleation, which governs the phase transition from a solute to a small solid phase. 

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