Instant Notes: Analytical Chemistry

as two parameters can be plotted as a single point with specified xand y

co-ordinates on a two-dimensional graph, the values of nparameters can be

represented by a point in n-dimensional space. Although n-co-ordinate

graphs cannot be visualized, they can be studied through appropriate

computer processing and manipulation. Where a number of substances have

similar sets of n co-ordinates, and therefore similar characteristics, they

produce closely-spaced groups of points described as clusters, the interpreta-

tion of this data being described as cluster analysis. Mathematical procedures

to detect clusters include principal component analysis(PCA) and factor

analysis(FA), which seek to simplify the data by projection from ndimen-

sions onto a line, plane or 3-D graph to reduce the number of dimensions

without losing information.

Cluster analysis can be used in many ways, e.g. to monitor clinical specimens

from hospital patients where, for example, the levels of pH, glucose, potassium,

calcium, phosphate and specific enzymes vary according to the absence, pres-

ence or severity of a particular disease. It can also be applied to the characteriza-

tion of glass fragments for forensic purposes through profiling and comparisons

of their trace metal contents, for identifying the source of a crude oil spillage on

the basis of the proportions of minor organic compounds and metals, and in the

classification of organic compounds with similar structural features to facilitate

the elucidation of unknown structures.

Multivariate modeling

Quantitative analysis for one or more analytes through the simultaneous

measurement of experimental parameters such as molecular UV or infrared

absorbance at multiple wavelengths can be achieved even where clearly defined

spectral bands are not discernible. Standards of known composition are used to

compute and refine quantitative calibration data assuming linear or nonlinear

models. Principal component regression(PCR) and partial least squares (PLS)

regressionare two multivariate regression techniques developed from linear

regression (Topic B4) to optimize the data.

B5 – Quality control and chemometrics 53

50

40

30

20

10

0

0 5 10 15

Copper (ppm)

Manganese (ppm)

Fig. 4. Copper and manganese distribution in geological samples showing three clusters with

differing proportions of each metal.