Biomedical Engineering Reference
In-Depth Information
it is the second function of chemometrics that is of most interest. Process data from
a spectrometer are analysed in a multivariate rather than a univariate way; i.e. for
each sample, the responses at multiple wavenumbers are taken into account. If the
spectrum of a sample was recorded at three wavenumbers using any spectroscopic
technique, a simple two-dimensional plot of response versus wavenumber could be
used to visualise the data. The same data can also represented by a single point in
three dimensions, where each dimension corresponds to a wavenumber.
An individual spectrum recorded on a spectrometer can have hundreds of data
points, and a single component can have a response in multiple places within the
one region, making the data highly correlated [
113
]. Rather than representing the
spectral data in two-dimensional space, chemometric techniques use multi-
dimensional space or hyperspace to represent the same spectrum by a single point.
As there is usually much redundant information in spectra due to variables being
highly correlated, data do not need to be represented in space with as many
dimensions as the original data points. The spectral data containing hundreds of
data points can be fully characterised in as few as 20 dimensions [
114
]. Chemo-
metric or multivariate calibration techniques allow the concentration of a given
analyte to be related to spectral features. They are also useful for distinguishing
real chemical information from instrument noise [
113
].
Pre-Treatments
Prior to analysing spectral data, a mathematical pre-treatment may be necessary.
Common pre-treatments include mean centring, mean normalisation and using the
first or second derivative of the spectra [
114
]. Leverage is a measure of how
extreme a data point is compared with the majority. A data point with high
leverage will have a high influence on any model created. Mean normalisation is
an adjustment to a data set that equalizes the magnitude of each sample. When the
spectra have been normalized, qualitative information that distinguishes one
sample from another is retained but information that would separate two samples
of identical composition but different concentration is removed. A standard normal
variate (SNV) pre-treatment is one which centres and scales individual spectra.
The effect of this pre-treatment is that on the vertical scale each spectrum is
centred on zero and varies roughly from -2 to +2. This effectively removes the
multiplicative interferences of scatter and particle size in spectral data [
115
].
The first derivate of a spectrum is the slope of the curve at every point. It has
peaks where the original has maximum slope and crosses zero where there was a
peak in the original spectrum. As the slope is not affected by additive baseline
offsets in the spectrum, calculating the first derivative is an effective method of
removing baseline effects. The second derivative is the slope of the first derivative.
It has peaks in roughly the same places as the original spectrum, but these peaks
are in the inverted direction. Calculating the second derivative of a spectrum
will remove additive baseline effects as well as multiplicative baseline effects
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