T.P. Wróbel et al.
514
( e.g. PARAFAC, tucker3), however, understanding the results can be quite complex and therefore, they have not become widely used. therefore, it is very important to understand, that none of the methods widely applied in imaging use the spatial information and relationship between pixels—almost all of them are based only
on chemical information contained in the spectra. there is currently one technique
that uses that spatial relationship in infrared imaging—3d Fourier Self-deconvolution [80] (3d-FSd). however, the principle here is to enhance the resolution of the
images, rather than to gain chemical information.
At step two of the process, the data are arranged in columns by pixels or samples,
with each row corresponding to a spectrum (Raman or infrared). this datablock
serves as an input for further analysis.
the next step is the last step common to most of the methods, since following
this step, the analysis can stop here or different parts of the results can be used for
different purposes. Also, this step is performed in another way in each of the techniques and this is where differentiation starts.
17.3.1.1 Exploratory Techniques (PCA, CA)
the beginning of an analysis of an unknown dataset normally starts with a need to
get a general overview of the variance present in the data. the two most important
techniques are Principal Component Analysis (PCA) and Cluster Analysis (CA).
their use is also widespread across all scientific disciplines and therefore their
understanding is extremely crucial. PCA is a Factor Analysis (FA) technique and
sometimes the naming is interchangeable, but it needs to be pointed out that PCA
is always a Factor Analysis technique, but there are other FA techniques than PCA.
PCA decomposes the data into abstract spectra (called loadings in this technique)
according to two conditions—covering the maximum variance with a loading and
each successive loading must be orthogonal to all of the previous. this causes that
usually a few loadings are enough to cover most of the variance in a dataset. It is
the very power of PCA that in a fast way it can find the main source of variation in
analyzed data and to possibly give it a chemical meaning by comparing the abstract
spectra. If the scores on the samples corresponding to a single loading are plotted
against another loading’s scores, a hidden structure of the data can sometimes be
revealed. In this way a possible grouping inside the dataset can be found, which is
another important advantage of PCA. unfortunately, the grouping may not always
appear, especially not in the way the user expects it to happen, e.g. to discriminate
control samples from ones influenced by a factor. this is one of the disadvantages
of PCA—it follows the biggest sources of variance, not necessarily the ones the
user is interested in. moreover, when dealing with spectra, it is very common to
have big variance sources coming from measurements, which sometimes can totally
dominate the analysis. Among such sources are very common scattering effects in
Ft-IR. In Raman spectroscopy it can be the intensity of the signal, which is dependent on the confocality of the microscope. this means that by using a confocal system the data is acquired only from a confocal surface and, in the case of biological
514
( e.g. PARAFAC, tucker3), however, understanding the results can be quite complex and therefore, they have not become widely used. therefore, it is very important to understand, that none of the methods widely applied in imaging use the spatial information and relationship between pixels—almost all of them are based only
on chemical information contained in the spectra. there is currently one technique
that uses that spatial relationship in infrared imaging—3d Fourier Self-deconvolution [80] (3d-FSd). however, the principle here is to enhance the resolution of the
images, rather than to gain chemical information.
At step two of the process, the data are arranged in columns by pixels or samples,
with each row corresponding to a spectrum (Raman or infrared). this datablock
serves as an input for further analysis.
the next step is the last step common to most of the methods, since following
this step, the analysis can stop here or different parts of the results can be used for
different purposes. Also, this step is performed in another way in each of the techniques and this is where differentiation starts.
17.3.1.1 Exploratory Techniques (PCA, CA)
the beginning of an analysis of an unknown dataset normally starts with a need to
get a general overview of the variance present in the data. the two most important
techniques are Principal Component Analysis (PCA) and Cluster Analysis (CA).
their use is also widespread across all scientific disciplines and therefore their
understanding is extremely crucial. PCA is a Factor Analysis (FA) technique and
sometimes the naming is interchangeable, but it needs to be pointed out that PCA
is always a Factor Analysis technique, but there are other FA techniques than PCA.
PCA decomposes the data into abstract spectra (called loadings in this technique)
according to two conditions—covering the maximum variance with a loading and
each successive loading must be orthogonal to all of the previous. this causes that
usually a few loadings are enough to cover most of the variance in a dataset. It is
the very power of PCA that in a fast way it can find the main source of variation in
analyzed data and to possibly give it a chemical meaning by comparing the abstract
spectra. If the scores on the samples corresponding to a single loading are plotted
against another loading’s scores, a hidden structure of the data can sometimes be
revealed. In this way a possible grouping inside the dataset can be found, which is
another important advantage of PCA. unfortunately, the grouping may not always
appear, especially not in the way the user expects it to happen, e.g. to discriminate
control samples from ones influenced by a factor. this is one of the disadvantages
of PCA—it follows the biggest sources of variance, not necessarily the ones the
user is interested in. moreover, when dealing with spectra, it is very common to
have big variance sources coming from measurements, which sometimes can totally
dominate the analysis. Among such sources are very common scattering effects in
Ft-IR. In Raman spectroscopy it can be the intensity of the signal, which is dependent on the confocality of the microscope. this means that by using a confocal system the data is acquired only from a confocal surface and, in the case of biological