17 Vibrational Microspectroscopy for Analysis of Atherosclerotic Arteries
515
samples, this may cause a large variation of the Raman signal when reaching the
border of the sample or a denser area.
Cluster Analysis is a group of techniques used for comparing pixels/samples
based on their similarity or dissimilarity. this is achieved by calculating a so called
distance (which is a measure of similarity) between two pixels/samples. the distance can be calculated currently in around 70 ways, but the ones most widely used
in spectroscopy are: Euclidean, manhattan, mahalonobis and based on Pearson’s
correlation coefficient (e.g. d-values). the algorithm calculates a distance matrix,
which contains relationships between all pixels/samples present in the dataset, by
comparing the spectra using a distance measure. then, based on the relationships
from distance matrix, a linkage is performed, which joins together pixels/samples
of closest values of distance measure forming clusters. By defining the number of
clusters the user determines the number of classes to which the dataset is split. In
the end, each pixel/sample is attributed a class membership value and these values
can be then used to create an image, in which each class is assigned a different color.
the safest version of CA is hierarchical Cluster Analysis (hCA), which uses all of
the pixel/sample relationships to create a full hierarchy of the samples with regard
to their similarity. however, since it uses all of that information it is very time
demanding to calculate. therefore, simplified versions have been invented, out of
which the K-means Clustering (KmC) is most widely spread. In this algorithm, a
defined K-number of clusters are assumed in the analysis—in hCA the analysis is
done without any assumption and only after the user chooses the number of classes.
during the analysis only the distances of the samples to cluster means are calculated and based on that assigned to the closest cluster. the process is iterative and
in the first step it gives random positions to the K-clusters. After each iteration the
position of the cluster mean is recalculated and the sample distances are corrected.
the algorithm repeats each step ‘moving’ the K-clusters means until in successive
steps the positions remain sufficiently the same. therefore, the analysis may not
be (and often is not) reproducible, since it may fall into local minima—this is the
biggest disadvantage of the K-means Clustering (KmC). however, due to strongly
enhanced computational efficiency it is a very popular method.
17.3.1.2 Classification (LDA, M-LDA, PCA)
the predominant aim of any classification technique is to find a mathematical
method of distinguishing samples of different classes in an unknown dataset. the
assignment is based on previous training of the model using a training dataset. usually, the training classes are obtained from exploratory analysis but may be as well
imposed by the user. the second situation is more common in biomedical research,
since it is often required to assign samples based on their spectra to a predefined set
of classes, e.g. different stages of atherosclerosis progression.
In terms of mathematical treatment this idea is most commonly performed on
the scores associated with abstract spectra (Fig. 17.5). In a simple space with two
abstract spectra the idea is to find a line, to which new unknown sample scores can
515
samples, this may cause a large variation of the Raman signal when reaching the
border of the sample or a denser area.
Cluster Analysis is a group of techniques used for comparing pixels/samples
based on their similarity or dissimilarity. this is achieved by calculating a so called
distance (which is a measure of similarity) between two pixels/samples. the distance can be calculated currently in around 70 ways, but the ones most widely used
in spectroscopy are: Euclidean, manhattan, mahalonobis and based on Pearson’s
correlation coefficient (e.g. d-values). the algorithm calculates a distance matrix,
which contains relationships between all pixels/samples present in the dataset, by
comparing the spectra using a distance measure. then, based on the relationships
from distance matrix, a linkage is performed, which joins together pixels/samples
of closest values of distance measure forming clusters. By defining the number of
clusters the user determines the number of classes to which the dataset is split. In
the end, each pixel/sample is attributed a class membership value and these values
can be then used to create an image, in which each class is assigned a different color.
the safest version of CA is hierarchical Cluster Analysis (hCA), which uses all of
the pixel/sample relationships to create a full hierarchy of the samples with regard
to their similarity. however, since it uses all of that information it is very time
demanding to calculate. therefore, simplified versions have been invented, out of
which the K-means Clustering (KmC) is most widely spread. In this algorithm, a
defined K-number of clusters are assumed in the analysis—in hCA the analysis is
done without any assumption and only after the user chooses the number of classes.
during the analysis only the distances of the samples to cluster means are calculated and based on that assigned to the closest cluster. the process is iterative and
in the first step it gives random positions to the K-clusters. After each iteration the
position of the cluster mean is recalculated and the sample distances are corrected.
the algorithm repeats each step ‘moving’ the K-clusters means until in successive
steps the positions remain sufficiently the same. therefore, the analysis may not
be (and often is not) reproducible, since it may fall into local minima—this is the
biggest disadvantage of the K-means Clustering (KmC). however, due to strongly
enhanced computational efficiency it is a very popular method.
17.3.1.2 Classification (LDA, M-LDA, PCA)
the predominant aim of any classification technique is to find a mathematical
method of distinguishing samples of different classes in an unknown dataset. the
assignment is based on previous training of the model using a training dataset. usually, the training classes are obtained from exploratory analysis but may be as well
imposed by the user. the second situation is more common in biomedical research,
since it is often required to assign samples based on their spectra to a predefined set
of classes, e.g. different stages of atherosclerosis progression.
In terms of mathematical treatment this idea is most commonly performed on
the scores associated with abstract spectra (Fig. 17.5). In a simple space with two
abstract spectra the idea is to find a line, to which new unknown sample scores can