278
P. Torruella et al.
The first practical approximation to the implementation of clustering algorithms
in EELS data treatment can be found in Torruella, Pau, et al. 2018. Clustering
analysis strategies for electron energy loss spectroscopy (EELS). Ultramicroscopy,
185, 42–48 [45].
In it, EELS simulation and experimental datasets were successfully segmented
after the implementation of the HAC algorithm following three different strategies:
(i) HAC in raw data, (ii) HAC followed by PCA, and (iii) PCA followed by HAC separation. All three strategies successfully retrieved segmented results, but the accuracy
and quantity of information provided was different in each case.
11.3.2.1 EELS Simulation Dataset
The simulated artificial EELS dataset consisted of a 128 × 128 pixels SI, with 1024
channels per spectrum. Four zones with different spectral features were created to
test the proficiency of the algorithm to segregate spectral components when detailed
analysis is required. The basic structure resembles a spherical core-shell NP, with
two additional elliptical internal zones (see Fig. 11.10a). The core of the particle
was filled with spectra corresponding a constant FeO composition. The shell was
filled with Fe x−1 O x+1 , where the ratio Fe/O linearly varied increasing O towards the
exterior. One of the elliptical zones inside the core was filled with FeCoO spectra to
simulate a precipitate of Co, and the other one was a void. All spectra were filled
with Gaussian and Poissonian noise to represent a real study case.
Raw data clustering segmentation was able to identify the regions of different
composition without any prior assumption of the data (such as the composition
and expected distribution of elements), identifying the four different zones of the
phantom. Despite the acceptable separation (Fig. 11.10b), some problems with the
cluster assignation for the FeO are present near the frontier core/shell, and the Fe/O
gradient is not well represented for the shell. This accounts for the incapacity of clustering approach to retrieve negative non-physical edges in the spectral components
separated and, thus, the incapacity of gradient composition detection. One hint of
the presence of this gradient can be obtained by the relaxation of the pD distance
threshold (i.e. relaxing the stopping criteria). Then, the shell will appear to contain
three different clusters (Fig. 11.10).
To avoid the loss of this information, by grouping within the same cluster boundaries spectra with similar features arising from different physical properties in the
sample, the first solution explored was the application of PCA to the HAC results.
This proved capable of identifying the linear gradient of the Fe/O composition in the
shell, retrieving a non-physical component with a negative edge in the decomposed
cluster linked to a decreasing quantity of iron towards the exterior (Fig. 11.10c).
The second possible solution was the implementation of HAC algorithms over the
score components extracted from the PCA calculations in the original EELS dataset.
This method yielded similar results to the previous one (see Fig. 11.10d). The main
difference resides now in the computational time. By first applying PCA, the number
of spectral components is reduced to 3 and, thus, the HCA algorithm iterates over
P. Torruella et al.
The first practical approximation to the implementation of clustering algorithms
in EELS data treatment can be found in Torruella, Pau, et al. 2018. Clustering
analysis strategies for electron energy loss spectroscopy (EELS). Ultramicroscopy,
185, 42–48 [45].
In it, EELS simulation and experimental datasets were successfully segmented
after the implementation of the HAC algorithm following three different strategies:
(i) HAC in raw data, (ii) HAC followed by PCA, and (iii) PCA followed by HAC separation. All three strategies successfully retrieved segmented results, but the accuracy
and quantity of information provided was different in each case.
11.3.2.1 EELS Simulation Dataset
The simulated artificial EELS dataset consisted of a 128 × 128 pixels SI, with 1024
channels per spectrum. Four zones with different spectral features were created to
test the proficiency of the algorithm to segregate spectral components when detailed
analysis is required. The basic structure resembles a spherical core-shell NP, with
two additional elliptical internal zones (see Fig. 11.10a). The core of the particle
was filled with spectra corresponding a constant FeO composition. The shell was
filled with Fe x−1 O x+1 , where the ratio Fe/O linearly varied increasing O towards the
exterior. One of the elliptical zones inside the core was filled with FeCoO spectra to
simulate a precipitate of Co, and the other one was a void. All spectra were filled
with Gaussian and Poissonian noise to represent a real study case.
Raw data clustering segmentation was able to identify the regions of different
composition without any prior assumption of the data (such as the composition
and expected distribution of elements), identifying the four different zones of the
phantom. Despite the acceptable separation (Fig. 11.10b), some problems with the
cluster assignation for the FeO are present near the frontier core/shell, and the Fe/O
gradient is not well represented for the shell. This accounts for the incapacity of clustering approach to retrieve negative non-physical edges in the spectral components
separated and, thus, the incapacity of gradient composition detection. One hint of
the presence of this gradient can be obtained by the relaxation of the pD distance
threshold (i.e. relaxing the stopping criteria). Then, the shell will appear to contain
three different clusters (Fig. 11.10).
To avoid the loss of this information, by grouping within the same cluster boundaries spectra with similar features arising from different physical properties in the
sample, the first solution explored was the application of PCA to the HAC results.
This proved capable of identifying the linear gradient of the Fe/O composition in the
shell, retrieving a non-physical component with a negative edge in the decomposed
cluster linked to a decreasing quantity of iron towards the exterior (Fig. 11.10c).
The second possible solution was the implementation of HAC algorithms over the
score components extracted from the PCA calculations in the original EELS dataset.
This method yielded similar results to the previous one (see Fig. 11.10d). The main
difference resides now in the computational time. By first applying PCA, the number
of spectral components is reduced to 3 and, thus, the HCA algorithm iterates over