Multivariate Statistical Analysis on a SEM/EDS Phase Map of Rare Earth Minerals

Abstract

The scanning electron microscope/X-ray energy dispersive spectrometer (SEM/EDS) system is widely applied to rare earth minerals (REMs) to qualitatively describe their mineralogy and quantitatively determine their composition. The performance of multivariate statistical analysis on the EDS raw dataset can enhance the efficiency and the accuracy of phase identification. In this work, the principal component analysis (PCA) and the blind source separation (BSS) algorithms were performed on an EDS map of a REM sample, assisting to achieve an efficient phase map analysis. The PCA significantly denoised the phase map and was used as a preprocessing step for the following BSS. The BSS separated the mixed EDS signals into a set of physically interpretable components, bringing convenience to the phase separation and identification. Through the comparison between the independent component analysis (ICA) and the nonnegative matrix factorization (NMF) algorithms, the NMF was confirmed to be more suitable for the EDS mapping analysis.

Correlative statistical microstructural assessment of precipitates and their distribution, with simultaneous electron backscatter diffraction and energy dispersive X-ray spectroscopy

“…A next step might involve application of direct linking of the EBSD and EDS data, e.g. using multivariate statistics has been used singularly to perform image segmentation (37) or in combination with EBSD as in McAuliffe et al (23), and this could assist in identification of the precipitates. However each of these methods on their own would not provide the type of information desired to relate to SCC.…”

SIGMA: Spectral Interpretation Using Gaussian Mixtures and Autoencoder

“…Multivariate statistical analysis (MSA) is a popular choice for automated solutions (Bosman et al., 2006; Kannan et al., 2018; Kotula et al., 2003; Malinowski & Howery, 1980; Teng & Gauvin, 2020). Principal component analysis (PCA) and non‐negative matrix factorization (NMF) are two widely used MSA algorithms for the exploration of the HSI‐EDS data (Jany et al., 2017; Kotula et al., 2003; Rossouw et al., 2015, 2016; Teng & Gauvin, 2020).…”

“…Multivariate statistical analysis (MSA) is a popular choice for automated solutions (Bosman et al., 2006; Kannan et al., 2018; Kotula et al., 2003; Malinowski & Howery, 1980; Teng & Gauvin, 2020). Principal component analysis (PCA) and non‐negative matrix factorization (NMF) are two widely used MSA algorithms for the exploration of the HSI‐EDS data (Jany et al., 2017; Kotula et al., 2003; Rossouw et al., 2015, 2016; Teng & Gauvin, 2020). These algorithms aim to extract the underlying features from the available HSI‐EDS data by reducing the dimensionality of the data, where high‐dimensional pixel‐wise data points are linearly projected onto a basis in a low‐dimensional space (Hotelling, 1933; Kotula et al., 2003; Potapov & Lubk, 2019; Tipping & Bishop, 1999).…”

“…exploration of the HSI-EDS data (Jany et al, 2017;Kotula et al, 2003;Rossouw et al, 2015Rossouw et al, , 2016Teng & Gauvin, 2020). These algorithms aim to extract the underlying features from the available HSI-EDS data by reducing the dimensionality of the data, where high-dimensional pixel-wise data points are linearly projected onto a basis in a low-dimensional space (Hotelling, 1933;Kotula et al, 2003;Potapov & Lubk, 2019;Tipping & Bishop, 1999).…”

Enhancing spatial resolution in Fourier transform infrared spectral image via machine learning algorithms

“…Similarly, Kim et al 21 employed a combination of PCA and independent component analysis (ICA) to significantly improve the spatial resolution of STEM-EDS, allowing for the observation of previously undetected depletion regions in light elements after data processing. Teng and Gauvin investigated the application of the non-negative matrix factorization (NMF) algorithm to SEM–EDS spectral image data for the purpose of phase classification in rare earth minerals 22 , and Muto and Shiga exploited the NMF algorithm to enhance spatial resolution by mitigating noise in STEM-EELS spectral image data 23 . A common thread in these previous studies is the achievement of notable enhancements in the SNR through the application of dimensionality reduction algorithms such as PCA, ICA and NMF.…”