Multivariate analysis applied to particle‐induced X‐ray emission mapping

Abstract

The use of particle‐induced X‐ray emission (PIXE) for elemental speciation and quantification has gained new attention thanks to mapping capabilities. Microprobes are able to raster a proton beam and produce elemental maps on the micrometre scale. Moreover, recent developments of in‐air PIXE instrumentation have enabled the acquisition of large area elemental maps. However, the amount of data produced is very large, and the data processing is not trivial. In this paper, we propose the use of multivariate analysis to process data of PIXE mapping. First, we apply the non‐negative matrix factorization (NMF), which is a nonsupervised machine‐learning algorithm, to decompose the data into a smaller number of components; then, we use the k‐means algorithm to divide the pixels into categories regarding similarities in the NMF results; finally, we sum the spectra of all pixels in the same category so that the results can be analyzed by standard procedures for PIXE quantification. This last step is important to enable the quantification of the elements found in each component by correctly accounting for matrix self‐absorptions. With the procedure described in this paper, not just, we reduced the number of variables, facilitating the reasoning process on the data by employing the multivariate analysis, but we also increased the counting statistics by summing similar pixels leading to better results concerning the quantification of trace elements. We also propose methods for both, the automatic determination of the optimal number of components to describe the dataset, and for the combined analysis of multiple detectors.

Ion beam analysis and big data: How data science can support next-generation instrumentation

“…The routines and the cascade of algorithms applied to process PIXE data on mappings are presented in [9].…”

“…Summing the similar pixels as determined by a clustering algorithm increases statistics and improves detection limits. It also enables the identification of patterns in the recorded spectra, enabling the discovery of the correlation between elements along the mapped area and revealing nuances hardly observed by the naked eye [9]. A similar implementation can be found elsewhere [10].…”

“…Machine learning tools have been adopted to process data of the large-area mapping device [9]. The designed cascade of algorithms can find similar regions (within a certain level of statistical significance) and sum the spectra of each pixel included in this region.…”

A Time-of-Flight Secondary Ion Mass Spectrometry/Multivariate Analysis (ToF-SIMS/MVA) Approach To Identify Phase Segregation in Blends of Incompatible but Extremely Similar Resins

“…Such an amount of memory could easily handle the 393 216 × 669 elements of the dataset, but the use of a training sets enables the analysis to be done in any conventional PC, and it has been shown to be effective for multivariate analysis of ToF-SIMS imaging data, in which neighbor pixels are highly correlated. − Furthermore, with reduced subsets, the total processing time is conveniently reduced to a few seconds for the dataset presented in this paper. Determination of number of NMF components by contrast analysis: NMF is performed several times for the subsampled dataset with a varying number of components. For each result, obtained with k components, the contrast G k of matrix W was calculated accordingly to the definition given by Silva et al: where w i are the columns of matrix W , as shown in Figure . The highest k that still presents a significant increment in contrast G k is considered the ideal number of components that contains relevant information on the dataset. NMF of the subsampled dataset.…”

“…For each result, obtained with k components, the contrast G k of matrix W was calculated accordingly to the definition by Silva et. al 20 :…”