Rapid multivariate analysis of 3D ToF‐SIMS data: graphical processor units (GPUs) and low‐discrepancy subsampling for large‐scale principal component analysis

Abstract

Principal component analysis (PCA) and other multivariate analysis methods have been used increasingly to analyse and understand depth-profiles in XPS, AES and SIMS. For large images or three-dimensional (3D) imaging depth-profiles, PCA has been difficult to apply until now simply because of the size of the matrices of data involved. In a recent paper, we described two algorithms, random vector 1 (RV1) and random vector 2 (RV2), that improve the speed of PCA and allow datasets of unlimited size, respectively. In this paper, we now apply the RV2 algorithm to perform PCA on full 3D time-of-flight SIMS data for the first time without subsampling. The dataset we process in this way is a 128 × 128 pixel depth-profile of 120 layers, each voxel having a 70 439 value mass spectrum associated with it. This forms over a terabyte of data when uncompressed and took 27 h to process using the RV2 algorithm using a conventional windows desktop personal computer (PC). While full PCA (e.g. using RV2) is to be preferred for final reports or publications, a much more rapid method is needed during analysis sessions to inform decisions on the next analytical step. We have therefore implemented the RV1 algorithm on a PC having a graphical processor unit (GPU) card containing 2880 individual processor cores. This increases the speed of calculation by a factor of around 4.1 compared with what is possible using a fast commercially available desktop PC having central processing units alone, and full PCA is performed in less than 7 s. The size of the dataset that can be processed in this way is limited by the size of the memory on the GPU card. This is typically sufficient for two-dimensional images but not 3D depth-profiles without sampling. We have therefore examined efficient sampling schemes that allow a good approximate solution to the PCA problem for large 3D datasets. We find that low-discrepancy series such as Sobol series sampling gives more rapid convergence than random sampling, and we recommend such methods for routine use. Using the GPU and low-discrepancy series together, we anticipate that any time-of-flight SIMS dataset, of whatever size, can be efficiently and accurately processed into PCA components in a maximum of around 10 s using a commercial PC with a widely available GPU card, although the longer RV2 approach is still to be preferred for the presentation of final results, such as in published papers.

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

“…The tests involved different ways of data normalization; different data preprocessing, other than Poisson scaling; the use of a variety of NMF algorithms, such as multiplicative update rules or alternating least-squares; removal of the standard samples from the dataset (or only some of them) and playing with different levels of pixel subsampling. The chosen data analysis workflow was as follows: Prior to any MVA, two preprocessing steps are performed: normalization of all maps intensities by total counts per pixel and Poisson scaling of the peak intensities. Selection of a subset of pixels using low discrepancy subsampling as proposed in ref . The computer used was a Dell Optiplex 9020 PC with a core i5 processor and 32 GB of RAM.…”

“…The computer used was a Dell Optiplex 9020 PC with a core i5 processor and 32 GB of RAM. 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 .…”

Spatially Resolved Mass Spectrometry at the Single Cell: Recent Innovations in Proteomics and Metabolomics

“…Data handling can be significantly more problematic with FT data that can contain millions of mass channels. Efficient peak picking algorithms and subsampling have been explored for hyperspectral data sets to address this problem, 278 , 279 along with software developments for image analysis. 280 However, data set sizes will remain a noteworthy issue in MSI as higher resolution imaging methods are developed.…”

Unsupervised machine learning for exploratory data analysis in imaging mass spectrometry

“…The loadings were calculated using a training set consisting of only 6.11% of the total number of pixels, and the IMS data was then projected on the loading vectors to create the (score) images. Cumpson et al () have similarly used a subsampling approach for the PCA analysis of large size 3D SIMS datasets, although here quasirandom Sobol sampling was used to obtain a more even spatial sampling throughout the sample. Graphical processing units (GPUs) were used to speed up the calculation of the PCs, as has also previously been demonstrated by Jones et al () for PCA, pLSA, and NMF (see Section II…”