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SIMS21, Poland 2017 - Peter J Cumpson abstract

Peter J Cumpson oral presentation (FN2-Tue2-1-2)

Overcoming nonlinearity in multivariate analysis of ToFSIMS data: Kernel Principal Component Analysis

Peter J Cumpson, Sadia Sheraz, Ian W Fletcher

SEAL - Newcastle University, Stephenson building, UK Newcastle-upon-Tyne, United Kingdom


Multivariate analysis is becoming increasingly important in the analysis of the enormous 2D and 3D imaging spectroscopic datasets produced by Time of Flight Secondary Ion Mass Spectrometry (ToFSIMS)[1,2]. Multivariate analysis makes use of large-scale linear matrix algebraic methods to extract common features from regions of spectra and images. Many important features of these data are otherwise nearly impossible to visualize just by plotting raw spectra or images.

An explicit assumption in using methods such as Principal Component Analysis (PCA) is that the underlying process is linear; that peak intensities are linearly related to the concentration of the species that give rise to them, and independent of the concentration of other species. This is never truly the case, and there are many examples where there are strong nonlinearities in ToFSIMS spectra – for example matrix effects where the presence of one species increases the ionization yield of a second. Applying linear multivariate tools such as PCA to our nonlinear data regularly leads to additional spurious components and makes the results difficult to interpret.

We apply a variant of PCA known as Kernel PCA[3] to ToFSIMS for the first time. In this technique the data are projected onto an implicit, very high dimensional space where we can more easily distinguish components even in the presence of nonlinearities. Until recently Kernel PCA would have been prohibitively demanding of computer time and memory, but recent advances in applying new, rapid and efficient PCA methods[4,5] now make it practical.

We compare the results of (a) conventional PCA and (b) Kernel PCA applied to ToFSIMS imaging from our Ionoptika J105 instrument: An organic crystal with small inorganic inclusions, a piece of invertebrate tissue, a plant leaf and fossil organic matter.

[1] D J Graham and D G Castner, Biointerphases 7 (2012) 49

[2] M S Wagner, D J Graham, D G Castner Applied Surface Science 252 (2006) 6575

[3] B Scholkopf, A Smola and K Mueller, Nonlinear Component Analysis as a Kernel

Eigenvalue Problem, Max-Planck-Institut für biologische Kybernetik, TR-44, Dec 1996

[4] P Cumpson, I Fletcher, N Sano, A Barlow, Surf. and Interface Anal. 48 (2016) 1328

[5] P Cumpson, N Sano, I Fletcher, J Portoles, M Bravo‐Sanchez, Surf. and Interface Anal. 47 (2015) 986.