Abstract
Spectroscopy rapidly captures a large amount of data that is not
directly interpretable. Principal component analysis is widely used to
simplify complex spectral datasets into comprehensible information by
identifying recurring patterns in the data with minimal loss of
information. The linear algebra underpinning principal component analysis
is not well understood by many applied analytical scientists and
spectroscopists who use principal component analysis. The meaning of
features identified through principal component analysis is often unclear.
This manuscript traces the journey of the spectra themselves through the
operations behind principal component analysis, with each step illustrated
by simulated spectra. Principal component analysis relies solely on the
information within the spectra, consequently the mathematical model is
dependent on the nature of the data itself. The direct links between model
and spectra allow concrete spectroscopic explanation of principal
component analysis, such as the scores representing
“concentration” or “weights”. The principal
components (loadings) are by definition hidden, repeated and uncorrelated
spectral shapes that linearly combine to generate the observed spectra.
They can be visualized as subtraction spectra between extreme differences
within the dataset. Each PC is shown to be a successive refinement of the
estimated spectra, improving the fit between PC reconstructed data and the
original data. Understanding the data-led development of a principal
component analysis model shows how to interpret application specific
chemical meaning of the principal component analysis loadings and how to
analyze scores. A critical benefit of principal component analysis is its
simplicity and the succinctness of its description of a dataset, making it
powerful and flexible.
© 2021 The Author(s)
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