Abstract
Analysis of time-resolved data typically involves discriminating noise against the signal and extracting time-independent components and their time-dependent contributions. Singular value decomposition (SVD) serves this purpose well, but the extracted time-independent components are not necessarily the physically meaningful spectra directly representing the actual dynamic or kinetic processes but rather a mathematically orthogonal set necessary for constituting the physically meaningful spectra. Converting the orthogonal components into physically meaningful spectra requires subsequent posterior analyses such as linear combination fitting (LCF) and global fitting (GF), which takes advantage of prior knowledge about the data but requires that all components are known or satisfactory components are guessed. Since in general not all components are known, they have to be guessed and tested via trial and error. In this work, we introduce a method, which is termed SVD-aided Non-Orthogonal Decomposition (SANOD), to circumvent trial and error. The key concept of SANOD is to combine the orthogonal components from SVD with the known prior knowledge to fill in the gap of the unknown signal components and to use them for LCF. We demonstrate the usefulness of SANOD via applications to a variety of cases.
Highlights
Typical experimental data consist of signal elements that have different physical origins
The details of the applications will be presented in the demonstrations with two different types of real experimental data that contain signal components with unknown origins, but before, we present these examples of SVD-aided Non-Orthogonal Decomposition (SANOD), we first demonstrate the advantage of linear combination fitting (LCF) over Singular value decomposition (SVD) in terms of extracting correct kinetics and signal components and the importance of correct input components for a successful LCF
To demonstrate the advantage of LCF using the prior knowledge over SVD in terms of extracting physically meaningful spectra, we prepared mock timeresolved X-ray liquidography (TRXL) data of a hypothetical chemical reaction
Summary
Typical experimental data consist of signal elements that have different physical origins. Posterior analyses, such as principal component analysis (PCA), are often followed to convert the information from SVD into the spectra corresponding to the chemical species responsible for the observed data In this stage, a model for the reaction kinetics has to be used as an input; various models need to be tested if the reaction kinetics is unknown. Numerous kinetics models may exist, the number can be reduced significantly through various methods, such as SVD-aided analysis using variable time ranges (V method) and SVD-aided pseudo-PCA (SAPPA).[33] These methods work well for TRXL data on proteins because the hydrodynamic response signal from the solvent, which is called the solvent heating signal, can be separated from the signal from proteins thanks to their different q regimes. SANOD allows us to exploit the prior knowledge on the shapes of signal components such as solvent heating signals in TRXL data to facilitate the data analysis
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