Global target analysis is commonly used when attempting to model / fit / deconvolve transient absorption (TA) data, but can really be used in any case where the data is represented by a 2D matrix defined by two experimental dimensions. In the case case of TA these dimensions are wavelength and time.
This script is intended as a demonstrations of basic approaches to the global target analysis. It should not be used as-is, but instead studied and understood. The purpose of this script is only to provide a path to learning the global target analysis methodology.
If a more automated approach is required, there are some excellent toolboxes for global analysis out there (see below). A thorough understanding of the methodology is, however, strongly recommended before using any automated approaches / toolboxes.
- Just like with any modelling, overfitting is a problem. 'With four parameters I can fit an elephant, and with five I can make it wiggle its trunk' - Jonny von Neumann (See Drawing an elephant with four complex parameters, Mayer et al. American Journal of Physics 78, 648 (2010), DOI: 10.1119/1.3254017)
- Local minima are very much of a problem in fitting / regression in general. Global target analysis is particularity susceptible to this problem since it deals with multidimensional and non-linear models. The code here uses a basic simplex solver (
fminseach) but, in general, one ought to consider a way of ensuring the solution is a global (putative) minimum. This can, for example, be achieved by using a solver more adapted to finding global minima (e.g.patternsearch) or using an exploratory algorithm (e.g.ga) to understand better the behaviour of the particular fitting problem. Note, however, that more advanced solvers require the (Global) Optimization Toolbox. - Global analysis as shown here assumes that parameters of the model in one dimension are invariant in the other. For example, the species-associated spectra are invariant in time (bar the scaling by the fraction of species present)
For further reading on global target analysis see the following:
- PyLDM - An open source package for lifetime density analysis of time-resolved spectroscopic data, Dorlhiac et al. PLoS Computational Biology 13(5), 2017, DOI: 10.1371/journal.pcbi.1005528
- Global and target analysis of time-resolved spectra, Stokkum et al. Biochimica et Biophysica Acta (BBA) - Bioenergetics 1657(2–3), 2004, DOI: 10.1016/j.bbabio.2004.04.011
- Ultrafast Toolbox from Imperial College London.
- GloTarAn - a modelling framework for global target analysis
- PyLDM - Lifetime density analysis software
- Add principal component analysis / SVD example