| 概要 | The development of chemometric methods for decades has followed a pattern of creating “iterative based methods” to identify the parameters of an empirical model; perhaps based on power and simplicity of the NIPALS algorithm. Such algorithms have the benefit of being relatively fast and easy to implement in a computer system since they use a very basic set of operations (additions, multiplications, a root square here and there). In the presenter’s view the most robust and powerful methods are those where the iterative algorithmic process can be proven to yield the same solution as the one found by analytically solving the objective function behind the method being parametrized.
There are situations though where these iterative methods will only find a sub-optimal for the parameter estimation problem (e.g. when data has missing samples) or will simply fail to obtain one due to the ill-conditioned nature of the matrices involved. In these cases, the simplicity of the iterative method has a cost, a sub-optimal (or non-existent) solution.
Optimization technology is at a point where problems with massive degrees of freedom can be solved. The definition of “simplicity” when it comes to solving mathematical problems has obviously moved since the days of the Intel 8086 and arguably the definition of what is “simple and quick” may have changed. Optimization has been proposed as a way to estimate parameters of latent variable methods where missing data is present in the system[1, 2]; as a way to simultaneously carry out curve resolution and kinetic parameter estimation[3, 4]; and ultimately as a way to completely move out of using empirical regressions to translate spectroscopic information into chemical one[5, 6].
This talk will review these proposals and will focus on the disruptive nature of the last one where the use of a fixed regression model is replaced by the use of real-time optimization and the use of Beer-Lambert’s law -or a modified version of BL.
[1] R.L.N. de la Fuente, S. Garcia‐Munoz, L.T.J.J.o.C. Biegler, An efficient nonlinear programming strategy for PCA models with incomplete data sets, 24 (2010) 301-311.
[2] E.H. Puwakkatiya‐Kankanamage, S. Garcia‐Munoz, L.T.J.J.o.C. Biegler, An optimization‐based undeflated PLS (OUPLS) method to handle missing data in the training set, 28 (2014) 575-584.
[3] W. Chen, L.T. Biegler, S.G. Munoz, An approach for simultaneous estimation of reaction kinetics and curve resolution from process and spectral data, Journal of Chemometrics, 30 (2016) 506-522.
[4] W. Chen, L.T. Biegler, S.G.J.A.J. Munoz, Kinetic parameter estimation based on spectroscopic data with unknown absorbing species, 64 (2018) 3595-3613.
[5] K. Muteki, D.O. Blackwood, B. Maranzano, Y. Zhou, Y.A. Liu, K.R. Leeman, G.L.J.I. Reid, E.C. Research, Mixture component prediction using iterative optimization technology (calibration-free/minimum approach), 52 (2013) 12258-12268.
[6] Z. Shi, J. Hermiller, S.G.J.A.J. Munoz, Estimation of mass‐based composition in powder mixtures using Extended Iterative Optimization Technology (EIOT), (2018). |
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