Biomedical Engineering Reference
In-Depth Information
the issues of large numbers of PLS model parameters and their interpretation.
However, there are also alternative approaches that can be applied, and these are
discussed in Sect. 4.2.1 with relevant bioprocessing examples.
4.2.1 Variants of PLS
Hierarchical PLS modelling, where causal (and sometimes also effect) variables
are split into blocks of related variables, has been reported to result in simplified
interpretation of PLS models if not in more accurate predictions [ 62 ]. The
temptation with MVDA methods is typically to include all available process data
in the analysis. However, it is now widely accepted and reported in literature that
prediction quality and the complexity of the multivariate models can be signifi-
cantly improved by eliminating variables with low informational content prior to
model building. Methods such as genetic algorithms, the jack-knife method or
bootstrapping have been used successfully [ 28 ]; For example Wold et al. [ 62 ]
argue that an interactive variable selection (IVS) strategy is not only simple and
straightforward, but more robust than other methods in the sense that it 'does not
forget the eliminated variables and thus does not distort the interpretation of the
model'. Ödman et al. [ 43 ] compared four different methods of variable selection,
namely genetic algorithms, interval PLS, principal variable (PV) selection and
three-way stepwise variable elimination, for predicting biomass and substrate
concentrations in fed-batch cultivations of Streptomyces coelicolor producing the
antibiotic actinorhodin. They observed that the variable elimination methods
yielded improved PLS models for both effect variables, although the methods did
not pre-select the same wavelength combination for biomass prediction.
Another modification of the PLS algorithm developed for spectral filtering
(similar to that mentioned in Sect. 3.2.1 ) is orthogonalised PLS (O-PLS), where
elimination of orthogonal variation with respect to effect variables Y from a given
causal variable set X is performed to improve the model predictions; For example
Guebel et al. [ 18 ] used this methodology to analyse the data from a continuous
E. col culture under glycerol pulse experiments, and stressed and successfully
demonstrated increased understanding of the metabolic pathways and responses of
the organism under these conditions.
A particular class of PLS model variations aims to address the issues associated
with the non-linear character of the data, in particular in bioprocessing. These
include incorporating polynomial relationships into the PLS structure [ 62 ], using
artificial neural networks (ANNs) as inner PLS models [ 31 ] or hybrid structures
incorporating mass balance equations based on first-principles understanding of
the process [ 55 ].
Search WWH ::




Custom Search